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(B) The right side compartment undergoes an adiabatic compression because the piston is adiabatic and frictionless.For an adiabatic process,the relati

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$4$

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(B) The right side compartment undergoes an adiabatic compression because the piston is adiabatic and frictionless.For an adiabatic process,the relation is $PV^{\gamma} = 	ext{constant}$.Given $\gamma = 1.5 = 3/2$.Let the initial state be $(P, V_1 = 9)$ and the final state be $(P_2 = \frac{27}{8}P, V_2)$.Since the piston is frictionless,the pressure on both sides must be equal at equilibrium. Thus,the final pressure on the right side is also $\frac{27}{8}P$.Using the adiabatic relation: $P_1 V_1^{\gamma} = P_2 V_2^{\gamma}$.$P(9)^{3/2} = \frac{27}{8}P(V_2)^{3/2}$.$(9)^{3/2} = \frac{27}{8} V_2^{3/2}$.$27 = \frac{27}{8} V_2^{3/2}$.$V_2^{3/2} = 8$.$V_2 = 8^{2/3} = (2^3)^{2/3} = 2^2 = 4 	ext{ litres}$.

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