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TFM
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Homework Statement
For a mole of nitrogen (N2) gas at room temperature and atmospheric pressure, compute the following: U, H, F, G, S and μ. The internal partition function is purely rotational, and the rotational constant ε for N2 is 0.00025 eV. The electronic ground state is not degenerate.
Homework Equations
[tex] Z_{total} = \frac{1}{N!}_1^N [/tex]
[tex] Z_1 = Z_{int} = \sum{exp(-E_{int}(s)/k_BT)} [/tex]
[tex] U = -\frac{\partial}{\partial \beta} ln z [/tex]
The Attempt at a Solution
Okay, I am having a slight problem calculating the Z value. I have used:
[tex] Z_1 = Z_{int} = \sum{exp(-E_{int}(s)/k_BT)} [/tex]
and inserted 300 K, E = 0.00025 eV abd the Boltzmann Constant (in eV) into this, and have got 9.67 *10^{-3}
I now want to use:
[tex] Z_{total} = \frac{1}{N!}_1^N [/tex]
but N is the number of particles, which is 1 Mole x Avagadros Number. This leaves with a large number which I have to find the factorial of, but it is too large for Excel. Have I gone wrong somewhere?
TFM