examples of the 1st law of thermodynamics

The First Law states that energy can neither be created nor destroyed. For example, heat can be converted into mechanical energy in a steam engine;. One of the most important things we can do with heat transfer is to use it to do work for us. Such a device is called a heat engine. Car engines and steam. Any form of energy that adds to the system is considered positive. Example: A Gas Compressor. Performing a 1st law energy balance.

: Examples of the 1st law of thermodynamics

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Examples of the 1st law of thermodynamics
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The first law of thermodynamics

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Sections 15.1 - 15.4

Thermodynamics

Thermodynamics is the study of systems involving energy in the form of heat and work. A good example of a thermodynamic system is gas confined by a piston in a cylinder. If the gas is heated, it will expand, doing work on the piston; this is one example of how a thermodynamic system can do work.

Thermal equilibrium is an important concept in thermodynamics. When two systems are in thermal equilibrium, there is no net heat transfer between them. This occurs when the systems are at the same temperature. In other words, systems at the same temperature will be in thermal equilibrium with each other.

The first law of thermodynamics relates changes in internal energy to heat added to a system and the work done by a system. The first law is simply a conservation of energy equation:

The internal energy has the symbol U. Q is positive if heat is added to the system, and negative if heat is removed; W is positive if work is done by the system, and negative if work is done on the system.

We've talked about how heat can be transferred, so you probably have a good idea about what Q means in the first law. What does it mean for the system to do work? Work is simply a force multiplied by the distance moved in the direction of the force. A good example of a thermodynamic system that can do work is the gas confined by a piston in a cylinder, as shown in the diagram.

If the gas is heated, it will expand and push the piston up, thereby doing work on the piston. If the piston is pushed down, on the other hand, the piston does work on the gas and the gas does negative work on the piston. This is an example of how work is done by a thermodynamic system. An example with numbers might make this clearer.

An example of work done

Consider a gas in a cylinder at room temperature (T = 293 K), with a volume of 0.065 m3. The gas is confined by a piston with a weight of 100 N and an area of 0.65 m2. The pressure above the piston is atmospheric pressure.

(a) What is the pressure of the gas?

This can be determined from a free-body diagram of the piston. The weight of the piston acts down, and the atmosphere exerts a downward force as well, coming from force = pressure x area. These two forces are balanced by the upward force coming from the gas pressure. The piston is in equilibrium, so the forces balance. Therefore:

Solving for the pressure of the gas gives:

The pressure in the gas isn't much bigger than atmospheric pressure, just enough to support the weight of the piston.

(b) The examples of the 1st law of thermodynamics is heated, expanding it and moving the piston up. If the volume occupied by the gas doubles, how much work has the gas done?

An assumption to make here is that the pressure is constant. Once the gas has expanded, the pressure will certainly be the same as before because the same free-body diagram applies. As long as the expansion takes place slowly, it is reasonable to assume that the pressure is constant.

If the volume has doubled, then, and the pressure has remained the same, the ideal gas law tells us that the temperature must have doubled too.

The work done by the gas can be determined by working out the force applied by the gas and calculating the distance. However, the force applied by the gas is the pressure times the area, so:

W = F s = P A s

and the area multiplied by the distance is a volume, specifically the change in volume of the gas. So, at constant pressure, work is just the pressure multiplied by the change in volume:

This is positive because the force and the distance moved are in the same direction, so this is work done by the gas.

The pressure-volume graph

As has been discussed, a gas enclosed by a piston in a cylinder can do work on the piston, the work being the pressure multiplied by the change in volume. If the volume doesn't change, no work is done. If the pressure stays constant while the volume changes, the work done is easy to calculate. On the other hand, if pressure and volume are both changing it's somewhat harder to calculate the work done.

As an aid in calculating the work done, it's a good idea to draw a pressure-volume graph (with pressure on the y axis and volume on the x-axis). If a system moves from one point on the graph to another and a line is drawn to connect the points, the work done is the area underneath this line. We'll go through some different thermodynamic processes and see how this works.

Types of thermodynamic processes

There are a number of different thermodynamic processes that can change the pressure and/or the volume and/or the temperature of a system. To simplify matters, consider what happens when something is kept constant. The different processes are then categorized as follows :

  1. Isobaric - the pressure is kept constant. An example of an isobaric system is a gas, being slowly heated or cooled, confined by a piston in a cylinder. The work done by the system in an isobaric process is simply the pressure multiplied by the change in volume, and the P-V graph looks like:

  2. Isochoric - the volume is kept constant. An example of this system is a gas in a box with fixed walls. The work done is zero in an isochoric process, and the P-V graph looks like:

  3. Isothermal - the temperature is kept constant. A gas confined by a piston in a cylinder is again an example of this, only this time the gas is not heated or cooled, but the piston is slowly moved so that the gas expands or is compressed. The temperature is maintained at a constant value by putting the system in contact with a constant-temperature reservoir (the thermodynamic definition of a reservoir is something large enough that it can transfer heat into or out of a system without changing temperature).

    If the volume increases while the temperature is constant, the pressure must decrease, and if the volume decreases the pressure must increase.

  4. Adiabatic - in an adiabatic process, no heat is added or removed from the system.

The isothermal and adiabatic processes should be examined in a little more detail.

Isothermal processes

In an isothermal process, the temperature stays constant, so the pressure and volume are inversely proportional to one another. The P-V graph for an isothermal process looks like this:

The work done by the system is still the area under the P-V curve, but because this is not a straight line the calculation is a little tricky, and really can only properly be done using calculus.

The internal energy of an ideal gas is proportional to the temperature, so if the temperature is kept fixed the internal energy does not change. The first law, which deals with changes in the internal energy, thus becomes 0 = Q - W, so Q = W. If the system does work, the energy comes from heat flowing into the system from the examples of the 1st law of thermodynamics if work is done on the system, heat flows out of the system to the reservoir.

Adiabatic processes

In an adiabatic process, no heat is added or removed from a system. The first law of thermodynamics is thus reduced to saying that the change in the internal energy of a system undergoing an adiabatic change is equal to -W. Since the internal energy is directly proportional to temperature, the work becomes:

An example of an adiabatic process is a gas expanding so quickly that no heat can be transferred. The expansion does work, and the temperature drops. This is exactly what happens with a carbon dioxide fire extinguisher, with the gas coming out at high pressure and cooling as it expands at atmospheric pressure.

Specific heat capacity of an ideal gas

With liquids and solids that are changing temperature, the heat associated with a temperature change is given by the equation:

A similar equation holds for an ideal gas, only instead of writing the equation in terms of the mass of the gas it is written in terms of the number of moles of gas, and use a capital C for the heat capacity, with units of J / (mol K):

For an ideal gas, the heat capacity depends on what kind of thermodynamic process the gas is experiencing. Generally, two different heat capacities are stated for a gas, the heat capacity at constant pressure (Cp) and the heat capacity at constant volume (Cv). The value at constant pressure is larger than the value at constant volume because at constant pressure not all of the heat goes into changing the temperature; some goes into doing work. On the other hand, at constant volume no work is done, so all the heat goes into changing the temperature. In other words, it takes less heat to produce a given temperature change at constant volume than it does at constant pressure, so Cv < Cp.

That's a qualitative statement about the two different heat capacities, but it's very easy to examine them quantitatively. The first law says:

We also know that PV = nRT, and at constant pressure the work done is:

Note that this applies for a monatomic ideal gas. For all gases, though, the following is true:

Another important number is the ratio of the two specific heats, represented by the Greek letter gamma (g). For a monatomic ideal gas this ratio is:

Источник: http://physics.bu.edu/~duffy/py105/Firstlaw.html

First law of thermodynamics

Law of physics linking conservation of energy and energy transfer

The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic processes, distinguishing two kinds of transfer of energy, as heat and as thermodynamic work, and relating them to a function of a body's state, called internal energy.

The law of conservation of energy states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but can be neither created nor destroyed.

For a thermodynamic process without transfer of matter, the first law is often formulated[1][nb 1]

{\displaystyle \Delta U=Q-W},

where \Delta U denotes the change in the internal energy of a closed system, Q denotes the quantity of energy supplied to the system as heat, and W denotes the amount of thermodynamic work done by the system on its surroundings. An equivalent statement is that perpetual motion machines of the first kind are impossible.

For processes that include transfer of matter, a further statement is needed: 'With due account of the respective reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then

{\displaystyle U_{0}=U_{1}+U_{2}},

where U_{0} denotes the internal energy of the combined system, and U_{1} and U_{2} denote the internal energies of the respective separated systems.'

History

In the first half of the eighteenth century, French philosopher and mathematician Émilie du Châtelet made notable contributions to the emerging theoretical framework of energy by proposing a form of the law of conservation of energy that recognized the inclusion of kinetic energy.[2][3] Empirical developments of the early ideas, in the century following, wrestled with contravening concepts such as the caloric theory of heat.

In 1840, Germain Hess stated a conservation law (Hess's Law) for the heat of reaction during chemical transformations.[4] This law was later recognized as a consequence of the first law of thermodynamics, but Hess's statement was not explicitly concerned with the relation between energy exchanges by heat and work.

In 1842, Julius Robert von Mayer made a statement that was expressed by Clifford Truesdell (1980) in the rendition "in a process at constant pressure, the heat used south dakota secretary of state sample ballot produce expansion is universally interconvertible with work", but this is not a general statement of the first law.[5][6]

The first full statements of the law came in 1850 from Rudolf Clausius,[7][8] and from William Rankine. Some scholars consider Rankine's statement less distinct than that of Clausius.[7]

Original statements: the "thermodynamic approach"

The original 19th-century statements of the first law of thermodynamics appeared in a conceptual framework in which transfer of energy as heat was taken as a primitive notion, not defined or constructed by the theoretical development of the framework, but rather presupposed as prior to it and already accepted. The primitive notion of heat was taken as empirically established, especially through calorimetry regarded as a subject in its own right, prior to thermodynamics. Jointly primitive with this notion of heat were the notions of empirical temperature and thermal equilibrium. This framework also took as primitive the notion of transfer of energy as work. This framework did not presume a concept of energy in general, but regarded it as derived or synthesized from the prior notions of heat and work. By one author, this framework has been called the "thermodynamic" approach.[8]

The first explicit statement examples of the 1st law of thermodynamics the first law of thermodynamics, by Rudolf Clausius in 1850, referred to cyclic thermodynamic processes.

In all cases in which work is produced by the agency of heat, a quantity of heat is consumed which is proportional to the work done; and conversely, by the expenditure of an equal quantity of work an equal quantity of heat is produced.[9]

Clausius also stated the law in another form, referring to the existence of a function of state of the system, the internal energy, and expressed it in terms of a differential equation for the increments of a thermodynamic process.[10] This equation may be described as follows:

In a thermodynamic process involving a closed system, the increment in the internal energy is equal to the difference between the heat accumulated by the system and the work done by it.

Because of its definition in terms of increments, the value is grated parmesan cheese bad for you the internal energy of a system is not uniquely defined. It is defined only up to an arbitrary additive constant of integration, which can be adjusted to give arbitrary reference zero levels. This non-uniqueness is in keeping with the abstract mathematical nature of the internal energy. The internal energy is customarily stated relative to a conventionally chosen standard reference state of the system.

The concept of internal energy is considered by Bailyn to be of "enormous interest". Its quantity cannot be immediately measured, but can only be inferred, by differencing actual immediate measurements. Bailyn likens it to the energy states of an atom, that were revealed by Bohr's energy relation = En''En'. In each case, an unmeasurable quantity (the internal energy, the atomic energy level) is revealed by considering the difference of measured quantities (increments of internal energy, quantities of emitted or absorbed radiative energy).[11]

Conceptual revision: the "mechanical approach"

In 1907, George H. Bryan wrote about systems between which there is no transfer of matter (closed systems): "Definition. When energy flows from one system or part of a system to another otherwise than by the performance of mechanical work, the energy so transferred is called heat."[12] This definition may be regarded as expressing a conceptual revision, as follows. This was systematically expounded in 1909 by Constantin Carathéodory, whose attention had been drawn to it by Max Born. Largely through Born's[13] influence, this revised conceptual approach to the definition of heat came which bank offers the best savings account be preferred by many twentieth-century writers. It might be called the "mechanical approach".[14]

Energy can also be transferred from one thermodynamic system to another in association with transfer of matter. Born points out that in general such energy transfer is not resolvable uniquely into work and heat moieties. In general, when there is transfer of energy associated with matter transfer, work and heat transfers can be distinguished only when they pass through walls physically separate from those for matter transfer.

The "mechanical" approach postulates the law of conservation of energy. It also postulates that energy can be transferred from one thermodynamic system to another adiabatically as work, and that energy can be held as the internal energy of a thermodynamic system. It also postulates that energy can be transferred from one thermodynamic system to another by a path that is non-adiabatic, and is unaccompanied by matter transfer. Initially, it "cleverly" (according to Bailyn) refrains from labelling as 'heat' such non-adiabatic, unaccompanied transfer of energy. It rests on the primitive notion of walls, especially adiabatic walls and non-adiabatic walls, defined as follows. Temporarily, only for purpose of this definition, one can prohibit transfer of energy as work across a wall of interest. Then walls of interest fall into two classes, (a) those such that arbitrary systems separated by them remain independently in their own previously established respective states of internal thermodynamic equilibrium; they are defined as adiabatic; and (b) those without such independence; they are defined as non-adiabatic.[15]

This approach derives the notions of transfer of energy as heat, and of temperature, as theoretical developments, not taking them as primitives. It regards calorimetry as a derived theory. It has an early origin in the nineteenth century, for example in the work of Helmholtz,[16] but also in the work of many others.[8]

Conceptually revised statement, according to the mechanical approach

The revised statement of the first law postulates that a change in the internal energy of a system due to any arbitrary process, that takes the system from a given initial thermodynamic state to a given final equilibrium thermodynamic state, can be determined through the physical existence, for those given states, of a reference process that occurs purely through stages of adiabatic work.

