Thermodynamics, Classical and Statistical
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The most important conception in thermodynamics is temperature. The essential properties of temperature will be described below. Anticipating this we may define thermodynamics as that part of physics concerned with the dependence on temperature of any equilibrium property. This definition may be illustrated by a simple example. Consider the distribution of two immiscible liquids such as mercury and water in a gravitational field. The equilibrium distribution is that in which the heavier liquid, mercury, occupies the part of accessible space where the gravitational potential is lowest and the lighter liquid, water, occupies the part of the remaining accessible space where the gravitational potential is lowest. This equilibrium distribution is, apart from the effect of thermal expansion which we neglect, independent of temperature. Consequently the problem does not involve thermodynamics, but only hydrostatics. Now consider by contrast the distribution in a gravitational field of two completely miscible fluids such as bromine and carbon disulphide. The relative proportions of the two substances will vary from place to place, the proportion of the heavier liquid, bromine, being greatest at the lowest gravitational potential and conversely. The precise relation between the composition and the gravitational potential depends on the temperature, assumed uniform, of the mixture. Clearly this is a problem in thermodynamics, not merely hydrostatics.
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- 1.For a simple clear account of this derivation see R. Eisenschitz: Sci. Progr. 170, 246 (1955).Google Scholar
- 1.Figs. 1–4 after E.A.Guggenheim: Thermodynamics, North Holland Publishing Company, Amsterdam 1950.Google Scholar
- 1.The present approach follows closely that of Tolman. The author is grateful to the Clarendon Press for permission to borrow freely from the text of “The Principles of Statistical Mechanics” by Tolman, parts of which have been taken over almost verbatim in Sects. 58 and 59.Google Scholar
- 1.In the previous chapter Q A denoted the partition function of a system A. Here Q A denotes the partition function of a molecule A. It should always be clear from the context whether A denotes a system or a molecule.Google Scholar
- 2.R. H. Fowler: Statistical Mechanics, p. 62. Cambridge 1936.Google Scholar