Following figure shows on adiabatic cylindrical container of volume `V_(0)` divided by an adiabatic smooth piston (area of cross-section = A ) in two equal parts. An ideal gas `(C_(p)//C_(y)=lambda)` is at pressure P and temperature T in left part and gas at pressure P and temperature T in right part. The piston is slowly displaced and released at a position where it can stay in equilibrium. The final pressure of the two parts will be (Suppose x = displacement of the piston)

Options

A. `P_(2)`
B. `P_(1)`
C. `(P_(1)(V_(0)/(2))^(lambda))/((V_(0)/(2)+Ax)^(lambda))`
D. `(P_(2)(V_(0)/(2))^(lambda))/((V_(0)/(2)+Ax)^(lambda))`

Answer

C