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A vertical, insulated cylinder contains an ideal gas. The top of the cylinder is closed off...

A vertical, insulated cylinder contains an ideal gas. The top of the cylinder is closed off by a piston of mass m that is free to move up and down with no appreciable friction. The piston is a height h above the bottom of the cylinder when supported only by the gas. Sand is now poured onto the piston very slowly until the weight of the sand is equal to the weight of the piston.

(a) Find an analytic expression for the new height of the piston
(b) Write an expression for the new height in terms of h if the gas were O2 and He

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