The pressure of an ideal gas varies with volume as $P = \alpha V,$ where $\alpha $ 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
  • A$\frac{{\alpha V}}{2}({m^2} - 1)$
  • B$\frac{{{\alpha ^2}{V^2}}}{2}({m^2} - 1)$
  • C$\frac{\alpha }{2}({m^2} - 1)$
  • D$\frac{{\alpha {V^2}}}{2}({m^2} - 1)$
AIEEE 2012, Medium
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