Show that the statistical definition of the internal energy (U = E, E,p;) and the entropy (S = -k E;p; In(e;)), where (p;) is the Boltzmann distribution, are consistent with the differential form of the fundamental equation of thermodynamics (dU = T'dS - PdV).

Show that the statistical definition of the internal energy (U = E, E,p;) and the entropy (S = -k E;p; In(e;)), where (p;) is the Boltzmann distribution, are consistent with the differential form of the fundamental equation of thermodynamics (dU = T'dS - PdV).

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter2: The First Law Of Thermodynamics

Section: Chapter Questions

Problem 2.92E

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Question

Show that the statistical definition of the internal energy (U = E; E;p;) and the entropy
(S = -k E,p; In(p)), where (p,) is the Boltzmann distribution, are consistent with the
differential form of the fundamental equation of thermodynamics (dU = Tds – PdV).

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