A rigid, well-insulated cylinder of gas initially contains N0 moles of an ideal

Question

A rigid, well-insulated cylinder of gas initially contains N0 moles of an ideal gas at a
temperature T0 and pressure P0. A venting valve is opened and the gas exits the tank.
Assume that the contents of the cylinder can be considered at equilibrium at all times. In
addition, assume the gas is ideal with heat capacity at constant volume, CV, independent
of temperature.
a) Derive an expression for the instantaneous temperature T in the cylinder as a function
of the number of moles of gas remaining in the cylinder, N.
b) What do you predict will be the final temperature, Tf, if you could completely evacuate
the tank to Nf = 0? Is this prediction physically attainable?

Explanation / Answer

At any instant PV = nRT where n is the number of moles of gas at that instant.

If n finally = 0, theoretically, T = 0

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