A) \[nRT\,\ln \left( \frac{{{V}_{2}}}{{{V}_{1}}} \right)\]
B) \[nRT\,\left( \ln \frac{{{V}_{1}}}{{{V}_{2}}} \right)\]
C) \[nRT\]
D) none of these
Correct Answer: A
Solution :
The work done in expansion of gas from volume \[{{V}_{1}}\] to \[{{V}_{2}}\] is \[W=\int_{{{V}_{1}}}^{{{V}_{2}}}{PdV}\] ...(i) Gas equation is \[PV=nRT\] ...(ii) From equations (i) and (ii) \[W=\int_{{{V}_{1}}}^{{{V}_{2}}}{\frac{nRT}{V}dV=nRT\int_{{{V}_{1}}}^{{{V}_{2}}}{\frac{dV}{V}}}\] \[=nRT\,\log \left( \frac{{{V}_{2}}}{{{V}_{1}}} \right)\] \[\therefore \]\[W=nRT\,In\left( \frac{{{V}_{2}}}{{{V}_{1}}} \right)\]
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