The revised statement is channel 69 news berks county

For a closed system, in any arbitrary process of interest that financial edge community credit union bay city michigan it from an initial to a final state of internal thermodynamic equilibrium, the change of internal energy is the same as that for a reference adiabatic work process that links those two states. This is so regardless of the path of the process of interest, and regardless of whether it is an adiabatic or a non-adiabatic process. The reference adiabatic work process may be chosen arbitrarily from amongst the class of all such processes.

This statement is much less close to the empirical basis than are the original statements,[17] but is often regarded as conceptually parsimonious in that it rests only on the concepts of adiabatic work and of non-adiabatic processes, not on the concepts of transfer of energy as heat and of empirical temperature that are presupposed by the original statements. Largely through the influence of Max Born, it is often regarded as theoretically preferable because of this conceptual parsimony. Born particularly observes that the revised approach avoids thinking in terms of what he calls the "imported engineering" concept of heat engines.[13]

Basing his thinking on the mechanical approach, Born in 1921, and again in 1949, proposed to revise the definition of heat.[13][18] In particular, he referred to the work of Constantin Carathéodory, who had in 1909 stated the first law without defining quantity of heat.[19] Born's definition was specifically for transfers of energy without transfer of matter, and it has been widely followed in textbooks (examples:[20][21][22]). Born observes that a transfer of matter between two systems is accompanied by a transfer of internal energy that cannot be resolved into heat and work components. There can be pathways to other systems, spatially separate from that of the matter transfer, that allow heat and work transfer independent of and simultaneous with the matter transfer. Energy is conserved in such transfers.

Description

Cyclic processes

The first law of thermodynamics for a closed system was expressed in two ways by Clausius. One way referred to cyclic processes and the inputs and outputs of the system, but did not refer to increments in the internal state of the system. The other way referred to an incremental change in the internal state of the system, and did not expect the process to be cyclic.

A cyclic process is one that can be repeated indefinitely often, returning the system to its initial state. Of particular interest for single cycle of a cyclic process are the net work done, and the net heat taken in (or 'consumed', in Clausius' statement), by the system.

In a cyclic process in which the system does net work on its surroundings, it is observed to be physically necessary not only that heat be taken into the system, but also, importantly, that some heat leave the system. The difference is the heat converted by the cycle into work. In each repetition of a cyclic process, the net work done by the system, measured in mechanical units, is proportional to the heat consumed, measured in calorimetric units.

The constant of proportionality is universal and independent of the system and in 1845 and 1847 was measured by James Joule, who described it as the mechanical equivalent of heat.

Sign conventions

In a non-cyclic process, the change in the internal energy of a system is equal to net energy added as heat to the system minus the thermodynamic work done by the system, both being measured in mechanical units. Taking \Delta U as a change in internal energy, one writes

{\displaystyle \Delta U=Q~-~W~~~~{\text{(sign convention of Clausius and generally in this article)}},}

where Q denotes the net quantity of heat supplied to the system by its surroundings and W denotes the net work done by the system. This sign convention is implicit in Clausius' statement of the law given above. It originated with the study of heat engines that produce useful work by consumption of heat; the key performance indicator of any heat engine is its thermal efficiency which is the quotient of the net work done, and the gross heat supplied. Thermal efficiency must be positive which necessitates that net work done and gross heat supplied must both be of the same sign; by convention both are given the positive sign.

Often nowadays, however, writers use the IUPAC convention by which the first law is formulated with thermodynamic work done on the system by its surroundings having a positive sign. With this now often used sign convention for work, the first law for a closed system may be written:[23]

{\displaystyle \Delta U=Q+W~~~~{\text{(sign convention of IUPAC)}}.}

(This convention follows physicists such as Max Planck,[24] and considers all net energy transfers to the system as positive and all net energy transfers from the system as negative, irrespective of any use for the system as an engine or other device.)

Continuing in the Clausius sign convention for work, when a system expands in a fictive quasistatic process, the thermodynamic work done by the system on the surroundings is the product, {\displaystyle P~\mathrm {d} V}, of pressure, P, and volume change, {\mathrm d}V, whereas the thermodynamic work done on the system by the surroundings is {\displaystyle -P\,\mathrm {d} V}. Using either sign convention for work, the change in internal energy examples of the 1st law of thermodynamics the system is:

{\displaystyle \mathrm {d} U=\delta Q-P\,\mathrm {d} V~~~~{\text{(quasi-static process)}},}

where \delta Q denotes the infinitesimal amount of heat supplied to the system from its surroundings and \delta denotes an inexact differential.

Work and heat are expressions of actual physical processes of supply or removal of energy, while the internal energy U is a mathematical abstraction that keeps account of the exchanges of energy that befall the system. Thus the term 'heat' for Q means "that amount of energy added or removed as heat in the thermodynamic sense", rather than referring to a form of energy examples of the 1st law of thermodynamics the system. Likewise, the term 'work energy' for W means "that amount of energy gained or lost through thermodynamic work". Internal energy is a property of the system whereas work done and heat supplied are not. A significant result of this distinction is that a given internal energy change \Delta U can be achieved by different combinations of heat and work. founders bank grand rapids may be signaled by saying that heat and work are path dependent, while change in internal energy depends only on the initial and final states of the process. It is necessary to bear in mind that thermodynamic work is measured by change in the system, not necessarily the same as work measured by forces and distances in the surroundings; this distinction is noted in the term 'isochoric work' (at constant volume).)

Various statements of the law for closed systems

The law is of great importance and generality and is consequently thought of from several points of view. Most careful textbook statements of the law express it for closed systems. It is stated in several ways, sometimes even by the same author.[8][25]

For the thermodynamics of closed systems, the distinction between transfers of energy as work and as heat is central and is within the scope of the present article. For the thermodynamics of open systems, such a distinction is beyond the scope of the present article, but some limited comments are made on it in the section below headed 'First law of thermodynamics for open systems'.

There are two main ways of stating a law of thermodynamics, physically or mathematically. They should be logically coherent and consistent with one another.[26]

An example of a physical statement is that of Planck (1897/1903):

It is in no way possible, either by mechanical, thermal, chemical, or other devices, to obtain perpetual motion, i.e. it is impossible to construct an engine which will work in a cycle and produce continuous work, or kinetic energy, from nothing.[27]

This physical statement is restricted neither to closed systems nor to systems with states that are strictly defined only for thermodynamic equilibrium; it has meaning also for open systems and for systems with states that are not in thermodynamic equilibrium.

An example of a mathematical statement is that of Crawford (1963):

For a given system we let ΔE kin = large-scale mechanical energy, ΔE pot = large-scale potential energy, and ΔE tot = total energy. The first two quantities are specifiable in terms of appropriate mechanical variables, and by definition
E^{{{\mathrm {tot}}}}=E^{{{\mathrm {kin}}}}+E^{{{\mathrm {pot}}}}+U\,\.
For any finite process, whether reversible or irreversible,
\Delta E^{{{\mathrm {tot}}}}=\Delta E^{{{\mathrm {kin}}}}+\Delta E^{{{\mathrm {pot}}}}+\Delta U\,\.
The first law in a form that involves the principle of conservation of energy more generally is
\Delta E^{{{\mathrm {tot}}}}=Q+W\,\.
Here Q and W are heat and work added, with no restrictions as to whether the process is reversible, quasistatic, or irreversible.[Warner, Am. J. Phys., 29, 124 (1961)][28]

This statement by Crawford, for W, uses the sign convention of IUPAC, not that of Clausius. Though it does not explicitly say so, this statement refers to closed systems, and to internal energy U defined for bodies in states of thermodynamic equilibrium, which possess well-defined temperatures.

The history of statements of the law for closed systems has two main periods, before and after the work of Bryan (1907),[29] of Carathéodory (1909),[19] and the approval of Carathéodory's work given by Born (1921).[18] The earlier traditional versions of the law for closed systems are nowadays often considered to be out of date.

Carathéodory's celebrated presentation of equilibrium thermodynamics[19] refers to closed systems, which are allowed to contain several phases connected by internal walls of various kinds of impermeability and permeability (explicitly including walls that are permeable only to heat). Carathéodory's 1909 version of the first chase freedom credit card online payment of thermodynamics was stated in an axiom which refrained from defining or mentioning temperature or quantity of heat transferred. That axiom stated that the internal energy of a phase in equilibrium is a function of state, that the sum of the internal energies of the phases is the total internal energy of the system, and that the value of the total internal energy of the system is changed by the amount of work done adiabatically on it, considering work as a form of energy. That article considered this statement to be an expression of the law of conservation of energy for such systems. This version is nowadays widely accepted as authoritative, but is stated in slightly varied ways by different authors.

Such statements of the first law for closed systems assert the existence of internal energy as a function of state defined in terms of adiabatic work. Thus heat is not defined calorimetrically or as due to temperature difference. It is defined as a residual difference between change of internal energy and work done on the system, when that work does not account for the whole of the change of internal energy and the system is not adiabatically isolated.[20][21][22]

The 1909 Carathéodory statement of the law in axiomatic form does not mention heat or temperature, but the equilibrium states to which it refers are explicitly defined by variable sets that necessarily include "non-deformation variables", such as pressures, which, within reasonable restrictions, can be rightly interpreted as empirical temperatures,[30] and the walls connecting the phases of the system are explicitly defined as possibly impermeable to heat or permeable only to heat.

According to Münster (1970), "A somewhat unsatisfactory aspect of Carathéodory's theory is that a consequence of the Second Law must be considered at this point [in the statement of the first law], i.e. that it is not always possible to reach any state 2 from any other state 1 by means of an adiabatic process." Münster instances that no adiabatic process can reduce the internal energy of a system at constant volume.[20] Carathéodory's paper asserts that its statement of the first law corresponds exactly to Joule's experimental arrangement, regarded as an instance of adiabatic work. It does not point out that Joule's experimental arrangement performed essentially irreversible work, through friction of paddles in a liquid, or passage of electric current through a resistance inside the system, driven by motion of a coil and inductive heating, or by an external current source, which can access the system only by the passage of electrons, and so is not strictly adiabatic, because electrons are a form of matter, which cannot penetrate adiabatic walls. The paper goes on to base its main argument on the possibility of quasi-static adiabatic work, which is essentially reversible. The paper asserts that it will avoid reference to Carnot cycles, and then proceeds to base its argument on cycles of forward and backward quasi-static adiabatic stages, with isothermal stages of zero magnitude.

Sometimes the concept of internal energy is not made explicit in the statement.[31][32][33]

Sometimes the existence of the internal energy is made explicit but work is not explicitly mentioned in the statement of the first postulate of thermodynamics. Heat supplied is then defined as the residual change in internal energy after work has been taken into account, in a non-adiabatic process.[34]

A respected modern author states the first law of thermodynamics as "Heat is a form of energy", which explicitly mentions neither internal energy nor adiabatic work. Heat is defined as energy transferred by thermal contact with a reservoir, which has a temperature, and is generally so large that addition and removal of heat do not alter its temperature.[35] A current student text on chemistry defines heat thus: "heat is the exchange of thermal energy between a system and its surroundings caused by a temperature difference." The author then explains how heat is defined or measured by calorimetry, in terms of heat capacity, specific heat capacity, molar heat capacity, and temperature.[36]

A respected text disregards the Carathéodory's exclusion of mention of heat from the statement of the first law for closed systems, and admits heat calorimetrically defined along with work and internal energy.[37] Another respected text defines heat exchange as determined by temperature difference, but also mentions that the Born (1921) version is "completely rigorous".[38] These versions follow the traditional approach that is now considered out of date, exemplified by that of Planck (1897/1903).[39]

Evidence for the first law of thermodynamics for closed systems

The first law of thermodynamics for closed systems was originally induced from empirically observed evidence, including calorimetric evidence. It is nowadays, however, taken to provide the definition of heat via the law of conservation of energy and the definition of work in terms of changes in the external parameters of a system. The original discovery of the law was gradual over a period of perhaps half a century or more, and some early studies were in terms of cyclic processes.[7]

The following is an account in terms of changes of state of a closed system through compound processes that are not necessarily cyclic. This account first considers processes for which the first law is easily verified because of their simplicity, namely adiabatic processes (in which there is no transfer as heat) and adynamic processes (in which there is no transfer as work).

Adiabatic processes

Main article: Adiabatic process

In an adiabatic process, there is transfer of energy as work but not as heat. For all adiabatic process that takes a system from a given initial state to a given final state, irrespective of how the work is done, the respective eventual total quantities of energy transferred as work are one and the same, determined just by the given initial and final states. The work done on the system is defined and measured by changes in mechanical or quasi-mechanical variables external to the system. Physically, adiabatic transfer of energy as work requires the existence of adiabatic enclosures.

