JEE MAIN - Physics (2025 - 3rd April Evening Shift - No. 6)
An ideal gas exists in a state with pressure $P_0$, volume $V_0$. It is isothermally expanded to 4 times of its initial volume $\left(\mathrm{V}_0\right)$, then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is
$\mathrm{P}_0 \mathrm{~V}_0(\ln 2-0.75)$
$\mathrm{P}_0 \mathrm{~V}_0(2 \ln 2-0.75)$
$\mathrm{P}_0 \mathrm{~V}_0(2 \ln 2-0.25)$
$\mathrm{P}_0 \mathrm{~V}_0(\ln 2-0.25)$
Explanation
_3rd_April_Evening_Shift_en_6_1.png)
$$\begin{aligned} & \omega_1=\mathrm{P}_0 \mathrm{v}_0 \ell \mathrm{n} 4 \\ & \omega_2=\frac{\mathrm{P}_0}{4}\left(-3 \mathrm{v}_0\right)=-\frac{3 \mathrm{P}_0 \mathrm{v}_0}{4} \\ & \omega_3=0 \\ & \mathrm{Q}_{\mathrm{T}}=\Delta \mathrm{U}_{\text {cyclic }}+\omega \\ & \mathrm{Q}_{\mathrm{T}}=\omega \quad\left(\Delta \mathrm{U}_{\text {cyclic }}=0\right) \\ & \mathrm{Q}_{\mathrm{T}}=\mathrm{P}_0 \mathrm{v}_0\left(\ln 4-\frac{3}{4}\right) \\ & =\mathrm{P}_0 \mathrm{v}_0(2 \ln 2-0.75) \end{aligned}$$
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