Clausius s formula

Here we will prove a stronger version of Boltzmann s //-theorem, which holds for more general gas-wall interactions and which gives a nonequilibrium analog of Clausius s formula... 

To obtain the analog of Clausius s formula from the Boltzmann equation we will impose an additional condition on the interactions of the gas molecules with the walls. We will assume that there exists a local temperature of the wall t wCp ) at every point p such that if the distribution of molecules incident on the surface at p, is a Maxwell-Boltzmann distribution with temperature T (ps), then the distribution of the reflected molecules is also a Maxwell-Boltzmann distribution with the same temperature. Using Eq. (33) we may express this thermostat condition as a condition on K w, v ) as... 

Entropy Change Clausius s View—Clausius, using macroscopic observations, proposed that the entropy change for a process can be related to the amount of heat transferred divided by the temperature (equation 13.2), provided the process is imagined to occur in a reversible way Consequently, an entropy change, AS, has the unit J Clausius s formula can be used to obtain expres-... 

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