As shown, a piston chamber of cross section area A is filled with an ideal gas. A sealed piston of mass m is at the middle height of the cylinder at equilibrium. The friction force between the chamber

Question

As shown, a piston chamber of cross section area A is filled with an ideal gas. A sealed piston of mass m is at the middle height of the cylinder at equilibrium. The friction force between the chamber wall and the piston can be ignored. The mass of the rest of the chamber is M. The atmosphere pressure is $P_{0}$ . If the piston is pulled slowly up to full height of chamber and temperature remains unchanged. The maximum value of M such that the chamber can be lifted off the ground is :

TestHub · Accepted Answer

PA = P 0 ​ A + mg P = P 0 ​ + A mg ​ PA + Mg = P 0 ​ A + N P 2 H ​ A = P ′ HA P ′ = 2 P ​ = 2 A P 0 ​ A + mg ​ N ′ = 0 P ′ A + Mg = P 0 ​ A M = g ( P 0 ​ − P ′ ) A ​ M = ( P 0 ​ − 2 P ​ ) g A ​ M = ( P 0 ​ − 2 P 0 ​ ​ − 2 A mg ​ ) g A ​ M = 2 g P 0 ​ A − mg ​

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