specific.3- a) Show that the entropy of the system in the grand canonical ensemble can be written as S =-kE, P,lnP,.b) Assuming that the total number of microstates accessible to a given statistical system is N, showthat the entropy of the system in part (a) is maximum when all n states are equally likely to occur.c) If, on the other hand, we have an ensemble of systems sharing energy (with mean value E), thenshow that the entropy, as given by the same formal expression, is maximum when P, oxe-BEr, Bbeing a constant to be determined by the given value of E.d) Further, if we have an ensemble of systems sharing energy (with mean valueË) and also sharingparticles (with mean value N), then show that the entropy, given by a similar expression, ismaximum when Ps xe-aNr-BEs, a and B being constants to be determined by the given valuesof N and E.

Answered: stem in part (a) is re have an ensemble

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stem in part (a) is re have an ensemble

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

specific.
3- a) Show that the entropy of the system in the grand canonical ensemble can be written as S =
-kE, P,lnP,.
b) Assuming that the total number of microstates accessible to a given statistical system is N, show
that the entropy of the system in part (a) is maximum when all n states are equally likely to occur.
c) If, on the other hand, we have an ensemble of systems sharing energy (with mean value E), then
show that the entropy, as given by the same formal expression, is maximum when P, oxe-BEr, B
being a constant to be determined by the given value of E.
d) Further, if we have an ensemble of systems sharing energy (with mean valueË) and also sharing
particles (with mean value N), then show that the entropy, given by a similar expression, is
maximum when Ps xe-aNr-BEs, a and B being constants to be determined by the given values
of N and E.

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