For instance, in Joule's experiment, the initial system is a tank of water with a paddle wheel inside. If we isolate the tank thermally, and move the paddle wheel with a pulley and a weight, we can relate the increase in temperature with the distance descended by the mass. Next, the system is returned to its initial state, isolated again, and the same amount of work is done on the tank using different devices (an electric motor, a chemical battery, a spring.). In every case, the amount of work can be measured independently. The return to the initial state is not conducted by doing adiabatic work on the system. The evidence shows that the final state of the water (in particular, its temperature and volume) is the same in every case. It is irrelevant if the work is electrical, mechanical, chemical. or if done suddenly or slowly, as long as it is performed in an adiabatic way, that is to say, without heat transfer into or out of the system.

Evidence of this kind shows that to increase the temperature of the water in the tank, the qualitative kind of adiabatically performed work does not matter. No qualitative kind of adiabatic work has ever been observed to decrease the temperature of the water in the tank.

A change from one state to another, for example an increase of both temperature and volume, may be conducted in several stages, for example by externally supplied electrical work on a resistor in the body, and adiabatic expansion allowing the body to do work on the surroundings. It needs to be shown that the time order of the stages, and their relative magnitudes, does not affect the amount of adiabatic work that needs to be done for the change of state. According to one respected scholar: "Unfortunately, it does not seem that experiments of this kind have ever been carried out carefully. . We must therefore admit that the statement which we have enunciated here, and which is equivalent to the first law of thermodynamics, is not well founded on direct experimental evidence."[17] Another expression of this view is ". no systematic precise experiments to verify this generalization directly have weekend at bernies 2 dvd been attempted."[40]

This kind of evidence, of independence of sequence of stages, combined with the above-mentioned evidence, of independence of qualitative kind of work, would show the existence of an important state variable that corresponds with adiabatic work, but not that such a state variable represented a conserved quantity. For the latter, another step of evidence is needed, which may be related to the concept of reversibility, as mentioned below.

That important state variable was first recognized and denoted U by Clausius in 1850, but he did not then name it, and he defined it in terms not only of work but also of heat transfer in the same process. It was also independently recognized in 1850 by Rankine, who also denoted it U ; and in 1851 by Kelvin who then called it "mechanical energy", and later "intrinsic energy". In 1865, after some hestitation, Clausius began calling his state function U "energy". In 1882 it was named as the internal energy by Helmholtz.[41] If 1st bank and trust broken bow ok routing number adiabatic processes were of interest, and heat could be ignored, the concept of internal energy would hardly arise or be needed. The relevant physics would be largely covered by the concept of potential energy, as was intended in the 1847 paper of Helmholtz on the principle of conservation of energy, though that did not deal with forces that cannot be described by a potential, and thus did not fully justify the principle. Moreover, that paper was critical of the early work of Joule that had by then been performed.[42] A great merit of the internal energy concept is that it frees thermodynamics from a restriction to cyclic processes, and allows a treatment in terms of thermodynamic states.

In an adiabatic process, adiabatic work takes the system either from a reference state O with internal energy U(O) to an arbitrary one A with internal energy U(A), or from the state A to the state O:

U(A)=U(O)-W_{{O\to A}}^{{\mathrm {adiabatic}}}\,\,{\mathrm {or}}\,\,U(O)=U(A)-W_{{A\to O}}^{{\mathrm {adiabatic}}}\.

Except under the special, and strictly speaking, fictional, condition of reversibility, only one of the processes  {\mathrm {adiabatic}},\,O\to A   or  {\mathrm {adiabatic}},\,{A\to O}\,  is empirically feasible by a simple application of externally supplied work. The reason for this is given as the second law of thermodynamics and is not considered in the present article.

The fact of such irreversibility may be dealt with in two main ways, according to different points of view:

  • Since the work of Bryan (1907), the most accepted way to deal with it nowadays, followed by Carathéodory,[19][22][43] is to rely on the previously established concept of quasi-static processes,[44][45][46] as follows. Actual physical processes of transfer of energy as work are always at least to some degree irreversible. The irreversibility is often due to mechanisms known as dissipative, that transform bulk kinetic energy into internal energy. Examples are friction and viscosity. If the process is performed more slowly, the frictional or viscous dissipation is less. In the limit of infinitely slow performance, the dissipation tends to zero and then the limiting process, though fictional rather than actual, is notionally reversible, and is called quasi-static. Throughout the course of the fictional limiting quasi-static process, the internal intensive variables of the system are equal to the external intensive variables, those that describe the reactive forces exerted by the surroundings.[47] This can be taken to justify the formula
    {\displaystyle W_{A\to O}^{\text{adiabatic, quasi-static}}=-W_{O\to A}^{\text{adiabatic, quasi-static}}\.}

     

     

     

     

    (1)

  • Another way to deal with it is to allow that experiments with processes of heat transfer to or from the system may be used to justify the formula (1) above. Moreover, it deals to some extent with the problem of lack of direct experimental evidence that the time order of stages of a process does not matter in the determination of internal energy. This way does not provide theoretical purity in terms of adiabatic work processes, but is empirically feasible, and is in accord with experiments actually done, such as the Joule experiments mentioned just above, and with older traditions.

The formula (1) above allows that to go by processes of quasi-static adiabatic work from the state A to the state B we can take a path that goes through the reference state O, since the quasi-static adiabatic work is independent of the path

-W_{{A\to B}}^{{\mathrm {adiabatic,\,quasi-static}}}=-W_{{A\to O}}^{{\mathrm {adiabatic,\,quasi-static}}}-W_{{O\to B}}^{{\mathrm {adiabatic,\,quasi-static}}}=W_{{O\to A}}^{{\mathrm {adiabatic,\,quasi-static}}}-W_{{O\to B}}^{{\mathrm {adiabatic,\,quasi-static}}}=-U(A)+U(B)=\Delta U

This kind of empirical evidence, coupled with theory of this kind, largely justifies the following statement:

For all adiabatic processes between two specified states of a closed system of any nature, the net work done is the same regardless the details of the process, and determines a state function called internal energy, U.

Adynamic processes

See also: Thermodynamic processes

A complementary observable aspect of the first law is about heat transfer. Adynamic transfer of energy as heat can be measured empirically by changes in the surroundings of the system of interest by calorimetry. This again requires the existence of adiabatic enclosure of the entire process, system and surroundings, though the separating wall between the surroundings and the system is thermally conductive or radiatively permeable, not adiabatic. A calorimeter can rely on measurement of sensible heat, which requires the existence of thermometers and measurement of temperature change in bodies of known sensible heat capacity under specified conditions; or it can rely on the measurement of latent heat, through measurement of masses of material that change phase, at temperatures fixed by the occurrence of phase changes under specified conditions in bodies of known latent heat of phase change. The calorimeter can be calibrated by adiabatically doing externally determined work on it. The most accurate method is by passing an electric current from outside through a resistance inside the calorimeter. The calibration allows comparison of calorimetric measurement of quantity of heat transferred with quantity of energy transferred as work. According to one textbook, "The most common device for measuring \Delta U is an adiabatic bomb calorimeter."[48] According to another textbook, "Calorimetry is widely used in present day laboratories."[49] According to one opinion, "Most thermodynamic data come from calorimetry."[50] According to another opinion, "The most common method of measuring "heat" is with a calorimeter."[51]

When the system evolves with transfer of energy as heat, without energy being transferred as work, in an adynamic process,[52] the heat transferred to the system is equal to the increase in its internal energy:

Q_{{A\to B}}^{{\mathrm {adynamic}}}=\Delta U\.

General case for reversible processes

Heat transfer is practically reversible when it is driven by practically negligibly small temperature gradients. Work transfer is practically reversible when it occurs so slowly that there are no frictional effects within the system; frictional effects outside the system should also be zero if the process is to be globally reversible. For a particular reversible process in general, the work done reversibly on the system, W_{{A\to B}}^{{{\mathrm {path}}\,P_{0},\,{\mathrm {reversible}}}}, and the heat transferred reversibly to the system, Q_{{A\to B}}^{{{\mathrm {path}}\,P_{0},\,{\mathrm {reversible}}}} are not required to occur respectively adiabatically or adynamically, but they must belong to the same particular process defined by its particular reversible path, P_{0}, through the space of thermodynamic states. Then the work and heat transfers can occur and be calculated simultaneously.

Putting the two complementary aspects together, the first law for a particular reversible process can be written

-W_{{A\to B}}^{{{\mathrm {path}}\,P_{0},\,{\mathrm {reversible}}}}+Q_{{A\to B}}^{{{\mathrm {path}}\,P_{0},\,{\mathrm {reversible}}}}=\Delta U\.

This combined statement is the expression the first law of thermodynamics for reversible processes for closed systems.

In particular, if no work is done on a thermally isolated closed system we have

\Delta U=0\,.

This is one aspect of the law of conservation of energy and can be stated:

The internal energy of an isolated system remains constant.

General case for irreversible processes

If, in a process of change of state of a closed system, the energy transfer is not under a practically zero temperature gradient and practically frictionless, then the process is irreversible. Then the heat and work transfers may be difficult to calculate, and irreversible thermodynamics is called for. Nevertheless, the first law still holds and provides a check on the measurements and calculations of the work done irreversibly on the system, W_{{A\to B}}^{{{\mathrm {path}}\,P_{1},\,{\mathrm {irreversible}}}}, and the heat transferred irreversibly to the system, Q_{{A\to B}}^{{{\mathrm {path}}\,P_{1},\,{\mathrm {irreversible}}}}, which belong to the same particular process defined by its particular irreversible path, P_{1}, through the space of thermodynamic states.

-W_{{A\to B}}^{{{\mathrm {path}}\,P_{1},\,{\mathrm {irreversible}}}}+Q_{{A\to B}}^{{{\mathrm {path}}\,P_{1},\,{\mathrm {irreversible}}}}=\Delta U\.

This means that the internal energy U is a function of state and that the internal energy change \Delta U between two states is a function only of the two states.

Overview of the weight of evidence for the law

The first law of thermodynamics is so general that its predictions cannot all be directly tested. In many properly conducted experiments it has been precisely supported, and never violated. Indeed, within its scope of applicability, the law is so reliably established, that, nowadays, rather than experiment being considered as testing the accuracy of the law, it is more practical and realistic to think of the law as testing the accuracy of experiment. An experimental result that seems to violate the law may be assumed to be inaccurate or wrongly conceived, for example due to failure to account for an important physical factor. Thus, some may regard it as a principle more abstract than a law.

State functional formulation for infinitesimal processes

When the heat and work transfers in the equations above are infinitesimal in magnitude, they are often denoted by δ, rather than exact differentials denoted by d, as a reminder that heat and work do not describe the state of any system. The integral of an inexact differential depends upon the particular add business account to paypal taken through the space of thermodynamic parameters while the integral of an exact differential depends only upon the initial and final states. If the initial and final states are the same, then the integral of an inexact differential may or may not be zero, but the integral of an exact differential is always zero. The path taken by a thermodynamic system through a chemical or physical change is known as a thermodynamic process.

The first law for a closed homogeneous system may be stated in terms that include concepts that are established in the second law. The internal energy U may then be expressed as a function of the system's defining state variables S, entropy, and V, volume: U = U (S, V). In these terms, T, the system's temperature, and P, its pressure, are partial derivatives of U with respect to S and V. These variables are important throughout thermodynamics, though not necessary for the statement of the first law. Rigorously, they are defined only when the system is in its own state of internal thermodynamic equilibrium. For some purposes, the concepts provide good approximations for scenarios sufficiently near to the system's internal thermodynamic equilibrium.

The first law requires that:

{\displaystyle dU=\delta Q-\delta W\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{(closed system, general process, quasi-static or irreversible).}}}

Then, for the fictive case of a reversible process, dU can be written in terms of exact differentials. One may imagine reversible changes, such that there is at each instant negligible departure from thermodynamic equilibrium within the system. This excludes isochoric work. Then, mechanical work is given by δW = −P dV and the quantity of heat added can be expressed as δQ = T dS. For these conditions

{\displaystyle dU=TdS-PdV\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{(closed system, reversible process).}}}

While this has been shown here for reversible changes, it is valid in general, as U can be considered as a thermodynamic state function of the defining state variables S and V:

{\displaystyle dU=TdS-PdV\,\,\,\,\,{\text{(closed system, general process, quasi-static or irreversible).}}}

 

 

 

 

(2)

Equation (2) is known as the fundamental thermodynamic relation for a closed system in the energy representation, for which the defining state variables are S and V, with respect to which T and P are partial derivatives of U.[53][54][55] It is only in the fictive reversible case, when isochoric work is excluded, that the work done and heat transferred are given by −P dV and T dS.

In the case of a closed system in which the particles of the system are of different types and, because chemical reactions may occur, their respective numbers are not necessarily constant, the fundamental thermodynamic relation for dU becomes:

{\displaystyle dU=TdS-PdV+\sum _{i}\mu _{i}dN_{i}.}

where dNi is the (small) increase in number of type-i particles in the reaction, and μi is known as the chemical potential of the type-i particles in the system. If dNi is expressed in mol then μi is expressed in J/mol. If the system has more external mechanical variables than just the volume that can change, the fundamental thermodynamic relation further generalizes to:

{\displaystyle dU=TdS-\sum _{i}X_{i}dx_{i}+\sum _{j}\mu _{j}dN_{j}.}

Here the Xi are the generalized forces corresponding to the external variables xi. The parameters Xi are independent of the size of the system and are called intensive parameters and the xi are proportional to the size and called extensive parameters.

