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(C) Given: $\gamma = \frac{C_p}{C_v} = \frac{3}{2}$.Case $I$: Isothermal process $(T = 	ext{constant})$For an isothermal process,$P_1 V_1 = P_2 V_2$.

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$3$

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(C) Given: $\gamma = \frac{C_p}{C_v} = \frac{3}{2}$.Case $I$: Isothermal process $(T = 	ext{constant})$For an isothermal process,$P_1 V_1 = P_2 V_2$.Given $P_1 = P$,$V_1 = V$,and $V_2 = 9V$.$P 	imes V = P_2 	imes 9V$$P_2 = \frac{P}{9}$.Case $II$: Adiabatic process $(PV^\gamma = 	ext{constant})$For an adiabatic process,$P_2 V_2^\gamma = P_3 V_3^\gamma$.Given $P_2 = \frac{P}{9}$,$V_2 = 9V$,and $V_3 = V$.$\frac{P}{9} 	imes (9V)^{3/2} = P_3 	imes (V)^{3/2}$$P_3 = \frac{P}{9} 	imes \left(\frac{9V}{V}ight)^{3/2}$$P_3 = \frac{P}{9} 	imes (9)^{3/2}$$P_3 = \frac{P}{9} 	imes (3^2)^{3/2} = \frac{P}{9} 	imes 3^3 = \frac{P}{9} 	imes 27 = 3P$.Therefore,the final pressure is $3P$.

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