An ideal gas is contained in a piston with that is initially

An ideal gas is contained in a piston with that is initially secured so that the gas is at p0 and V0. The cylindrical piston has circular area a, and the distance from the movable end to the back is d. The movable end is attached to a pulley system in such a way that when the gas is allowed to expand, a mass with mass m is raised. After the gas is allowed to expand, the piston is raised by a distance y. The system is in thermal isolation, and once it is released and allowed to come to equilibrium, what is the value of y in terms of the other given variables?

Solution

Work done by the expansion of gas = P₀V₀

Work required to raise the weight = mgy

Equating, P₀V₀ = mgy

y = P₀V₀ / mg