For an open system, there can be transfers of particles as well as energy into or out of the system during a process. For this case, the first law of thermodynamics still holds, in images of jennifer holliday form that the internal energy is a function of state and the change of internal energy in a process is a function only of its initial and final states, as noted in the section below headed First law of thermodynamics for open systems.

A useful idea examples of the 1st law of thermodynamics mechanics is that the energy gained by a particle is equal to the force applied to the particle multiplied by the displacement of the particle while that force is applied. Now consider the first law without the heating term: dU = −PdV. The pressure P can be viewed as a force (and in fact has units of force per unit area) while dVis the displacement (with units of distance times area). We may say, with respect to this work term, that a pressure difference forces a transfer of volume, and that the product of the two (work) is the amount of energy transferred out of the system as a result of the process. If one were to make this term negative then this would be the work done on the system.

It is useful to view the TdS term in the same light: here the temperature is known as a "generalized" force (rather than an actual mechanical force) and the entropy is a generalized displacement.

Similarly, a difference in chemical potential between groups of particles in the system drives a chemical reaction that changes the numbers of particles, and the corresponding product is the amount of chemical potential energy transformed in process. For example, consider a system consisting of two phases: liquid water and water vapor. There is a generalized "force" of evaporation that drives water molecules out of the liquid. There is a generalized "force" of condensation that drives vapor molecules out of the vapor. Only when these two "forces" (or chemical potentials) are equal is there equilibrium, and the net rate of transfer zero.

The two thermodynamic parameters that form a generalized force-displacement pair are called "conjugate variables". The two most familiar pairs are, of course, pressure-volume, and temperature-entropy.

Fluid dynamics

Main article: First law of thermodynamics (fluid mechanics)

In fluid dynamics, the first law of thermodynamics reads .[56]

Spatially inhomogeneous systems

Classical thermodynamics is initially focused on closed homogeneous systems (e.g. Planck 1897/1903[39]), which might be regarded as 'zero-dimensional' in the sense that they have no spatial variation. But it is desired to study also systems with distinct internal motion and spatial inhomogeneity. For such systems, the principle of conservation of energy is expressed in terms not only of internal energy as defined for homogeneous systems, but also in terms of kinetic energy and potential energies of parts of the inhomogeneous system with respect to each other and with respect to long-range external forces.[57] How the total energy of a system is allocated between these three more specific kinds of energy varies according to the purposes of different writers; this is because these components of energy are to some extent mathematical artefacts rather than actually measured physical quantities. For any closed homogeneous component of an inhomogeneous closed system, if E denotes the total energy of that component system, one may write

E=E^{{{\mathrm {kin}}}}+E^{{{\mathrm {pot}}}}+U

where E^{{{\mathrm {kin}}}} and E^{{{\mathrm {pot}}}} denote respectively the total kinetic energy and the total potential energy of the component closed examples of the 1st law of thermodynamics system, and U denotes its internal energy.[28][58]

Potential energy can be exchanged with the surroundings of the system when the surroundings impose a force field, such as gravitational or electromagnetic, on the system.

A compound system consisting of two interacting closed homogeneous component subsystems has a potential energy of interaction E_{{12}}^{{{\mathrm {pot}}}} between the subsystems. Thus, in an obvious notation, one may write

Источник: https://en.wikipedia.org/wiki/First_law_of_thermodynamics

First Law of Thermodynamics Definition

The first law of thermodynamics is the physical law which states that the total energy of a system and its surroundings remain constant. The law is also known as the law of conservation of energy, which states energy can transform from one form into another, but can neither be created nor destroyed within an isolated system. Perpetual motion machines of the first kind are impossible, according to the first law of thermodynamics. In other words, it is not possible to construct an engine that will cycle and produce work continuously from nothing.

First Law of Thermodynamics Equation

The equation for the first law can be confusing because there are two different sign conventions in use.

In physics, particularly when discussing heat engines, the change in the energy of a system equals the heat flow in the system from the surroundings minus the work done by the system on the surroundings. The equation for the law may be written:

ΔU = Q - W

Here, ΔU is the change in the internal energy of a closed system, Q is the heat supplied to the system, and W is the amount of work done by the system on the surroundings. This version of the law follows the sign convention of Clausius.

However, the IUPAC uses the sign convention proposed by Max Planck. Here, net energy transfer to a system is positive and net energy transfer from a system are negative. The equation then becomes:

ΔU = Q + W

Sources

  • Adkins, C. J. (1983). Equilibrium Thermodynamics (3rd ed.). Cambridge University Press. ISBN 0-521-25445-0.
  • Bailyn, M. (1994). A Survey of Thermodynamics. American Institute of Physics Press. New York. ISBN 0-88318-797-3.
  • Denbigh, K. (1981). The Principles of Chemical Equilibrium With Applications in Chemistry and Chemical Engineering (4th ed.). Cambridge University Press. Cambridge UK. ISBN 0-521-23682-7.
Источник: https://www.thoughtco.com/first-law-of-thermodynamics-definition-604343

1.3 The first two laws of thermodynamics

The natural laws which govern the environment and which are, therefore, of interest to us are the first two laws of thermodynamics. These relate to closed systems. Strictly speaking, the earth is not a closed system as it receives energy from the sun, but it is almost a closed system.

First law of thermodynamics

The First Law states that whenever energy is converted in form, its total quantity remains unchanged. In other words, energy (or matter) can be neither created nor destroyed.

Common and Stagl (2005) use the example of coal-fired electricity generating plant. The coal is heated which produces electricity. A by-product of this process is waste heat that is transported away as cooling water or gases. In addition, various waste gases are emitted into the atmosphere, which cause pollution, such as acid rain.

Second law of thermodynamics

This law states that in a closed system, entropy does not decrease.

Entropy could be described as a measure of the 'disorderedness' of energy. For instance, ordered energy is useful and an example of this is the energy stored in a battery. However, disordered energy is not useful, and an example is the energy dispersed into the environment by a fire.

Entropy is a thermodynamic property of matter and is related to the amount of energy that can be transferred from one system to another in the form of work. For a given system with a fixed amount of energy, the value of the entropy ranges from zero to a maximum. If the entropy is at its maximum, then the amount of work that can be transferred is equal to zero; if the entropy is at zero, then the amount of work that can be transferred is equal to the energy of the system.

During an irreversible process the entropy of a system always increases.

The key points to remember from the above are that, because of these natural laws:

  • increased extraction of minerals by the production process leads to an increase in wastes
  • there is a limit on the substitutability of inputs
  • since production and consumption lead to the dissipation of matter, scarce energy is needed for recycling

The importance of these two laws relates to the use, re-use and recycling of the environment after interactions with the economy.

Let us look more closely at the subject of recycling, as this would seem to offer a chance for the economy to retain the use of scarce resources.

Recycling

There is a hierarchy of resource use that includes recycling. This is referred to as the 3R's - reduce, re-use and recycle. The final and least appealing option after resource use is to dispose of any remaining waste.

There are now many materials which are routinely recycled and re-used. For example, glass bottles have been collected and re-used by a number of drinks companies for many years. In various countries this practice is encouraged by the use of deposit-refund schemes. (Choe and Fraser 1998) Other examples include paper, metal, glass, plastic, textiles, and garden waste.

For instance, in the Netherlands, household waste that can be composted is collected separately from other household waste and is composted by the local authorities. To encourage citizens to participate in this scheme, householders received some free compost soon after the scheme was set up. However, there are clearly costs involved in such a scheme:

  • separate waste bins were provided for the compostable waste
  • information was provided to householders
  • householders use time to separate their waste
  • costs of separate collection and of dealing with the compost

In the Netherlands, chemical household waste is also collected separately, with similar costs involved. There are numerous examples of different economic instruments used to deal with waste at both the household and industry levels. (Choe and Fraser 1998, and Pearce 2005).

There are clearly limits to what resources can be re-used and recycled. These limits are not only dictated by the laws of thermodynamics but also by the costs associated with re-using and recycling many items.

Источник: https://www.soas.ac.uk/cedep-demos/000_P521_EEM_K3736-Demo/unit1/page_09.htm

Do you find it hard to understand first law of thermodynamics and its problems? Do not worry we have you covered ! The first law of thermodynamics states that; for any spontaneous or non spontaneous reaction the sum of energy of the system and its surrounding remain constant. In simple English the law states that the energy can never be created nor destroyed; but can only change from one form to another.

You can find example for this statement in form of electric heater, fan and i.c engine which convert one form of energy to another. To better understand the law in a step by step approach without much confusion; lets start from basics.

Basics OF Thermodynamics

Thermodynamics is the part of science that deals with energy conversion in its different forms. It helps understand whether a particular change ( physical or chemical ) will occur under a specific condition; ignoring internal structure of its atom and molecule. There are three basic laws of thermodynamics that generalize into firstsecond and third law of thermodynamics.

System And Surrounding

The part of universe under thermodynamic consideration is known as system while everything else is called its surrounding. There is a thin physical or imaginary line in between known as boundary; which divide  the system from surrounding. For example 500 ml water in a kettle is the system while the air inside along with the kettle itself is the surrounding. The system is further classified into three types based upon the nature of its boundary:-

System and surrounding

1 ) Isolated System: The system with a closed and isolated boundary which do not allow for the transfer of matter or energy to and from the surrounding is called isolated system. For example a insulated water bottle with hot water inside; water can not escape the container nor does the heat or the water vapour.

2 ) Closed System: A system with a closed boundary which do not allow for physical transfer of matter; but allow energy to flow to and from the system and its surroundings in form of heat, radiation and work. For example water in a pressure cooker can not transfer the matter ( until depressurized ); but allow heat energy to flow from the system to outside surrounding.

3 ) Open System: A open system does not have any physical boundary and is open to the surrounding allowing both matter and energy to flow without any restriction. For example water boiling in a jar or open kettle; where the water vapour and heat energy is lost to the surrounding.

Thermodynamic Process

When a system undergoes change in its state or any of its condition such as temperature, pressure or volume then the operation is termed as thermodynamic process. You might already know some of these thermodynamic process; but for the scale of good let’s discuss various types of thermodynamic process:-

1 ) Isothermal Process: The thermodynamic process in which the temperature remains constant during the change of state. For example evaporation of water at 100 degree centigrade; at 100 degree the water change its state from liquid to gas under constant temperature.

2 ) Adiabatic Process: The thermodynamic process in which there is no flow of heat in or out of the system.  For example the compression and expansion of air due to sound waves propagating through the medium.

Isobaric Process Explained

3 ) Isobaric Process: These are the thermodynamic process in which pressure remains constant during the change of state. For example boiling water in a open system will lead to change of state without change in pressure as the vapor expands at atmospheric pressure.

4 ) Isochoric Process: the thermodynamic process in which the volume remains constant during the change of state. For example when water is boiler in a closed container the state will change at constant volume.

5 ) Reversible Process: A thermodynamic process which go for an indefinite time with any given point in between the initial and final state is in equilibrium; so that it can be recovered with certain change in the state at any time. There is no practical example of reversible process.

6 ) Irreversible Process: The thermodynamic process that happen in one step from start to finish and can not be reversed is known as irreversible process. For irreversible process the system is at equilibrium only at start and end of the process. For example two gas when mixed together is a irreversible process.

7 ) Spontaneous Process: A thermodynamic process is defined to be spontaneous if and only if the process take place without any external influence or work. The spontaneous process must always proceed of its own unaffected by the external factors.

8 ) Non-Spontaneous Process: A non-spontaneous process is the exact opposite of the spontaneous process. It requires external influence and effort to proceed forward in form of work and catalyst in reaction.

Internal Energy

A internal energy of a system is the total ( kinetic + potential ) energy of the random molecules under motion. In other words it is the total energy of a system which remains constant. For example air inside a balloon have some energy; now if the balloon flow with the wind at 0.5 km/hr does the internal energy of the closed system i.e balloon change? No ! Now if we catch the balloon and press it; will the internal energy change? No ! In any case there can be a change in pressure, kinetic or potential energy of the system but its internal energy remains same.

In even better way; suppose you have one brother whom you have given your 5 rupees ( consider it your currency ) and have left with 10 rupees. Now in a closed system of your family ( You + your brother ) the total money remains constant i.e 15 rupees. Internal energy is just similar to that and is represented by ” ΔU ” and is given by the sum of of heat transfer and negative work done according to the first law of thermodynamics.

ΔU = Q – W

Note: For a thermodynamic process from state A to B the change in internal energy is given by ΔU = U2 – U1 and is always independent of the path or the process.

Work Done On The System For Isothermal Process

Learn First Law of Thermodynamics in Simple Language

Consider a closed system of cylinder with a frictionless piston moving upward. Now the ideal gas in the system is expanding reversibly from v1 to v2 while the pressure decrease from p1 to p2 at a constant temperature. Now as this is a reversible process it will go through a infinite number of steps in between v1 and v2.

