**Question:**

**Consider a system of N distinguishable independent particles, each of which can be in the state +ε _{0} or −ε_{0} . Let the number of particles with energy ±ε_{0 }be N_{±} , so that the energy is,**

**E = N _{+} ε_{0} − N_{-} ε_{0} = 2N_{+} ε_{0} − N ε_{0}**

**Evaluate the partition function Q by summing exp(−E/kT ) over levels and compare your result to Q = q ^{N}. 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 C_{V} for this system.**

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