# Thermodynamic operation

A thermodynamic operation is a theoretical conceptual device for the expression of reasoning about systems and processes in thermodynamics. It means that an intentional or wilful or animate operator imposes a manipulation or change of constraint that unites or subdivides systems, or of the type of enclosure or partition or wall between systems.[1][2][3][4]

A thermodynamic operation requires a contribution from an animate operator. 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. The statement requires that the process of transfer be "by means of inanimate material agency": the process must not include a thermodynamic operation. If a process were other than "by means of inanimate material agency", it might easily include a thermodynamic operation. Then the application of the second law would have to be indirect, because the operation might have the effect of creating a heat pump, so that one is no longer looking at a purely spontaneous or natural thermodynamic process. 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]

### Natural processes contrasted with actions of Maxwell's demon

Planck held that all natural thermodynamic processes are irreversible and proceed in the sense towards thermodynamic equilibrium.[9] 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.

### 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 the main 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 composition of two systems into one. It is imagined that the two systems, separated from their surroundings, are put together and regarded as subsystems of a new composite system. The composite system may be imagined to be given its new overall surroundings. With this, there may be set up the possibility of interactions between the subsystems and between the composite system and its overall surroundings, such as by putting them in 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][10][11][12][13]

### 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.[14] This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent and parallel volume element of the system, and the effect is to leave the system thermodynamically unchanged. The thermodynamic operation of scaling is the creation of a new such system from an old one, the size of the new system being a real scalar multiple of that of the old one, the intensive variables of the new system being the same as those of the old one. Traditionally the size is stated by the mass of the system, but sometimes it is stated by the entropy, or by the volume.[15][16][17][18] 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. Mathematically, the function that yields the variable is said to be a mathematically homogeneous function of the first degree, a comfortable coincidence with the physical thermodynamic homogeneity of such systems.

## 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, Proc. Roy. Soc., June.
9. ^ Guggenheim, A.E. (1949/1967), p. 12.
10. ^ Tisza, L. (1966), pp. 41, 50, 121.
11. ^ Carathéodory, C. (1909).
12. ^ Planck, M. (1935). Bemerkungen über Quantitätsparameter, Intenstitätsparameter und stabiles Gleichgewicht, Physica, 2: 1029–1032.
13. ^ Callen, H.B. (1960/1985), p. 18.
14. ^ Planck, M. (1897/1903), p. 3.
15. ^ Landsberg, P.T. (1961), pp. 129–130.
16. ^ Tisza, L., (1966), p. 45.
17. ^ Haase, R. (1971), p. 3.
18. ^ 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.
• Carathéorory, C. (1909). "Untersuchungen über die Grundlagen der Thermodynamik". Mathematische Annalen 67: 355–386. doi:10.1007/BF01450409. 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.