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Consider a two state system consisting of N distinguishable and indeppendent particles where each particle can occupy one of two states separated by an energy E. What is the entropy of the system at:

(A) T=0

(B) T=infinity

I'm assuming this refers to the canonical ensemble (different energies), so I have tried to apply the following formula:

S = E/T + klnZ

however this produces an infinite entropy at zero temperature (contradicting the third law of thermodynamics). Is there another way of calculating this?? Many thanks.