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
  $\frac{\alpha V^2}{2}(m^2 - 1)$
• B
  $\frac{\alpha^2 V^2}{2}(m^2 - 1)$
• C
  $\frac{\alpha}{2}(m^2 - 1)$
• D
  $\frac{\alpha V}{2}(m^2 - 1)$