Finite-time thermodynamics of a porous plug

Three related systems, two of which describe diffusion of an ideal gas through a porous plug, are optimized so as to minimize the work required to move the plug from one equilibrium position to another equilibrium position in a given time τ. All systems follow a ‘‘turnpike’’ (i.e., boundary-singular-boundary branch) trajectory, and the dissipation (work required) is proportional to (Δl${)}^2$/τ, where Δl is the distance moved, at least for slow processes. The result is of interest as a lower bound for the separation of gases by diffusion.