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Thermodynamic operation

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Thermodynamic operation

A thermodynamic operation is a manipulation or externally imposed change of connection or wall between thermodynamic systems, real or imagined.[1][2][3][4]

A thermodynamic operation requires a contribution from an animate agency, or at least an agency that does not come from the passive properties of the systems. Perhaps the first expression of the distinction between a thermodynamic operation and a thermodynamic process is in Kelvin's statement of the second law of thermodynamics: "It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the surrounding objects." A sequence of events that occurred other than "by means of inanimate material agency" would entail an action by an animate agency. Such an agency could impose some thermodynamic operations. They might create a heat pump, which of course would comply with the law, taking its operation into account. A Maxwell's demon conducts an extreme kind of thermodynamic operation.[5]

Distinction between thermodynamic operation and thermodynamic process

A typical thermodynamic operation is a removal of an initially separating wall, a manipulation that unites two systems into one undivided system. A typical thermodynamic process consists of a redistribution of a conserved quantity between a system and its surroundings across an unchanging semi-permeable wall between them.[6] More generally, a process can be considered as a transfer of some quantity that is defined by an extensive state variable of the system, so that a transfer balance equation can be written.[7] As a small historical point, Kelvin spoke of a thermodynamic operation when he meant what in this article is called a thermodynamic operation followed by a thermodynamic process.[8] According to Uffink, "... thermodynamic processes only take place after an external intervention on the system (such as: removing a partition, establishing thermal contact with a heat bath, pushing a piston, etc.). They do not correspond to the autonomous behaviour of a free system."[9]

Natural processes contrasted with actions of Maxwell's demon

Planck held that all natural thermodynamic processes are irreversible and proceed in the sense of increase of entropy sum.[10] In these terms, it would be by thermodynamic operations that, if he could exist, Maxwell's demon would conduct unnatural affairs, which include transitions in the sense away from thermodynamic equilibrium. They are physically theoretically conceivable up to a point, but are not natural processes.

Examples of thermodynamic operations

Thermodynamic cycle

A thermodynamic cycle is constructed as a sequence of stages or steps. Each stage consists of a thermodynamic operation followed by a thermodynamic process. For example, an initial thermodynamic operation of a cycle of a Carnot heat engine could be taken as the setting of the working body, at a known high temperature, into contact with a thermal reservoir at the same temperature (the hot reservoir), through a wall permeable only to heat, while it remains in mechanical contact with the work reservoir. This thermodynamic operation is followed by a thermodynamic process, in which the expansion of the working body is so slow as to be effectively reversible, while internal energy is transferred as heat from the hot reservoir to the working body and as work from the working body to the work reservoir. Theoretically, the process terminates eventually, and this ends the stage. The engine is then subject to another thermodynamic operation, and the cycle proceeds into another stage. The cycle completes when the thermodynamic variables (the thermodynamic state) of the working body return to their initial values.

Virtual thermodynamic operations

A refrigeration device passes a working substance through successive stages, overall constituting a cycle. This may be brought about not by moving or changing separating walls around an unmoving body of working substance, but rather by moving a body of working substance to bring about exposure to a cyclic succession of unmoving unchanging walls. The effect is virtually a cycle of thermodynamic operations. The kinetic energy of bulk motion of the working substance is not a significant feature of the device, and the working substance may be practically considered as nearly at rest.

Composition of systems

For many chains of reasoning in thermodynamics, it is convenient to think of the combination of two systems into one. It is imagined that the two systems, separated from their surroundings, are juxtaposed and (by a shift of viewpoint) regarded as constituting a new, composite system. The composite system is imagined amid its new overall surroundings. This sets up the possibility of interaction between the two subsystems and between the composite system and its overall surroundings, for example by allowing contact through a wall with a particular kind of permeability. This conceptual device was introduced into thermodynamics mainly in the work of Carathéodory, and has been widely used since then.[2][3][11][12][13][14]

Scaling of a system

A thermodynamic system consisting of a single phase, in the absence of external forces, in its own state of internal thermodynamic equilibrium, is homogeneous.[15] This means that the material in any region of the system can be interchanged with the material of any congruent and parallel region of the system, and the effect is to leave the system thermodynamically unchanged. The thermodynamic operation of scaling is the creation of a new homogeneous system whose size is a multiple of the old size, and whose intensive variables have the same values. Traditionally the size is stated by the mass of the system, but sometimes it is stated by the entropy, or by the volume.[16][17][18][19] For a given such system Φ, scaled by the real number λ to yield a new one λΦ, a state variable X(.) such that X(λΦ) = λ X(Φ) is said to be extensive. Such a function X is called a homogeneous function of degree 1 (the power-law homogeneity in the scaling direction is not related to the spatial homogeneity of the system).

