A) \[\frac{\alpha V}{2}\left( {{m}^{2}}-1 \right)\]
B) \[\frac{{{\alpha }^{2}}{{V}^{2}}}{2}\left( {{m}^{2}}-1 \right)\]
C) \[\frac{\alpha }{2}\left( {{m}^{2}}-1 \right)\]
D) \[\frac{\alpha {{V}^{2}}}{2}\left( {{m}^{2}}-1 \right)\]
Correct Answer: D
Solution :
Given \[P=\alpha V\] Work done, \[w=\int\limits_{V}^{mV}{PdV}\] \[=\int\limits_{V}^{mV}{\alpha V\,dV}=\frac{\alpha {{V}^{2}}}{2}({{m}^{2}}-1).\]
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