The following figure shows an adiabatic cylin | vedclass

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(C) Since the piston is in equilibrium,both gases must be at the same final pressure $P_f$.Given the displacement of the piston is $x$ and the area of

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$\frac{P_1 (V_0/2)^\gamma}{(V_0/2 + Ax)^\gamma}$

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(C) Since the piston is in equilibrium,both gases must be at the same final pressure $P_f$.Given the displacement of the piston is $x$ and the area of cross-section is $A$,the final volumes of the left and right parts are:$V_L = V_0/2 + Ax$ and $V_R = V_0/2 - Ax$.Since the container and piston are adiabatic,both gases undergo adiabatic processes.For the left gas:$P_1 (V_0/2)^\gamma = P_f (V_0/2 + Ax)^\gamma$$P_f = \frac{P_1 (V_0/2)^\gamma}{(V_0/2 + Ax)^\gamma}$ ... $(i)$For the right gas:$P_2 (V_0/2)^\gamma = P_f (V_0/2 - Ax)^\gamma$$P_f = \frac{P_2 (V_0/2)^\gamma}{(V_0/2 - Ax)^\gamma}$ ... $(ii)$Both expressions represent the final pressure $P_f$. Thus,option $(C)$ is a valid expression for the final pressure.

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