A) \[{{C}_{V}}\,\ln \,2\]
B) \[{{C}_{p}}\,\ln \,2\]
C) \[R\,\ln \,2\]
D) \[({{C}_{V}}-R)\,\ln \,2\]
Correct Answer: D
Solution :
[d] When there is simultaneously change in temperature and volume (or pressure) \[\Delta S=n{{C}_{V}}{{\log }_{e}}\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)+nR\,{{\log }_{e}}\left( \frac{{{V}_{2}}}{{{V}_{1}}} \right)\] \[={{C}_{V}}{{\log }_{e}}\left( \frac{2}{1} \right)+R\,\,{{\log }_{e}}\left( \frac{1}{2} \right)\] \[={{C}_{V}}{{\log }_{e}}2-R\,\,{{\log }_{e}}2\] \[=({{C}_{V}}-R){{\log }_{e}}2\]
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