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
AIEEE 2012, Medium
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$\text { Given } P=\alpha V $
$\text { Work done, } w=\int_{V}^{mV} P d V $
$=\int_{m}^{m V} a V d V=\frac{\alpha V^{2}}{2}\left(m^{2}-1\right)$
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