Following figure shows on adiabatic cylindrical container of volume 
divided by an adiabatic smooth piston (area of cross-section = A) in two equal parts. An ideal gas 
is at pressure P 1 and temperature T 1 in left part and gas at pressure P 2 and temperature T 2 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)
Text Solution
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As finally the piston is in equilibrium, both the gases must be at same pressure 
. It is given
that displacement of piston be in final state x and if A is the area of cross-section of the piston. Hence the final volumes of the left and right part finally can be given by figure as
As it is given that the container walls and the piston are adiabatic in left side and the gas undergoes adiabatic expansion and on the right side the gas undergoes adiabatic compressive. Thus we have for initial and final state of gas on left side
......(i)
Similarly, for gas in right side, we have
......(ii)
From eq. (i) and (ii)
⇒ ⇒ 
Now from equation (i) 
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