The pressure and volume of an ideal gas are related as $\mathrm{PV}^{3 / 2}=\mathrm{K}$ (Constant). The work done when the gas is taken from state $A\left(P_1, V_1, T_1\right)$ to state $\mathrm{B}\left(\mathrm{P}_2, \mathrm{~V}_2, \mathrm{~T}_2\right)$ is :
JEE MAIN 2024, Diffcult
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For $\mathrm{PV}^{\mathrm{x}}=$ constant
If work done by gas is asked then
${W}=\frac{\mathrm{nR} \Delta \mathrm{T}}{1-\mathrm{x}}$
Here x $=\frac{3}{2}$
$ W =\frac{\mathrm{P}_2 \mathrm{~V}_2-\mathrm{P}_1 \mathrm{~V}_1}{-\frac{1}{2}}$
$=2\left(\mathrm{P}_1 \mathrm{~V}_1-\mathrm{P}_2 \mathrm{~V}_2\right) \ldots . \text { Option (1) is correct }$
If work done by external is asked then
$\mathrm{W}=-2\left(\mathrm{P}_1 \mathrm{~V}_1-\mathrm{P}_2 \mathrm{~V}_2\right) \ldots \ldots$ Option $(2)$ is correct
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