∴,

As we know work done ( W ) = Force wells fargo home mortgage login page F ) X distance / displacement ( h )

So, for one step in the infinite series;

dw = F x dl

= P X A X dh

= p x dv ( as, volume = area x height )

As we have learn that the work done on the system is negative; the total work done on the system is:

And from ideal gas equation we know P X V = nRT

And From ideal gas equation we know P1V1 = P2V2

Or,

First Law of Thermodynamics

Suppose you are in a auditorium with 200 others and there is no air conditioner. Now if the auditorium is closed it works well as an example of closed system; As you all exhale carbon dioxide along with some heat increasing the heat of the auditorium exponentially. Now you all will start to feel the heat and start to sweat.

Your body heat is absorbed and taken away by your sweat which then evaporate further increasing the auditorium temperature along with stinking smell. Now this process of increasing auditorium temperature through lost heat is a perfect example of first law of thermodynamics. Here in the closed system of auditorium no heat is lost but is only transfered from your body to atmosphere.

Let’s understand it in a different way; If you know what a pendulum is, initially when you set it in motion, it start oscillating. If you don’t know much about thermodynamics, the pendulum might seems, that it will go on forever without any external power / force / energy powering it (A perpetual motion machine, in another words); but pendulum is not a perpetual motion machine. It is so because perpetual motion is impossible according to the law of physics, and one of the reason is first law of thermodynamics.

As a Thermodynamics system work, it loses heat, when work is done on the system, it gains heat. Heat is converted into work and work is converted into heat. Together the work and heat transferred into or out of the system represent the change in its Internal energy.

First law of thermodynamics

It is important to know, if heat is transferred into the system, Heat Q is positive and if heat Q is transferred out of the system Q is negative and if Work W is done by the system, work W is positive, if work is being done on the system, it is negative.

Here you’ll notice that first law of thermodynamics describe only two factors, work and heat as effecting the change in internal energy. That is because as long as system is closed there first convenience bank abilene texas aren’t any other factor involved. So the amount of heat lost by the system is exactly equals to amount of work done by the system and visa-versa.

This stated, basically the first law of thermodynamics is a way to describe conservation of energy. There’s always some kind of heat lose through friction, even this tiny amount eventually leads to run out of energy needed to drive the work; and therefore pendulum is not perpetual motion machine, it relies on the force exerted initially by hand for oscillation.

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Difference Between First and Second Law of Thermodynamics

First_second_law_of_thermodynamics_img

The First Law of the Thermodynamics is related to the conservation of energy, while the Second Law of Thermodynamics argue that some of the thermodynamics processes are impermissible and does not entirely follow the First Law of Thermodynamics.

The word ‘thermodynamics‘ is where can i donate unwanted dog food from the Greek words, where “Thermo” means heat and “dynamics” means power. So thermodynamics is the study of energy which exists in various forms like light, heat, electrical and chemical energy.

Thermodynamics is very vital part of the physics and its related field like chemistry, material science, environmental science, etc. Meanwhile ‘Law’ means the system of the rules. Therefore laws of thermodynamics deal with the one of the forms of energy which is heat, their behaviour under different circumstances corresponding to the mechanical work.

Though we know that there are four laws of thermodynamics, starting from the examples of the 1st law of thermodynamics law, first law, second law and the third law. But the most used are the first and the second laws, hence in this content, we will be discussing and differentiating the first and second laws.

Content: First Vs Second Laws of Thermodynamics

  1. Comparison Chart
  2. Definition
  3. Key Differences
  4. Conclusion

Comparison Chart

Basis for ComparisonFirst Law of ThermodynamicsSecond Law of Thermodynamics
Statement
Energy can neither be created nor be destroyed.
The entropy (degree of disorders) of an isolated system never decreases instead always increases.
Expression
ΔE = Q + W, is used for the calculation of the value if any two quantity is known. ΔS = ΔS(system) + ΔS(surrounding) > 0
Expression implies that The change in the internal energy of a system is equal to the sum of the heat flow into the system and work done on the system by the surrounding. The total change in the entropy is the sum of the change examples of the 1st law of thermodynamics the entropy of the system and surrounding which will increase for any real process and cannot be less than 0.
Example
1. Electric bulbs, when lighten converts electric energy into the light energy (radiant energy) and heat energy (thermal energy).
2. Plants convert the sunlight (light or radiant energy) into chemical energy in the process of photosynthesis.
1. The machines convert the highly useful energy like fuels into the less useful energy, which is not equal to the energy taken up while starting the process.
2. The heater in the room uses the electric energy and give out heat to the room, but the room in return can't provide the same energy to the heater.

Definition of First Law of Thermodynamics

The first law of thermodynamics state that ‘energy can neither be created nor be destroyed‘ it can only be transformed from one state to another. This is also known as the law of conservation.

There are many examples to explain the above statement, like an electric bulb, which uses electrical energy and converts into the light and heat energy.

All kinds of machines and engines use some or the other kind of fuel in order to perform work and give out different results. Even the living organisms, eat food which gets digest and provides energy to perform different activities.

ΔE = Q + W

It can be expressed by the simple equation as ΔE, which is the change in the internal energy of a system is equal to the sum of heat (Q) that flows across the boundaries of the surrounding and the work is done (W) on the system by the surrounding. But suppose if the heat flow was out the system then the ‘Q’ would be negative, similarly if the work was done was by the system then the ‘W’ would also be negative.

So we can say that the whole process relies on two factors, which are heat and work, and a slight change in these will result in the change in the internal energy of a system. But as we all know that this process is not so spontaneous and is not applicable every time, like energy never spontaneously flow from a lower temperature to the higher temperature.

Definition of Second Law of Thermodynamics

There are several ways to express the second law of thermodynamics, but before then that we need to understand that why the second law was introduced. We think that in the actual process of day to day life the first law of thermodynamics should satisfy, but it is not mandatory.

For example, consider an electric bulb in a room which will cover the electric energy into heat (thermal) and light energy and the room will get lighten, but the reverse is not possible, that if we provide the same amount of light and heat to the bulb, it will convert into the electric energy. Though this explanation does not oppose the first law of thermodynamics, in reality, it is not possible also.

According to the Kelvin-Plancks statement “It is impossible for any device that operates in a cycle, receives heat from a single reservoir and converts it 100% into work, i.e., there is no heat engine that has the thermal efficiency of 100%”.

Even, Clausius said that “it is impossible to construct a device that operates in a cycle and transfer heat from a low-temperature reservoir to a high-temperature reservoir in the absence of external work”.

So from the above statement, it is clear that the Second Law of Thermodynamics explains about the way the energy transformation takes place in a particular direction only, which is not cleared in the first law of thermodynamics.

The Second Law of Thermodynamics also known as Law of Increased Entropy, which says that over time the entropy or degree of disorders in a system will always increase. Thake an example, that why we get more messed up, after starting any work with all the plannings as the work progresses. So, with the increase in time, the disorders or disorganization also increases.

This phenomenon is applicable in every system, that with the use of useful energy, the unusable energy will be given away.

ΔS = ΔS(system) + ΔS(surrounding) > 0

As described earlier, the delS that are the total change in the entropy is the sum of the change in the entropy of the system and surrounding which will increase for any real process and cannot be less than 0.

Key Differences Between First and Second Laws of Thermodynamics

Given below are the essential points to differentiate between First and Second Laws of Thermodynamics:

  1. According to the First Law of Thermodynamics ‘Energy can neither be created nor be destroyed, it can only be transformed from one form to another’. According to the Second Law of Thermodynamics, which do not violate the first law, but says that energy which is transformed from one state to another not always useful and 100% as taken. So it can be stated that ‘ The entropy (degree of disorders) of an isolated system never decreases rather always increases’.
  2. The First Law of Thermodynamics can be expressed as ΔE = Q + W, is used for the calculation of the value, if any two quantity is known, while the Second Law of Thermodynamics can be expressed as ΔS = ΔS(system) + ΔS(surrounding) > 0.
  3. Expressions imply that the change in the internal energy of a system is equal to the sum of the heat flow into the system and work done on the system by the surrounding in the First Law. In the Second Law, the total change in the entropy is the sum of the change in the entropy of the system and surrounding which will increase for any real process and cannot be less than 0.

Conclusion

In this article, we discussed the Thermodynamics, which is not limited to examples of the 1st law of thermodynamics physics or machinery like refrigerators, cars, washing machine but this concept is applicable to everyone’s day to day work. Though here we distinguished the two most confusing Laws of Thermodynamics, as we know there are two more, which are easy to understand and not so contradictory.

Источник: https://biodifferences.com/difference-between-first-and-second-law-of-thermodynamics.html
examples of the 1st law of thermodynamics

Examples of the 1st law of thermodynamics -

Difference Between First and Second Law of Thermodynamics

First_second_law_of_thermodynamics_img

The First Law of the Thermodynamics is related to the conservation of energy, while the Second Law of Thermodynamics argue that some of the thermodynamics processes are impermissible and does not entirely follow the First Law of Thermodynamics.

The word ‘thermodynamics‘ is derived from the Greek words, where “Thermo” means heat and “dynamics” means power. So thermodynamics is the study of energy which exists in various forms like light, heat, electrical and chemical energy.

Thermodynamics is very vital part of the physics and its related field like chemistry, material science, environmental science, etc. Meanwhile ‘Law’ means the system of the rules. Therefore laws of thermodynamics deal with the one of the forms of energy which is heat, their behaviour under different circumstances corresponding to the mechanical work.

Though we know that there are four laws of thermodynamics, starting from the zeroth law, first law, second law and the third law. But the most used are the first and the second laws, hence in this content, we will be discussing and differentiating the first and second laws.

Content: First Vs Second Laws of Thermodynamics

  1. Comparison Chart
  2. Definition
  3. Key Differences
  4. Conclusion

Comparison Chart

Basis for ComparisonFirst Law of ThermodynamicsSecond Law of Thermodynamics
Statement
Energy can neither be created nor be destroyed.
The entropy (degree of disorders) of an isolated system never decreases instead always increases.
Expression
ΔE = Q + W, is used for the calculation of the value if any two quantity is known. ΔS = ΔS(system) + ΔS(surrounding) > 0
Expression implies that The change in the internal energy of a system is equal to the sum of the heat flow into the system and work done on the system by the surrounding. The total change in the entropy is the sum of the change in the entropy of the system and surrounding which will increase for any real process and cannot be less than 0.
Example
1. Electric bulbs, when lighten converts electric energy into the light energy (radiant energy) and heat energy (thermal energy).
2. Plants convert the sunlight (light or radiant energy) into chemical energy in the process of photosynthesis.
1. The machines convert the highly useful energy like fuels into the less useful energy, which is not equal to the energy taken up while starting the process.
2. The heater in the room uses the electric energy and give out heat to the room, but the room in return can't provide the same energy to the heater.

Definition of First Law of Thermodynamics

The first law of thermodynamics state that ‘energy can neither be created nor be destroyed‘ it can only be transformed from one state to another. This is also known as the law of conservation.

There are many examples to explain the above statement, like an electric bulb, which uses electrical energy and converts into the light and heat energy.

All kinds of machines and engines use some or the other kind of fuel in order to perform work and give out different results. Even the living organisms, eat food which gets digest and provides energy to perform different activities.

ΔE = Q + W

It can be expressed by the simple equation as ΔE, which is the change in the internal energy of a system is equal to the sum of heat (Q) that flows across the boundaries of the surrounding and the work is done (W) on the system by the surrounding. But suppose if the heat flow was out the system then the ‘Q’ would be negative, similarly if the work was done was by the system then the ‘W’ would also be negative.

So we can say that the whole process relies on two factors, which are heat and work, and a slight change in these will result in the change in the internal energy of a system. But as we all know that this process is not so spontaneous and is not applicable every time, like energy never spontaneously flow from a lower temperature to the higher temperature.

Definition of Second Law of Thermodynamics

There are several ways to express the second law of thermodynamics, but before then that we need to understand that why the second law was introduced. We think that in the actual process of day to day life the first law of thermodynamics should satisfy, but it is not mandatory.

For example, consider an electric bulb in a room which will cover the electric energy into heat (thermal) and light energy and the room will get lighten, but the reverse is not possible, that if we provide the same amount of light and heat to the bulb, it will convert into the electric energy. Though this explanation does not oppose the first law of thermodynamics, in reality, it is not possible also.

According to the Kelvin-Plancks statement “It is impossible for any device that operates in a cycle, receives heat from a single reservoir and converts it 100% into work, i.e., there is no heat engine that has the thermal efficiency of 100%”.

Even, Clausius said that “it is impossible to construct a device that operates in a cycle and transfer heat from a low-temperature reservoir to a high-temperature reservoir in the absence of external work”.

So from the above statement, it is clear that the Second Law of Thermodynamics explains about the way the energy transformation takes place in a particular direction only, which is not cleared in the first law of thermodynamics.

The Second Law of Thermodynamics also known as Law of Increased Entropy, which says that over time the entropy or degree of disorders in a system will always increase. Thake an example, that why we get more messed up, after starting any work with all the plannings as the work progresses. So, with the increase in time, the disorders or disorganization also increases.

This phenomenon is applicable in every system, that with the use of useful energy, the unusable energy will be given away.

ΔS = ΔS(system) + ΔS(surrounding) > 0

As described earlier, the delS that are the total change in the entropy is the sum of the change in the entropy of the system and surrounding which will increase for any real process and cannot be less than 0.

