The initial pressure and volume of a gas is ' $\mathrm{P}$ ' and ' $\mathrm{V}$ ' respectively. First by…

The initial pressure and volume of a gas is ' $\mathrm{P}$ ' and ' $\mathrm{V}$ ' respectively. First by isothermal process gas is expanded to volume ' $9 \mathrm{~V}$ ' and then by adiabatic process its volume is compressed to ' $\mathrm{V}$ ' then its final pressure is (Ratio of specific heat at constant pressure to constant volume $=\frac{3}{2}$ )
  1. $6 \mathrm{~A}$
  2. 27P
  3. 3P
  4. 9P

Solution

$\frac{C_p}{C_v}=\frac{3}{2}$ Case I: Isothermal process $\begin{aligned} & \mathrm{P}_1 \mathrm{~V}_1=\mathrm{P}_2 \mathrm{~V}_2 \\ & \mathrm{PV}=\mathrm{P}_2 \times 9 \mathrm{~V} \\ & \therefore \mathrm{P}_2=\frac{\mathrm{P}}{9} \end{aligned}$ Case II: Adiabatic process $\begin{aligned} & \mathrm{P}_2 \mathrm{~V}_2^\gamma=\mathrm{P}_3 \mathrm{~V}_3^\gamma \\ & \frac{\mathrm{P}}{9}(9 \mathrm{~V})^\gamma=\mathrm{P}_3(\mathrm{~V})^\gamma \\ & \mathrm{P}_3=\left(\frac{\mathrm{P}}{9}\right) 9^\gamma=\left(\frac{\mathrm{P}}{9}\right) 9^{3 / 2}=\frac{\mathrm{P}}{9} \times 27=3 \mathrm{P} \end{aligned}$

Asked in: MHT CET 2021 (24 Sep Shift 1)

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