A monoatomic gas at pressure ' $\mathrm{P}$ ', having volume ' $\mathrm{V}$ ' expands isothermally to a volume ' $2 \mathrm{~V}$ ' and then adiabatically to a volume ' $16 \mathrm{~V}$ '. The final pressure of the gas is (Take $\gamma=5 / 3$ )

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Aicharya · Accepted Answer

After isothermal expansion: $\begin{aligned} & P_1 V_1=P_2 V_2 \ & P_2=P_1 \frac{V_1}{V_2} \ & P_2=P_1 \frac{V}{2 V} \ & P_2=\frac{P}{2} \end{aligned}$ After adiabatic expansion: $\begin{aligned} & \mathrm{P}_2 \mathrm{~V}_2^\gamma=\mathrm{P}_3 \mathrm{~V}_3^\gamma \ & \mathrm{P}_3=\mathrm{P}_2\left(\frac{\mathrm{V}_2}{\mathrm{~V}_3}ight)^\gamma \ & \mathrm{P}_3=\frac{\mathrm{P}}{2}\left(\frac{2 \mathrm{~V}}{16 \mathrm{~V}}ight)^{5 / 3} \ & \mathrm{P}_3=\frac{\mathrm{P}}{2}\left(\frac{1}{8}ight)^{5 / 3} \ & \mathrm{P}_3=\frac{\mathrm{P}}{64} \end{aligned}$

A monoatomic gas at pressure ' $\mathrm{P}$ ', having volume ' $\mathrm{V}$ ' expands isothermally to a…

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