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Find the average energy and the heat capacity at constant volume for a two-state system. Take...

Find the average energy and the heat capacity at constant volume for a two-state system. Take the two energies of the system to be ± ε/2. (b) Show that the result for CV is proportional to 1/T2 for kT >>ε , and that it is of the form CV ≈ (constant/T2 e ^(−ε/kT) at low temperature, kT << ε

Science   Advanced-Physics   
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Answer #1

The partition function of the two state system is

This can also be written in terms of hyperbolic functions

where

the average energy is

Therefore

the heat capacity is

b) For high temperature

therefore

For low temperature

,

therefore

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