Suppose there are $N$ distuinguishable particles. Each particle can have energy either $\epsilon_1$ or $\epsilon_2 $. $ n_1$ particles have energy $\epsilon_1 $and $n_2$ particles have $\epsilon_2$ i.e. $N=n_1 + n_2$. What is the partition function? Is it $$Z= [\exp(-\beta \epsilon_1)+\exp(-\beta \epsilon_2)]^{N}$$ or $$Z=\exp(-\beta \epsilon_1 n_1)+\exp((-\beta \epsilon_2 n_2)~?$$
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1$\begingroup$ It's the first. $\endgroup$– marchCommented Apr 19 at 18:30
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$\begingroup$ Is this for Z_total? If so shouldn't there be a factor of 1/N! In front? $\endgroup$– RudyJDCommented Apr 19 at 19:25
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$\begingroup$ @RudyJD 1/N! is for indistinguishable particles. $\endgroup$– Mr. WayneCommented Apr 19 at 20:32
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$\begingroup$ @Mr.Wayne, oops thank you I misread your question. $\endgroup$– RudyJDCommented Apr 19 at 20:51
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$\begingroup$ @march I think it should be $exp(-\epsilon_1 \beta n_1)exp(-\epsilon_2 \beta n_2)$ $\endgroup$– Mr. WayneCommented Apr 20 at 5:19
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