Initial pressure and volume of a gas are $P$ and $V$ respectively. First it is expanded isothermally to volume $4V$ and then compressed adiabatically to volume $V$ . The final pressure of gas will be (given $\gamma = 3/2$ )
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In isothermal process $\mathrm{P}_{1} \mathrm{V}_{1}=\mathrm{P}_{2} \mathrm{V}_{2}$
$\Rightarrow \mathrm{PV}=\mathrm{P}_{2} \times 4 \mathrm{V} \quad \because \mathrm{P}_{2}=\mathrm{P} / 4$
In adiabatic process
$\mathrm{P}_{2} \mathrm{V}_{2}^{\gamma}=\mathrm{P}_{3} \mathrm{V}_{3}^{\gamma} \Rightarrow \frac{\mathrm{P}}{4} \times(4 \mathrm{V})^{15}=\mathrm{P}_{3} \mathrm{V}^{15} \Rightarrow \mathrm{P}_{3}=2 \mathrm{P}$
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