question_answer

The pressure of an ideal gas varies with volume as \[P=\alpha V,\] where a is a constant. One mole of the gas is allowed to undergo expansion such that its volume becomes 'm times its initial volume. The work done by the gas in the process is                                                                                                                                     [JEE ONLINE 19-05-2012]

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 :

[d] Given

Work done,