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(a) Given that U – U(0) = kT² (d), (where U(0) is the internal energy at T = 0), derive mathematically, step-by-step the expression of the entropy S(T) in terms of the canonical partition function Q, without making use for the Helmholtz energy, A, relation A(T) - A(0) = -kTINQ. (b) Express the total canonical partition function of an ideal diatomic gas of N molecules, in terms of the different molecular partition functions contributing to its value. (c) For a pure substance (i.e., a one component system) in the absence of any non- expansion work, justify mathematically why and how the variation of chemical potential with temperature is directly related to the molar entropy Sm of the substance.

(a) Given that U – U(0) = kT² (d), (where U(0) is the internal energy at T = 0), derive mathematically, step-by-step the expression of the entropy S(T) in terms of the canonical partition function Q, without making use for the Helmholtz energy, A, relation A(T) - A(0) = -kTINQ. (b) Express the total canonical partition function of an ideal diatomic gas of N molecules, in terms of the different molecular partition functions contributing to its value. (c) For a pure substance (i.e., a one component system) in the absence of any non- expansion work, justify mathematically why and how the variation of chemical potential with temperature is directly related to the molar entropy Sm of the substance.

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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Please complete all the following parts of the question thank you and provide reasonings and which equations and why were they used. THANK YOU

(a) Given that U - U(0) = kT² (¹), (where U(0) is the internal energy at T = 0), derive ƏT mathematically, step-by-step the expression of the entropy S(T) in terms of the canonical partition function Q, without making use for the Helmholtz energy, A, relation A(T) - A(0) = -kTlnQ. (b) Express the total canonical partition function of an ideal diatomic gas of N molecules, in terms of the different molecular partition functions contributing to its value. (c) For a pure substance (i.e., a one component system) in the absence of any non- expansion work, justify mathematically why and how the variation of chemical potential with temperature is directly related to the molar entropy Sm of the substance.
Transcribed Image Text:(a) Given that U - U(0) = kT² (¹), (where U(0) is the internal energy at T = 0), derive ƏT mathematically, step-by-step the expression of the entropy S(T) in terms of the canonical partition function Q, without making use for the Helmholtz energy, A, relation A(T) - A(0) = -kTlnQ. (b) Express the total canonical partition function of an ideal diatomic gas of N molecules, in terms of the different molecular partition functions contributing to its value. (c) For a pure substance (i.e., a one component system) in the absence of any non- expansion work, justify mathematically why and how the variation of chemical potential with temperature is directly related to the molar entropy Sm of the substance.
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