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As far as I'm concerned the relation between internal energy and heat capacity is:

Cv=dE/dT

However with with i cannot get a reasonable answer.

The expression for the total internal energy of a system is given by:

[tex]E= \frac{N \Delta E}{exp( \Delta E/kT) +1 } }[/tex]

Where N is the total number of particles, T is the temperature, k is the Boltzmann constant.

When i differentiate it I get an expression which is negative and inversely proportional to the temperature, not to the square temperature....