What Is the Entropy of a Two-State System at Zero and Infinite Temperatures?

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I'm having difficulty with this problem:

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.
 
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Have you actually done the calculation? Are you sure the answer you get is infinity? If you're really confused, go back to what you know. Maybe you should try calculating just the partition function.
 
^ Well the E/T term in the entropy would automatically go to infinity at 0K...
 
Why? The average energy E which appears in your equation depends on temperature, right?
 

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