A) 10 R
B) 20 R
C) 30 R
D) 40 R
Correct Answer: B
Solution :
\[W=\int{\rho dV=\int{\frac{RT}{V}\,\,dV}}\] Since, \[V=K{{T}^{2/3}}\] \[\Rightarrow \] \[dV=\frac{2}{3}K{{T}^{-1}}dT\] Eliminating K, we find \[\frac{dV}{V}=\frac{2}{3}\frac{dT}{T}\] Hence, \[W=\int_{{{T}_{1}}}^{{{T}_{2}}}{\frac{2}{3}\,\frac{RT}{T}dT}\] \[=\frac{2}{3}R({{T}_{2}}-{{T}_{1}})\] \[=\frac{2}{3}R(30)=20R\]
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