Partition Function and Heat Capacity of Two-State Particles

Question:
Consider a system of N distinguishable independent particles, each of which can be in the state +ε0 or −ε0 . Let the number of particles with energy ±ε0 be N± , so that the energy is,

Evaluate the partition function Q by summing exp(−E/kT ) over levels and compare your result to Q = qN . Do not forget the degeneracy of the levels, which in this case is the number of ways that N+ particles out of N can be in the + state. Calculate and plot the heat capacity CV for this system.

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