QUESTIONS 1. (20/20) The canonical partition function for a system of N two-level impurities in a solid matrix is obtain

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Questions 1 20 20 The Canonical Partition Function For A System Of N Two Level Impurities In A Solid Matrix Is Obtain 1 (61.52 KiB) Viewed 79 times

QUESTIONS 1. (20/20) The canonical partition function for a system of N two-level impurities in a solid matrix is obtained as Z(N,T) = = (1+e-Be)" where e is the energy of the excited level, with the ground-state energy assumed to be zero. (a) Calculate the Helmholtz free energy F = -kgt InZ (b) Calculate the entropy of the system OFI S = OT N (c) Calculate the internal energy of the system alnZ E =- ap (d) Assume the energy of the system to be NE E 2 Calculate the entropy of the system in this case. Repeat the calculation for 3N E- 4 Compare the two results and comment on them. (e) The occupation probabilities of the two energy levels are given by p(n) = e-Beni 1+e-Be where n; takes the values 0 and 1 for the ground and the excited state, respectively. Calculate the occupational probabilities of the two levels for the two values of the internal energy given in (d).