Key Differences Between First and Second Laws of Thermodynamics

Given below are the essential points to differentiate between First and Second Laws of Thermodynamics:

  1. According to the First Law of Thermodynamics ‘Energy can neither be created nor be destroyed, it can only be transformed from one form to another’. According to the Second Law of Thermodynamics, which do not violate the first law, but says that energy which is transformed from one state to another not always useful and 100% as taken. So it can be stated that ‘ The entropy (degree of disorders) of an isolated system never decreases rather always increases’.
  2. The First Law of Thermodynamics can be expressed as ΔE = Q + W, is used for the calculation of the value, if any two quantity is known, while the Second Law of Thermodynamics can be expressed as ΔS = ΔS(system) + ΔS(surrounding) > 0.
  3. Expressions imply that the change in the internal energy of a system is equal to the sum of the heat flow into the system and work done on the system by the surrounding in the First Law. In the Second Law, the total change in the entropy is the sum of the change in the entropy of the system and surrounding which will increase for any real process and cannot be less than 0.

Conclusion

In this article, we discussed the Thermodynamics, which is not limited to the physics or machinery like refrigerators, cars, washing machine but this concept is applicable to everyone’s day to day work. Though here we distinguished the two most confusing Laws of Thermodynamics, as we know there are two more, which are easy to understand and not so contradictory.

Источник: https://biodifferences.com/difference-between-first-and-second-law-of-thermodynamics.html

1.3 The first two laws of thermodynamics

The natural laws which govern the environment and which are, therefore, of interest to us are the first two laws of thermodynamics. These relate to closed systems. Strictly speaking, the earth is not a closed system as it receives energy from the sun, but it is almost a closed system.

First law of thermodynamics

The First Law states that whenever energy is converted in form, its total quantity remains unchanged. In other words, energy (or matter) can be neither created nor destroyed.

Common and Stagl (2005) use the example of coal-fired electricity generating plant. The coal is heated which produces electricity. A by-product of this process is waste heat that is transported away as cooling water or gases. In addition, various waste gases are emitted into the atmosphere, which cause pollution, such as acid rain.

Second law of thermodynamics

This law states that in a closed system, entropy does not decrease.

Entropy could be described as a measure of the 'disorderedness' of energy. For instance, ordered energy is useful and an example of this is the energy stored in a battery. However, disordered energy is not useful, and an example is the energy dispersed into the environment by a fire.

Entropy is a thermodynamic property of matter and is related to the amount of energy that can be transferred from one system to another in the form of work. For a given system with a fixed amount of energy, the value of the entropy ranges from zero to a maximum. If the entropy is at its maximum, then the amount of work that can be transferred is equal to zero; if the entropy is at zero, then the amount of work that can be transferred is equal to the energy of the system.

During an irreversible process the entropy of a system always increases.

The key points to remember from the above are that, because of these natural laws:

  • increased extraction of minerals by the production process leads to an increase in wastes
  • there is a limit on the substitutability of inputs
  • since production and consumption lead to the dissipation of matter, scarce energy is needed for recycling

The importance of these two laws relates to the use, re-use and recycling of the environment after interactions with the economy.

Let us look more closely at the subject of recycling, as this would seem to offer a chance for the economy to retain the use of scarce resources.

Recycling

There is a hierarchy of resource use that includes recycling. This is referred to as the 3R's - reduce, re-use and recycle. The final and least appealing option after resource use is to dispose of any remaining waste.

There are now many materials which are routinely recycled and re-used. For example, glass bottles have been collected and re-used by a number of drinks companies for many years. In various countries this practice is encouraged by the use of deposit-refund schemes. (Choe and Fraser 1998) Other examples include paper, metal, glass, plastic, textiles, and garden waste.

For instance, in the Netherlands, household waste that can be composted is collected separately from other household waste and is composted by the local authorities. To encourage citizens to participate in this scheme, householders received some free compost soon after the scheme was set up. However, there are clearly costs involved in such a scheme:

  • separate waste bins were provided for the compostable waste
  • information was provided to householders
  • householders use time to separate their waste
  • costs of separate collection and of dealing with the compost

In the Netherlands, chemical household waste is also collected separately, with similar costs involved. There are numerous examples of different economic instruments used to deal with waste at both the household and industry levels. (Choe and Fraser 1998, and Pearce 2005).

There are clearly limits to what resources can be re-used and recycled. These limits are not only dictated by the laws of thermodynamics but also by the costs associated with re-using and recycling many items.

Источник: https://www.soas.ac.uk/cedep-demos/000_P521_EEM_K3736-Demo/unit1/page_09.htm

It is the most important law for analyzing most systems and quantifying how thermal energy is transformed to other forms of energy. It follows perpetual motion machines of the first kind are impossible.

One of the most wonderful properties of the universe is that energy can be transformed from one type to another and transferred from one object to another. Moreover, when transformed from one type to another and transferred from one object to another, the total amount of energy is always the same. It is one of the elementary properties of the universe.

In thermodynamics, the concept of energy is broadened to account for other observed changes. The principle of conservation of energy is extended to include a wide variety of ways systems interact with their surroundings. The only ways the energy of a closed system can be changed are through a transfer of energy by work or by heat. Further, based on the experiments of Joule and others, a fundamental aspect of the energy concept is that energy is conserved. This principle is known as the first law of thermodynamics. The first law of thermodynamics can be written in various forms:

where Eint represents the internal energy of the material, which depends only on the material’s state (temperature, pressure, and volume), Q is the net heat added to the system, and W is the net work done by the system. We must be careful and consistent in following the sign conventions for Q and W. Because W in the equation is the work done by the system, then if work is done on the system, W will be negative, and Eint will increase.

Similarly, Q is positive for heat added to the system, so Q is negative if heat leaves the system. This tells us the following: The internal energy of a system tends to increase if the system absorbs heat or if positive work is done on the system. Conversely, the internal energy tends to decrease if heat is lost by the system or negative work is done on the system. It must be added Q and W are path-dependent, while Eint is path-independent.

The internal energy Eint of a system tends to increase if energy is added as heat Q and tends to decrease if energy is lost as work W is done by the system.

First Law in Terms of Enthalpy dH = dQ + Vdp

The enthalpy is defined to be the sum of the internal energy E plus the product of the pressure p and volume V. In many thermodynamic analyses, the sum of the internal energy U and the product of pressure p and volume V appears. Therefore it is convenient to give the combination a name, enthalpy, and a distinct symbol, H.

H = U + pV

See also: Enthalpy

The first law of thermodynamics in terms of enthalpy shows us why engineers use the enthalpy in thermodynamic cycles (e.g.,, Brayton cycle or Rankine cycle).

The classical form of the law is the following equation:

dU = dQ  – dW

In this equation, dW is equal to dW = pdV and is known as the boundary work.

Boundary Work - pdV Work

Boundary work occurs because the mass of the substance contained within the system boundary causes a force, the pressure times the surface area, to act on the boundary surface and make it move. Boundary work (or pΔV Work) occurs when the volume V of a system changes. It is used for calculating piston displacement work in a closed system. This happens when steam or gas contained in a piston-cylinder device expands against the piston and forces the piston to move.

Since H = U + pV, therefore dH = dU + pdV + Vdp and we substitute dU = dH – pdV – Vdp into the classical form of the law:

dH – pdV – Vdp = dQ – pdV

We obtain the law in terms of enthalpy:

dH = dQ + Vdp

or

dH = TdS + Vdp

In this equation, the term Vdp is a flow process work. This work,  Vdp, is used for open flow systems like a turbine or a pump in which there is a “dp”, i.e., change in pressure. There are no changes in the control volume. As can be seen, this form of the law simplifies the description of energy transfer. At constant pressure, the enthalpy change equals the energy transferred from the environment through heating:

Isobaric process (Vdp = 0):

dH = dQ     →     Q = H2 – H1

At constant entropy, i.e., in isentropic process, the enthalpy change equals the flow process work done on or by the system:

Isentropic process (dQ = 0):

dH = Vdp     →     W = H2 – H1

It is obvious, and it will be very useful in the analysis of both thermodynamic cycles used in power engineering, i.e., in the Brayton and Rankine cycles.

Example: First Law of Thermodynamics and Brayton Cycle

Let assume the ideal Brayton cycle that describes the workings of a constant pressureheat engine. Modern gas turbine engines and airbreathing jet engines also follow the Brayton cycle. This cycle consist of four thermodynamic processes:

  1. first law - example - brayton cycle

    Isentropic compression – ambient air is drawn into the compressor, where it is pressurized (1 → 2). The work required for the compressor is given by WC = H2 – H1.

  2. Isobaric heat addition – the compressed air then runs through a combustion chamber, burning fuel, and air or another medium is heated (2 → 3). It is a constant-pressure process since the chamber is open to flow in and out. The net heat added is given by Qadd = H3 – H2
  3. Isentropic expansion – the heated, pressurized air then expands on a turbine, gives up its energy. The work done by the turbine is given by WT = H4 – H3
  4. Isobaric heat rejection – the residual heat must be rejected to close the cycle. The net heat rejected is given by Qre = H4 – H1

As can be seen, we can describe and calculate (e.g.,, thermodynamic efficiency) such cycles (similarly for Rankine cycle) using enthalpies.

Internal Energy

In thermodynamics, internal energy (also called thermal energy) is defined as the energy associated with microscopic forms of energy. It is an extensive quantity, and it depends on the size of the system or on the amount of substance it contains. The SI unit of internal energy is the joule (J). It is the energy contained within the system, excluding the kinetic energy of motion of the system as a whole and the system’s potential energy. Microscopic forms of energy include those due to the rotation, vibration, translation, and interactions among the molecules of a substance. None of these forms of energy can be measured or evaluated directly. Still, techniques have been developed to evaluate the change in the total sum of all these microscopic forms of energy.

In addition, energy can be stored in the chemical bonds between the atoms that make up the molecules. This energy storage on the atomic level includes energy associated with electron orbital states, nuclear spin, and binding forces in the nucleus.

Microscopic Energy

Internal energy involves energy on a microscopic scale. It may be divided into microscopic potential energy, Upot, and microscopic kinetic energy, Ukin, components:

U = Upot + Ukin

Microscopic Energy - Internal Energywhere the microscopic kinetic energy, Ukin, involves the motion of all the system’s particles regarding the center-of-mass frame. For an ideal monatomic gas, this is just the translational kinetic energy of the linear motion of the atoms. Monoatomic particles do not rotate or vibrate. The kinetic theory of gases well describes the behavior of the system. Kinetic theory is based on the fact that during an elastic collision between a molecule with high kinetic energy and one with low kinetic energy, part of the energy will transfer to the molecule of lower kinetic energy. However, for polyatomic gases, there is rotational and vibrational kinetic energy as well.

The microscopic potential energy, Upot, involves the chemical bonds between the atoms that make up the molecules, binding forces in the nucleus, and the physical force fields within the system (e.g.,, electric or magnetic fields).

There is a significant component of potential energy associated with the intermolecular attractive forces in liquids and solids.

Heat in Thermodynamics

We’ve seen that the internal energy changes with Q, the net heat added to the system, and W, which is the network done by the system. We now examine how the work is done and the heat added to the system during a thermodynamic process depending on the details of how the process takes place.

zeroth-law-of-thermodynamics-heatWhile internal energy refers to the total energy of all the molecules within the object, heat is the amount of energy flowing spontaneously from one body to another due to their temperature difference. Heat is a form of energy, but it is energy in transit. Heat is not a property of a system. However, the transfer of energy as heat occurs at the molecular level due to a temperature difference.

Consider a block of metal at high temperatures that consist of atoms oscillating intensely around their average positions. At low temperatures, the atoms continue to oscillate but with less intensity. If a hotter block of metal is put in contact with a cooler block, the intensely oscillating atoms at the edge of the hotter block give off their kinetic energy to the less oscillating atoms at the edge of the cool block. In this case, there is energy transfer between these two blocks, and heat flows from the hotter to the cooler block by these random vibrations.

In general, when two objects are brought into thermal contact, heat will flow between them until they come into equilibrium with each other.  When a temperature difference does exist, heat flows spontaneously from the warmer system to the colder system. Heat transfer occurs by conduction or by thermal radiation. When the flow of heat stops, they are said to be at the same temperature. They are then said to be in thermal equilibrium.

As with work, the amount of heat transferred depends upon the path and not simply on the initial and final conditions of the system. There are actually many ways to take the gas from state i to state f.

Also, as with work, it is important to distinguish between heat added to a system from its surroundings and heat removed from a system to its surroundings. Q is positive for heat added to the system, so Q is negative if heat leaves the system. Because W in the equation is the work done by the system, then if work is done on the system, W will be negative, and Eint will increase.

The symbol q is sometimes used to indicate the heat added to or removed from a system per unit mass. It equals the total heat (Q) added or removed divided by the mass (m).

Heat Capacity

Table of specific heat capacitiesDifferent substances are affected to different magnitudes by the addition of heat. When a given amount of heat is added to different substances, their temperatures increase by different amounts. This proportionality constant between the heat Q that the object absorbs or loses and the resulting temperature change T of the object is known as the heat capacity C of an object.

C = Q / ΔT

Heat capacity is an extensive property of matter, meaning it is proportional to the size of the system. Heat capacity C has the unit of energy per degree or energy per kelvin. When expressing the same phenomenon as an intensive property, the heat capacity is divided by the amount of substance, mass, or volume. Thus the quantity is independent of the size or extent of the sample.