Statements of laws

Thermodynamic operations appear in the statements of the laws of thermodynamics. For the zeroth law, one considers operations of thermally connecting and disconnecting systems. For the second law, some statements contemplate an operation of connecting two initially unconnected systems. For the third law, one statement is that no sequence of thermodynamic operations can bring a system to absolute zero temperature.

References

1. ^ Tisza, L. (1966), pp. 41, 109, 121, originally published as 'The thermodynamics of phase equilibrium', Annals of Physics, 13: 1–92.
2. ^ a b Giles, R. (1964), p. 22.
3. ^ a b Lieb, E.H., Yngvason, J. (1999). The physics and mathematics of the second law of thermodynamics, Physics Reports, 314: 1–96, p. 14.
4. ^ Callen, H.B.(1960/1985), p. 15.
5. ^ Bailyn, M. (1994), pp. 88, 100.
6. ^ Tisza, L. (1966), p. 47.
7. ^ Gyarmati, I. (1970), p. 18.
8. ^ Kelvin, Lord (1857). On the alteration of temperature accompanying changes of pressure in fluids, , JuneProc. Roy. Soc..
9. ^ Uffink, J. (2001). Bluff your way in the second law of thermodynamics, Stud. Hist. Phil. Mod. Phys., 32(3): 305–394, publisher Elsevier Science.
10. ^ Guggenheim, A.E. (1949/1967), p. 12.
11. ^ Tisza, L. (1966), pp. 41, 50, 121.
12. ^ Carathéodory, C. (1909).
13. ^ Planck, M. (1935). Bemerkungen über Quantitätsparameter, Intenstitätsparameter und stabiles Gleichgewicht, Physica, 2: 1029–1032.
14. ^ Callen, H.B. (1960/1985), p. 18.
15. ^ Planck, M. (1897/1903), p. 3.
16. ^ Landsberg, P.T. (1961), pp. 129–130.
17. ^ Tisza, L., (1966), p. 45.
18. ^ Haase, R. (1971), p. 3.
19. ^ Callen, H.B. (1960/1985), pp. 28–29.

Bibliography for citations

• Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of Physics Press, New York, ISBN 0-88318-797-3.
• Callen, H.B. (1960/1985). Thermodynamics and an Introduction to Thermostatistics, (1st edition 1960) 2nd edition 1985, Wiley, New York, ISBN 0-471-86256-8.
• A translation may be found here. Also a mostly reliable translation is to be found at Kestin, J. (1976). The Second Law of Thermodynamics, Dowden, Hutchinson & Ross, Stroudsburg PA..
• Giles, R. (1964). Mathematical Foundations of Thermodynamics, Macmillan, New York.
• Guggenheim, E.A. (1949/1967). Thermodynamics. An Advanced Treatment for Chemists and Physicists, fifth revised edition, North-Holland, Amsterdam.
• Gyarmati, I. (1967/1970). Non-equilibrium Thermodynamics. Field Theory and Variational Principles, translated from the 1967 Hungarian by E. Gyarmati and W.F. Heinz, Springer-Verlag, New York.
• Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of Thermodynamics, pages 1–97 of volume 1, ed. W. Jost, of Physical Chemistry. An Advanced Treatise, ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.
• Landsberg, P.T. (1961). Thermodynamics with Quantum Statistical Illustrations, Interscience, New York.
• Planck, M., (1897/1903). Treatise on Thermodynamics, translated by A. Ogg, Longmans, Green, & Co., London.
• Tisza, L. (1966). Generalized Thermodynamics, M.I.T Press, Cambridge MA.
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