Discussion
The volume of a perfect gas is doubled, the number of atoms N and the energy E being held constant, the change in entropy will be :
Answer: C
The entropy change is Nk ln 2.
At constant N and energy E (free expansion of an ideal gas), only the volume term of the Sackur-Tetrode entropy changes: \(S = Nk\ln V + \) terms independent of V. So:
\[ \Delta S = Nk\ln\frac{2V}{V} = Nk\ln 2 \]
The answer depends only on the ratio of volumes, so options containing ln V or ln 2V alone cannot be a change in entropy.
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