Specific Heat Capacity

The heat capacity of a substance per unit mass is called the substance’s specific heat capacity (cp). The subscript p indicates that the heat capacity and specific heat capacity apply when the heat is added or removed at constant pressure.

cp = Q / mΔT

Specific Heat Capacity of Ideal Gas

In the Ideal Gas Model, the intensive properties cv and cp are defined for pure, simple compressible substances as partial derivatives of the internal energy u(T, v) and enthalpy h(T, p), respectively:

Specific Heat at Constant Volume and Constant Pressure

where the subscripts v and p denote the variables held fixed during differentiation. The properties cvand cp are referred to as specific heats (or heat capacities). Under certain special conditions, they relate the temperature change of a system to the amount of energy added by heat transfer. Their SI units are J/kg K, or J/mol K. Two specific heats are defined for gases, constant volume (cv), and constant pressure (cp).

Molar specific heats - ideal gasAccording to the first law of thermodynamics, for a constant volume process with a monatomic ideal gas, the molar specific heat will be:

Cv = 3/2R = 12.5 J/mol K

because

U = 3/2nRT

It can be derived that the molar specific heat at constant pressure is:

Cp = Cv + R = 5/2R = 20.8 J/mol K

This Cp is greater than the molar specific heat at constant volume Cv because energy must now be supplied not only to raise the temperature of the gas but also for the gas to do work because, in this case, volume changes.

Latent Heat of Vaporization

Latent heat of vaporization - water at 0.1 MPa, 3 MPa, 16 MPa

In general, when a material changes phase from solid to liquid or from liquid to gas, a certain amount of energy is involved in this change of phase. In the case of liquid to gas phase change, this amount of energy is the enthalpy of vaporization (symbol ∆Hvap; unit: J), also known as the (latent) heat of vaporization or heat of evaporation. Latent heat is the amount of heat added to or removed from a substance to produce a phase change. This energy breaks down the intermolecular attractive forces and must provide the energy necessary to expand the gas (the pΔV work). When latent heat is added, no temperature change occurs. The enthalpy of vaporization is a function of the pressure at which that transformation takes place.

Latent heat of vaporization – water at 0.1 MPa (atmospheric pressure)

hlg = 2257 kJ/kg

Latent heat of vaporization – water at 3 MPa (pressure inside a steam generator)

hlg = 1795 kJ/kg

Latent heat of vaporization – water at 16 MPa (pressure inside a pressurizer)

hlg = 931 kJ/kg

The heat of vaporization diminishes with increasing pressure while the boiling point increases. It vanishes completely at a certain point called the critical point. Above the critical point, the liquid and vapor phases are indistinguishable, and the substance is called a supercritical fluid.

The heat of vaporization is the heat required to completely vaporize a unit of saturated liquid (or condense a unit mass of saturated vapor). It is equal to hlg = hg − hl.

The heat necessary to melt (or freeze) a unit mass at the substance at constant pressure is the heat of fusion and is equal to hsl = hl − hs, where hs is the enthalpy of saturated solid and hl is the enthalpy of saturated liquid.

Phase changes - enthalpy of vaporization

Work in Thermodynamics

In thermodynamics, work performed by a system is the energy transferred by the system to its surroundings. Kinetic energy, potential energy, and internal energy are forms of energy that are properties of a system. Work is a form of energy, but it is energy in transit. A system contains no work. Work is a process done by or on a system. In general, work is defined for mechanical systems as the action of a force on an object through a distance.

W = F . d

where:

W = work (J)

F = force (N)

d = displacement (m)

pΔV Work

pdV Work - Thermodynamics

Pressure-volume work (or pΔV Work) occurs when the volume V of a system changes. The pΔV Work is equal to the area under the process curve plotted on the pressure-volume diagram. It is also known as boundary workBoundary work occurs because the mass of the substance within the system boundary causes a force, the pressure times the surface area, to act on the boundary surface and move it. Boundary work (or pΔVWork) occurs when the volumeVof a system changes. It is used for calculating piston displacement work in a closed system. This happens when steam or gas contained in a piston-cylinder device expands against the piston and forces the piston to move.

Example:

Consider a frictionless piston that is used to provide a constant pressure of 500 kPa in a cylinder containing steam (superheated steam) of a volume of 2 m3  at 500 K.

Calculate the final temperature if 3000 kJ of heat is added.

Solution:

Using steam tables we know, that the specific enthalpy of such steam (500 kPa; 500 K) is about 2912 kJ/kg. Since at this condition, the steam has a density of 2.2 kg/m3, then we know there is about 4.4 kg of steam in the piston at enthalpy of 2912 kJ/kg x 4.4 kg = 12812 kJ.

When we use simply Q = H2 − H1, then the resulting enthalpy of steam will be:

H2 = H1 + Q = 15812 kJ

From steam tables, such superheated steam (15812/4.4 = 3593 kJ/kg) will have a temperature of 828 K (555°C). Since at this enthalpy, the steam has a density of 1.31 kg/m3, it is obvious that it has expanded by about 2.2/1.31 = 1.67 (+67%). Therefore the resulting volume is 2 m3 x 1.67 = 3.34 m3 and ∆V = 3.34 m3 – 2 m3 = 1.34 m3.

The p∆V part of enthalpy, i.e., the work done is:

W = p∆V = 500 000 Pa x 1.34 m3 = 670 kJ

———–

During the volume change, the pressure and temperature may also change. To calculate such processes, we would need to know how pressure varies with volume for the actual process by which the system changes from state i to state f. The first law of thermodynamics and the work can then be expressed as:

Work in Thermodynamics - general formula

Work in Thermodynamics - path dependency

When a thermodynamic system changes from an initial state to a final state, it passes through a series of intermediate states. We call this series of states a path. There are always infinitely many different possibilities for these intermediate states. When they are all equilibrium states, the path can be plotted on a pV-diagram. One of the most important conclusions is that:

The work done by the system depends not only on the initial and final states but also on the intermediate states—that is, on the path.

Q and W are path-dependent, whereas ΔEint is path-independent. As can be seen from the picture (p-V diagram), work is a path-dependent variable. The blue area represents the pΔV Work done by a system from an initial state i to a final state f. Work W is positive because the system’s volume increases. The second process shows that work is greater, and that depends on the path of the process.

Moreover, we can take the system through a series of states forming a closed loop, such i ⇒ f ⇒ i. In this case, the final state is the same as the initial state, but the total work done by the system is not zero. A positive value for work indicates that work is done by the system in its surroundings. A negative value indicates that work is done on the system by its surroundings.

Cyclic process - work

Example: Turbine Specific Work

engineering thermodynamics

A high-pressure stage of steam turbine operates at a steady state with inlet conditions of  6 MPa, t = 275.6°C, x = 1 (point C). Steam leaves this turbine stage at a pressure of 1.15 MPa, 186°C, and x = 0.87 (point D). Calculate the enthalpy difference between these two states. Determine the specific work transfer.

The enthalpy for the state C can be picked directly from steam tables, whereas the enthalpy for the state D must be calculated using vapor quality:

h1, wet = 2785 kJ/kg

h2, wet = h2,s x + (1 – x ) h2,l  = 2782 . 0.87 + (1 – 0.87) . 790 = 2420 + 103 = 2523 kJ/kg

Δh = 262 kJ/kg

Since in adiabatic process dh = dw, Δh = 262 kJ/kg is the turbine-specific work.

Four Special Cases of the First Law of Thermodynamics

The first law of thermodynamics finds application in several special cases:

Adiabatic Process:

An adiabatic process is one in which there is no heat transfer into or out of the system. It occurs very rapidly, or a system is well insulated with no energy transfer as heat occurs between the system and its environment. Therefore dQ = 0 in the first law of thermodynamics, which is then:

dQ = 0, dEint = – dW

Isochoric Process:

An isochoric process is one in which there is no change in volume. An isochoric process is a constant-volume process. When the volume of a thermodynamic system is constant, it does no work in its surroundings. Therefore dW = 0 in the first law of thermodynamics, which is then:

dW = 0, dEint = dQ

In an isochoric process, all the energy added as heat (that is, Q is positive) remains in the system as internal energy increases (increase in temperature).

Cyclic Process:

A process that eventually returns a system to its initial state is called a cyclic process. After a cycle, all the properties have the same value they had at the beginning.

For such a process, the final state is the same as the initial state, so the total internal energy change must be zero. Steam (water) that circulates through a closed cooling loop undergoes a cycle. The first law of thermodynamics is then:

dEint = 0, dQ = dW

Thus, the process’s network must equal the net amount of energy transferred as heat.

Free Expansion:

This is an adiabatic process in which no transfer of heat occurs between the system and its environment, and no work is done on or by the system. These types of adiabatic processes are called free expansion. It is an irreversible process in which a gas expands into an insulated evacuated chamber. It is also called Joule expansion. For an ideal gas, the temperature doesn’t change (see: Joule’s Second Law). However, real gases experience a temperature change during free expansion. In free expansion, Q = W = 0, and the first law requires that:

dEint = 0

A free expansion can not be plotted on a P-V diagram because the process is rapid, not quasistatic. The intermediate states are not equilibrium states, and hence the pressure is not clearly defined.

Источник: https://www.nuclear-power.com/nuclear-engineering/thermodynamics/laws-of-thermodynamics/first-law-of-thermodynamics/

First Law of Thermodynamics: Definition & Example

The laws of thermodynamics are some of the most important laws in all of physics, and understanding how to apply each one of them is a crucial skill for any physics student.

The first law of thermodynamics is essentially a statement of the conservation of energy, but there are many uses for this specific formulation you’ll need to understand if you want to solve problems involving things like heat engines.

Learning what adiabatic, isobaric, isochoric and isothermal processes are, and how to apply the first law of thermodynamics in these situations, helps you mathematically describe the behavior of a thermodynamic system as it evolves in time.

Internal Energy, Work and Heat

The first law of thermodynamics – like the other laws of thermodynamics – requires an understanding of some key terms. The ​internal energy of a system​ is a measure of the total kinetic energy and potential energy of an isolated system of molecules; intuitively, this just quantifies the amount of energy contained in the system.

Thermodynamic work​ is the amount of work a system does on the environment, for example, by the heat-induced expansion of a gas pushing a piston outwards. This is an example of how heat energy in a thermodynamic process can be converted into mechanical energy, and it is the core principle behind the operation of many engines.

In turn, ​heat​ or ​thermal energy​ is the thermodynamic energy transfer between two systems. When two thermodynamic systems are in contact (not separated by an insulator) and are at different temperatures, heat transfer occurs in this way, from the hotter body towards the colder one. All of these three quantities are forms of energy, and so are measured in joules.

The First Law of Thermodynamics

The first law of thermodynamics states that the heat added to the system adds to its internal energy, while the work done by the system reduces the internal energy. In symbols, you use ​∆U​ to denote the change in internal energy, ​Q​ to stand for heat transfer and ​W​ for the work done by the system, and so the first law of thermodynamics is:

∆U = Q - W

The first law of thermodynamics therefore relates the internal energy of the system to two forms of energy transfer that can take place, and as such it’s best thought of as a statement of the law of conservation of energy.

Any changes to the internal energy of the system come from either heat transfer or work done, with heat transfer ​to​ the system and work done ​on​ the system increasing internal energy, and heat transfer ​from​ the system and work done ​by​ it reducing the internal energy. The expression itself is easy to use and understand, but finding valid expressions for the heat transfer and work done to use in the equation can be challenging in some cases.

Example of the First Law of Thermodynamics

Heat engines are a common type of thermodynamic system that can be used to understand the basics of the first law of thermodynamics. Heat engines essentially convert heat transfer into usable work through a four-step process that involves heat being added to a reservoir of gas to increase its pressure, it expanding in volume as a result, the pressure reducing as heat is extracted from the gas and finally the gas being compressed (i.e., reduced in volume) as work is done on it to bring it back into the original state of the system and start the process over again.

This same system is often idealized as a ​Carnot cycle​, in which all of the processes are reversible and involve no change in entropy, with a stage of isothermal (i.e., at the same temperature) expansion, a stage of adiabatic expansion (with no heat transfer), a stage of isothermal compression and a stage of adiabatic compression to bring it back to the original state.

Both of these processes (the idealized Carnot cycle and the heat engine cycle) are usually plotted on a ​PV​ diagram (also called a pressure-volume plot), and these two quantities are related by the ideal gas law, which states:

PV = nRT

Where ​P​ = pressure, ​V​ = volume, ​n​ = the number of moles of the gas, ​R​ = the universal gas constant = 8.314 J mol−1 K−1 and ​T​ = temperature. In combination with the first law of thermodynamics, this law can be used to describe the stages of a heat engine cycle. Another useful expression gives the internal energy ​U​ for an ideal gas:

U = \frac{3}{2}nRT

The Heat Engine Cycle

A simple approach to analyzing the heat engine cycle is to imagine the process taking place on a straight-sided box in the ​PV​ plot, with each stage either taking place at a constant pressure (an isobaric process) or a constant volume (an isochoric process).

