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

$$\frac{\alpha V^2}{2}(m^2-1)$$