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Internal energy of a molecule with 4 energy eigenstates

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The molecule has four states with the following energies:

E_1 = -1

E_2 = E_3 = 0

E_4 = 1

We assume that these energies are measured in some arbitray units. Then the partition function is:

Z = sum over r of exp(-beta E_r) =

exp(beta) + 2 + exp(-beta)

The internal energy of the ...

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