First, starting from ​V1, heat is added and the pressure rises from ​P1 to ​P2, and since the volume remains constant, you know that the work done is zero. To tackle this stage of the problem, you make two versions of the ideal gas law for the first and second state (remembering that ​V​ and ​n​ are constant): ​P1V1 = ​nRT1 and ​P2V1 = ​nRT2, and then subtract the first from the second to get:

V_1 (P_2-P_1) = nR (T_2 -T_1)

Solving for the change in temperature gives:

(T_2 - T_1) = \frac{ V_1 (P_2 - P_1)}{nR}

If you look for the change in internal energy, you can then insert this into the expression for internal energy ​U​ to get:

\begin{aligned} ∆U &= \frac{3}{2}nR∆T \\ \\ &=\frac{3}{2} nR \bigg(\frac{ V_1 (P_2 - P_1)}{nR}\bigg) \\ \\ &=\frac{3}{2} V_1 (P_2 -P_1) \end{aligned}

For the second stage in the cycle, the volume of the gas expands (and so the gas does work) and more heat is added in the process (to maintain a constant temperature). In this case, the work ​W​ done by the gas is simply the change in volume multiplied by the pressure ​P2, which gives:

W = P_2 (V_2 -V_1)

And the change in temperature is found with the ideal gas law, as before (except keeping ​P2 as a constant and remembering that the volume changes), to be:

T_2 - T_1 = \frac{ P_2 (V_2 - V_1)}{nR}

If you want to find out the exact amount of heat added, you can use the specific heat equation at a constant pressure to find it. However, you can directly calculate the internal energy of the system at this point as before:

\begin{aligned} ∆U &= \frac{3}{2}nR∆T \\ \\ &=\frac{3}{2}nR\bigg(\frac{ P_2 (V_2 – V_1)}{nR}\bigg) \\ \\ &=\frac{3}{2} P_2 (V_2 – V_1) \end{aligned}

The third stage is essentially the reverse of the first stage, so the pressure decreases at a constant volume (this time ​V2), and heat is extracted from the gas. You can work through the same process based on the ideal gas law and the equation for the internal energy of the system to get:

∆U = -\frac{3}{2} V_2 (P_2 - P_1)

Note the leading minus sign this time because the temperature (and therefore the energy) has decreased.

Finally, the last stage sees the volume decrease as work is done on the gas and heat extracted in an isobaric process, producing a very similar expression to last time for the work, except with a leading minus sign:

W = -P_1 (V_2 -V_1)

The same calculation gives the change in internal energy as:

∆U = -\frac{3}{2} P_1 (V_2 - V_1)

Other Laws of Thermodynamics

Источник: https://sciencing.com/first-law-of-thermodynamics-definition-example-13722772.html

What Is the First Law of Thermodynamics?

The First Law of Thermodynamics states that heat is a form of energy, and thermodynamic processes are therefore subject to the principle of conservation of energy. This means that heat energy cannot be created or destroyed. It can, however, be transferred from one location to another and converted to and from other forms of energy. 

Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. In particular, it describes how thermal energy is converted to and from other forms of energy and how it affects matter. The fundamental principles of thermodynamics are expressed in four laws.

“The First Law says that the internal energy of a system has to be equal to the work that is being done on the system, plus or minus the heat that flows in or out of the system and any other work that is done on the system," said Saibal Mitra, a professor of physics at Missouri State University. "So, it’s a restatement of conservation of energy." 

Mitra continued, "The change in internal energy of a system is the sum of all the energy inputs and outputs to and from the system similarly to how all the deposits and withdrawals you make determine the changes in your bank balance.” This is expressed mathematically as: ΔU = Q – W, where ΔU is the change in the internal energy, Q is the heat added to the system, and W is the work done by the system. 

History

Scientists in the late 18th and early 19th centuries adhered to caloric theory, first proposed by Antoine Lavoisier in 1783, and further bolstered by the work of Sadi Carnot in 1824, according to the American Physical Society. Caloric theory treated heat as a kind of fluid that naturally flowed from hot to cold regions, much as water flows from high to low places. When this caloric fluid flowed from a hot to a cold region, it could be converted to kinetic energy and made to do work much as falling water could drive a water wheel. It wasn’t until Rudolph Clausius published "The Mechanical Theory of Heat" in 1879 that caloric theory was finally put to rest. 

Thermodynamic systems

Energy can be divided into two parts, according to David McKee, a professor of physics at Missouri Southern State University. One is our human-scale macroscopic contribution, such as a piston moving and pushing on a system of gas. Conversely, things happen at a very tiny scale where we can’t keep track of the individual contributions. 

McKee explains, “When I put two samples of metal up against each other, and the atoms are rattling around at the boundary, and two atoms bounce into each other, and one of the comes off faster than the other, I can’t keep track of it. It happens on a very small time scale and a very small distance, and it happens many, many times per second. So, we just divide all energy transfer into two groups: the stuff we’re going to keep track of, and the stuff we’re not going to keep track of. The latter of these is what we call heat.”

Thermodynamic systems are generally regarded as being open, closed or isolated. According to the University of California, Davis, an open system freely exchanges energy and matter with its surroundings; a closed system exchanges energy but not matter with its surroundings; and an isolated system does not exchange energy or matter with its surroundings. For example, a pot of boiling soup receives energy from the stove, radiates heat from the pan, and emits matter in the form of steam, which also carries away heat energy. This would be an open system. If we put a tight lid on the pot, it would still radiate heat energy, but it would no longer emit matter in the form of steam. This would be a closed system. However, if we were to pour the soup into a perfectly insulated thermos bottle and seal the lid, there would be no energy or matter going into or out of the system. This would be an isolated system. 

In practice, however, perfectly isolated systems cannot exist. All systems transfer energy to their environment through radiation no matter how well insulated they are. The soup in the thermos will only stay hot for a few hours and will reach room temperature by the following day. In another example, white dwarf stars, the hot remnants of burned-out stars that no longer produce energy, can be insulated by light-years of near perfect vacuum in interstellar space, yet they will eventually cool down from several tens of thousands of degrees to near absolute zero due to energy loss through radiation. Although this process takes longer than the present age of the universe, there’s no stopping it.

Heat engines

The most common practical application of the First Law is the heat engine. Heat engines convert thermal energy into mechanical energy and vice versa. Most heat engines fall into the category of open systems. The basic principle of a heat engine exploits the relationships among heat, volume and pressure of a working fluid. This fluid is typically a gas, but in some cases it may undergo phase changes from gas to liquid and back to a gas during a cycle. 

When gas is heated, it expands; however, when that gas is confined, it increases in pressure. If the bottom wall of the confinement chamber is the top of a movable piston, this pressure exerts a force on the surface of the piston causing it to move downward. This movement can then be harnessed to do work equal to the total force applied to the top of the piston times the distance that the piston moves. 

There are numerous variations on the basic heat engine. For instance, steam engines rely on external combustion to heat a boiler tank containing the working fluid, typically water. The water is converted to steam, and the pressure is then used to drive a piston that converts heat energy to mechanical energy. Automobile engines, however, use internal combustion, where liquid fuel is vaporized, mixed with air and ignited inside a cylinder above a movable piston driving it downward. 

Refrigerators, air conditioners and heat pumps

Refrigerators and heat pumps are heat engines that convert mechanical energy to heat. Most of these fall into the category of closed systems. When a gas is compressed, its temperature increases. This hot gas can then transfer heat to its surrounding environment. Then, when the compressed gas is allowed to expand, its temperature becomes colder than it was before it was compressed because some of its heat energy was removed during the hot cycle. This cold gas can then absorb heat energy from its environment. This is the working principal behind an air conditioner. Air conditioners don’t actually produce cold; they remove heat. The working fluid is transferred outdoors by a mechanical pump where it is heated by compression. Next, it transfers that heat to the outdoor environment, usually through an air-cooled heat exchanger. Then, it is brought back indoors, where it is allowed to expand and cool so it can absorb heat from the indoor air through another heat exchanger. 

A heat pump is simply an air conditioner run in reverse. The heat from the compressed working fluid is used to warm the building. It is then transferred outside where it expands and becomes cold, thereby allowing it to absorb heat from the outside air, which even in winter is usually warmer than the cold working fluid. 

Geothermal or ground-source air conditioning and heat pump systems use long U-shaped tubes in deep wells or an array of horizontal tubes buried in a large area through which the working fluid is circulated, and heat is transferred to or from the earth. Other systems use rivers or ocean water to heat or cool the working fluid. 

Additional resources

Here are three other explanations of the First Law of Thermodynamics:

Jim Lucas is a contributing writer for Live Science. He covers physics, astronomy and engineering. Jim graduated from Missouri State University, where he earned a bachelor of science degree in physics with minors in astronomy and technical writing. After graduation he worked at Los Alamos National Laboratory as a network systems administrator, a technical writer-editor and a nuclear security specialist. In addition to writing, he edits scientific journal articles in a variety of topical areas.
Источник: https://www.livescience.com/50881-first-law-thermodynamics.html

First Law of Thermodynamics for an open system


In this video we will learn first law of thermodynamics in a practical way.


A detailed webpage version of the video is given below.


Applications of first law of Thermodynamics

First law of thermodynamics when it is applied to an open system has got tremendous applications all across industries. Using this law you can predict how much is the pressure drop across the nozzle, or how much is the energy required by the pump to pump the fluid out, or what is the heat transfer in heat exchanger, or what is the amount of work produced by the turbine.

In a nutshell first law simply means conservation of energy, or it states that energy is getting transformed from one form to another form.

First law for closed system

We will understand how first law is applied for a thermodynamic system by analyzing a simple example, an example of piston cylinder arrangement. Here the cylinder has got some gas inside it. Assume there is no air leakage to the surrounding. So this is an example of closed system where mass does not change. Assume the gas is absorbing some heat Q from the surrounding; also assume that this gas is able to push the piston upwards due to high pressure of gas. So the gas is doing some work on the piston with quantity W.

So there are 2 energy interactions to the gas, it will increase by a quantity Q, because it is absorbing energy. And it will decrease by a quantity W since it is losing energy by doing some work. So you can write change in energy (E) of gas as follows.

ΔE = Q - W

This is first law of thermodynamics for a closed system. Same equation you can write in differential form as follows. It is in form of rate of change of quantities per unit time.

dE / dt = Q - W

First law for an open system

Now we are going to open the system, or open the cylinder as shown below.

The system is no more closed now, it’s an open system. The mass is continuously varying. It can have an inlet mass flow rate at particular pressure and particular velocity. Similarly there will be exit flow rate of particular pressure and velocity. Here also our objective is the same. We want to find out energy change of the gas or the system. But here it is not possible to pin point a particular quantity of gas. The gas is continuously flowing. So before proceeding to the energy change calculation, we have to define a system first, a control volume where you will do energy balance.

Here the dotted line represents the control volume, or the space at which we will do energy balance. Here you can see there are 4 energy interactions to the system. 2 energy interactions which are coming to the system and another 2 energy interactions which leave the system. So if you want to find out energy change in system you should add energy transfer due to heat flow and inlet mass flow and subtract energy transfer due to work done and exit mass flow. So for an open system change in energy will be as follows.

Note that the flow stream has got 3 components of energy. Internal energy, kinetic energy and potential energy. Z represents the altitude of flow stream. This equation is the first law of thermodynamics for an open system.

Concept of flow work and enthalpy – More useful form of first law

But for an open system the term W, work done by the gas should be carefully examined. Here the gas is doing work to push the cylinder up, plus it is doing work to suck the fluid in or eject the fluid out. Or to maintain the flow gas has to do some work. This kind of work, the work which is required to maintain the flow is known as flow work. So the total work done by the system will be summation of visible work and flow work.

W = W cv + Flow work

Wcv represents the visible work, in this case the work done by the gas on the piston. And we know flow work is the work required to eject the fluid out or suck the fluid out. The work required to eject the fluid out will be force at exit portion multiplied by velocity of this stream. Force is same as pressure at that portion times area. So we can represent flow work like this.

W = Wcv + (P2A2)V2 - (P1A1)V1

If you do some rearrangement to the equation by substituting volumetric flow rate as mass flow rate into specific volume, by representing u+Pv as a new property enthalpy,

h = u+Pv

the above equation will be simplified like this.

This is the final and most useful form of first law of thermodynamics for an open system.

One application of first law

We will work out one interesting example using firs law equation in this section. A pump problem, where fluid is getting pumped from point 1 to point 2.

We want to find out what’s the energy required by the pump to perform this action. To find out that we will use equation derived for first law of thermodynamics for an open system.We can assume the pump operation is in steady state. So energy of the pump does not change with time. So you can put first term in equation as zero. And usually there will not be any heat transfer to the pump. So you can put that term also as zero.

If cross sectional areas of point 1 and point 2 are equal, then velocities will be equal, so from this equation velocity part also get cancelled out. You can also assume height difference between inlet and outlets are negligible. So the altitude term also gets cancelled out. And finally what remains is this.

Wcv = m1(h11 - h2)

Work done by the control volume is mass flow rate times change in enthalpy. If you want work done on control volume or energy required by the pump, you have to just reverse the sign.

Wpump = m1(h1 - h2)

Using the same approach you can solve lot of other energy transfer problems in industries.



ABOUT THE AUTHOR



This article is written by Sabin Mathew, an IIT Delhi postgraduate in mechanical engineering. Sabin is passionate about understanding the physics behind complex technologies and explaining them in simple words. He is the founder of Learn Engineering educational platform. To know more about the author check this link


Источник: https://www.lesics.com/first-law-of-thermodynamics-for-an-open-system.html

1 Replies to “Examples of the 1st law of thermodynamics”

  1. That is why we glorify liberal democracy. The power of money not people power. We elect people that will be bought by money, money money.

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