The pressure of an ideal gas varies with volume as $P=\alpha V$, where $\alpha$ is a constant. One mole of…
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
$\frac{\alpha V}{2}\left(m^2-1\right)$
$\frac{\alpha^2 V^2}{2}\left(m^2-1\right)$
$\frac{\alpha}{2}\left(m^2-1\right)$
$\frac{\alpha V^2}{2}\left(m^2-1\right)$
Solution
Given $P=\alpha V$
Work done, $w=\int_V^{m V} P d V$
$=\int_V^{m V} \alpha V d V=\frac{\alpha V^2}{2}\left(m^2-1\right)$.