Q137 / 150 · MHT CET 2024 (10 May Shift 1) · Physics

Initial pressure and volume of a gas are ' $P$ ' and ' $V$ ' respectively. First its volume is expanded to ' 4 V ' by isothermal process and then again its volume is reduced to ' V ' by adiabatic process then its final pressure if $\left(\gamma=\frac{3}{2}\right)$

  • A
    P
  • Correct answer
    B
    $\quad 2 \mathrm{P}$
  • C
    3 P
  • D
    4 P

Solution

After isothermal expansion, $\begin{aligned} & P_1 V_1=P_2 V_2 \\ & P V=P_2 \times 4 V \\ \therefore \quad & P_2=\frac{P}{4} \end{aligned}$ After adiabatic compression, $\begin{array}{lll} & P_2 V_2^\gamma=P_3 V_3^\gamma & \\ & \frac{P}{4}(4 V)^\gamma=P_3(V)^\gamma & \ldots\left(\text { given } V_3=\dot{V}\right) \\ \therefore \quad & P_3=\frac{P}{4} 4^\gamma=\frac{P}{4} 4^{3 / 2} & \ldots\left(\text { given }, \gamma=\frac{3}{2}\right) \\ \therefore \quad & P_3=\frac{P}{4} \times 8=2 P & \end{array}$

Hence, the correct answer is option: 'B'.

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