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
Medium
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(b) In isothermal process ${P_1}{V_1} = {P_2}{V_2}$
or $PV = {P_2} \times 4V$
$\therefore {P_2} = \frac{P}{4}$
In adiabatic process
${P_2}{V_2}^\gamma = {P_3}{V_3}^\gamma $==> $\frac{P}{4} \times {(4V)^{1.5}} = {P_2}{V^{1.5}}$==> ${P_3} = 2P$
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