Question 859: Thermodynamics & KTG

Question

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 $$\gamma=5 / 3$$ )

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:
$$\begin{aligned}
& \mathrm{P}_2 \mathrm{~V}_2^\gamma=\mathrm{P}_3 \mathrm{~V}_3^\gamma \
& \mathrm{P}_3=\mathrm{P}_2\left(\frac{\mathrm{V}_2}{\mathrm{~V}_3}ight)^\gamma \
& \mathrm{P}_3=\frac{\mathrm{P}}{2}\left(\frac{2 \mathrm{~V}}{16 \mathrm{~V}}ight)^{5 / 3} \
& \mathrm{P}_3=\frac{\mathrm{P}}{2}\left(\frac{1}{8}ight)^{5 / 3} \
& \mathrm{P}_3=\frac{\mathrm{P}}{64}
\end{aligned}$$

Answer

$$\mathrm{P} / 64$$

Answer

$$\mathrm{P} / 32$$

Answer

$$16 \mathrm{P}$$

Answer

$$32 \mathrm{P}$$

Thermodynamics & KTG

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

Choose the correct answer: