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Second law of thermodynamics, entropy

Problem 2.157

A vessel of volume \(V_{0}\) contains \(N\) molecules of an ideal gas. Find the probability of \(n\) molecules getting into a certain separated part of the vessel of volume \(V\). Examine, in particular, the case \(V=V_{0} / 2\)

Reveal Answer
Pn=N!n!(N−n)!pn(1−p)N−n, where p=V/V0P_{n}=\frac{N !}{n !(N-n) !} p^{n}(1-p)^{N-n}, \text { where } p=V / V_{0}
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