A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same $P, V, T$. Heating is started from left side until pressure changes to $27P/8$. If initial volume of each compartment was $9$ litres then the final volume in right-hand side compartment is ______ litres. (for this ideal gas $C_P/C_V = 1.5$)
Answer: (B) $4$
Concept. The right gas gets no heat, so it is compressed adiabatically; the free piston equalises the pressures.
Step 1. Adiabatic relation.
$$P(9)^{1.5} = \frac{27P}{8}V^{1.5}$$
Step 2. Solve. $V = 9\left(\dfrac{8}{27}\right)^{2/3} = 9 \times \dfrac49 = 4$ litres.
Answer. $4$ (Option B).
Solution by Sreeraj P, M.Sc Physics
