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 (1) $\frac { \alpha V } { 2 } \left( m ^ { 2 } - 1 \right)$ (2) $\frac { \alpha ^ { 2 } V ^ { 2 } } { 2 } \left( m ^ { 2 } - 1 \right)$ (3) $\frac { \alpha } { 2 } \left( m ^ { 2 } - 1 \right)$ (4) $\frac { \alpha V ^ { 2 } } { 2 } \left( m ^ { 2 } - 1 \right)$
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\\
(1) $\frac { \alpha V } { 2 } \left( m ^ { 2 } - 1 \right)$\\
(2) $\frac { \alpha ^ { 2 } V ^ { 2 } } { 2 } \left( m ^ { 2 } - 1 \right)$\\
(3) $\frac { \alpha } { 2 } \left( m ^ { 2 } - 1 \right)$\\
(4) $\frac { \alpha V ^ { 2 } } { 2 } \left( m ^ { 2 } - 1 \right)$