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Chapter 3

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Problem 10

Please note: there is a factor of "2" different from the book. I do not know where it comes from.

We have for the problem:

and

We use the Stirling approximation: N! ~~

We expand the powers:

and the logarithms using the Taylor expansion:

And simplify:

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Problem 7

The energy is obtained by taking the derivative of the partition function with respect to the temperature:

In the case where ε>> τ, then Ub is zero. When the energy levels are separated by an energy much larger than the energy available for that tempreature, the levels will not be occupied.

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Problem 6, p. 85, Thermal physics

Partition function,when is small

Partition function,when is large:

Converted by *Mathematica*
September 27, 2002