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

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Homework Help Overview

The discussion revolves around calculating the entropy of a two-state system consisting of N distinguishable and independent particles at two extreme temperatures: zero and infinite. The original poster is exploring the implications of the canonical ensemble and is encountering difficulties with the entropy formula.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply the entropy formula S = E/T + klnZ, questioning the outcome at zero temperature. Some participants suggest revisiting the calculation of the partition function, while others point out the behavior of the E/T term at low temperatures.

Discussion Status

The discussion is ongoing, with participants exploring different aspects of the entropy calculation and questioning the assumptions made about temperature and energy. There is no explicit consensus yet, but guidance has been offered regarding the partition function and the implications of temperature on energy.

Contextual Notes

Participants are considering the third law of thermodynamics in relation to the entropy at zero temperature, indicating a potential conflict in the original poster's calculations. The nature of the two-state system and the assumptions about distinguishability and independence are also under examination.

raintrek
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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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