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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