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stem in part (a) is re have an ensemble

stem in part (a) is re have an ensemble

Chemistry
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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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.
Transcribed Image Text: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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