A ``porous plug'' experiment is carried out by installing a porous plug in a plastic pipe. To the left of the plug the gas is maintained at a pressure slightly higher than atmospheric by a movable piston. To the right of the plug there is a freely sliding piston, and the right-hand end of the pipe is open to the atmosphere. What is the fractional difference of velocities of the pistons?
((a)) Express the answer in terms of atmospheric pressure Pa, the driving pressure Ph, and cp, α, κT, and v (assuming that the pressure difference is small enough that no distinction need be made between the values of the latter quantities on the two sides of the plug).
((b)) Evaluate this result for an ideal gas, and express the deviation from this result in terms of the second virial coefficient, carrying results only to first order in B(T) or its derivatives (the heat capacity cp is to be left as an unspecified quantity in the solution).