Response to the following problem:
A thin-walled metal container of volume V contains a gas at high pressure. Connected to the container is a capillary tube and stopcock. When the stopcock is opened slightly, the gas leaks slowly into a cylinder equipped with a nonleaking, frictionless piston, where the pressure remains constant at the atmospheric value Po.
(a) Show that, after as much gas as possible has leaked out, an amount of work has been done, where Vo is the volume of the gas at atmospheric pressure and temperature.
W = -P0(V0 -V)
(b) How much work would be done if the gas leaked directly into the atmosphere?