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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 $$27 P/8$$. If initial volume of each compartment was 9 litres then the final volume in right-hand side compartment is __________ litres. (for this ideal gas $$C_P/C_V = 1.5$$)
$$P_i V_i^\gamma = P_f V_f^\gamma$$
$$P \cdot (9)^{\frac{3}{2}} = \left(\frac{27}{8}P\right) \cdot (V_f)^{\frac{3}{2}}$$
$$(V_f)^{\frac{3}{2}} = \frac{8}{27} \cdot (9)^{\frac{3}{2}}$$
$$V_f = \left(\frac{2}{3}\right)^2 \cdot 9 = \frac{4}{9} \times 9 = 4 \text{ litres}$$
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