A) \[RT\ln \frac{{{V}_{1}}}{{{V}_{2}}}\]
B) \[RT\ln \frac{{{V}_{2}}}{{{V}_{1}}}\]
C) \[R({{T}_{2}}-{{T}_{1}})\ln \frac{{{V}_{2}}}{{{V}_{1}}}\]
D) \[R({{V}_{2}}-{{V}_{1}})\ln \frac{{{T}_{2}}}{{{T}_{1}}}\]
Correct Answer: B
Solution :
Key Idea: Ideal gas equation is \[PV=RT\] Work done in isothermal process is \[W=\int_{{{V}_{1}}}^{{{V}_{2}}}{p\,\,dV}\] From ideal gas law\[PV=RT\] \[\therefore \] \[W=\int_{{{V}_{1}}}^{{{V}_{2}}}{\left( \frac{RT}{V} \right)}dV=RT\int_{{{V}_{1}}}^{{{V}_{2}}}{\frac{dV}{V}}\] \[\Rightarrow \] \[W=RT\ln \left( \frac{{{V}_{2}}}{{{V}_{1}}} \right)\]
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