$1\, mole$ of an ideal monoatomic gas at temperature $'T_0'$ expands slowly according to the law $P = KV$, where $K$ is a constant. If the final temperature of the gas is $2T_0$. Find the heat supplied to the gas
Medium
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$\mathrm{Q}=\Delta \mathrm{U}+\Delta \mathrm{w}$
$\Delta \mathrm{U}=\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T}=1 \times \frac{3}{2} \mathrm{R} \times\left(2 \mathrm{T}_{0}-\mathrm{T}_{0}\right)=\frac{3}{2} \mathrm{RT}_{0}$
Work $=\frac{\mu R \Delta T}{n-1}=\frac{1 \times R \times\left(2 T_{0}-T_{0}\right)}{2} \Rightarrow\left(\frac{R T_{0}}{2}\right)$
$\mathrm{Q}=\frac{3}{2} \mathrm{RT}_{0}+\frac{\mathrm{RT}_{0}}{2}$
$=2 \mathrm{RT}_{0}$
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