A) \[RT{{\log }_{10}}\frac{{{V}_{2}}}{{{V}_{1}}}\]
B) \[RT{{\log }_{10}}\frac{{{V}_{1}}}{{{V}_{2}}}\]
C) \[RT{{\log }_{e}}\frac{{{V}_{2}}}{{{V}_{1}}}\]
D) \[RT{{\log }_{e}}\frac{{{V}_{1}}}{{{V}_{2}}}\]
Correct Answer: C
Solution :
For isothermal process \[PV=RT\Rightarrow P=\frac{RT}{V}\] \[\therefore \]W\[=PdV=\int_{\,{{V}_{1}}}^{\,{{V}_{2}}}{\frac{RT}{V}dV=RT}{{\log }_{e}}\frac{{{V}_{2}}}{{{V}_{1}}}\]
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