Follow up to
Intuitively, why is a reversible process one in which the system is always at equilibrium?
and
How slow is a reversible adiabatic expansion of an ideal gas?
Suppose you have a piston with some air in it and you perform a slow, reversible expansion. The air in the piston must be in an equilibrium state the entire time.
Now suppose you do the expansion quickly. During the expansion, the air is not in an equilibrium state. My question is: should it have well-defined state variables? Should the pressure be well-defined, for example?
Presumably there is air moving around in bulk and a pressure gauge would give different readings depending on where you put it. Similarly, there is a mean kinetic energy of the molecules that might be used to define $T$, but there is no $\beta$ exponential factor because the kinetic energies of the molecules will not follow a simple, single-parameter distribution. This would indicate that concepts like pressure and temperature are not well-defined when out of equilibrium.
Is that right, and is it always the case? Can I have a process where I know what the pressure and temperature are the entire time, but the system is not in equilibrium?
Best Answer
Strictly speaking there are no reversible processes in Nature; it is an idealization that enables one to get bounds on efficiency of nonequilibrium processes by using techniques of equilibrium thermodynamics only.
A reversible process is therefore primarily a theoretical concept for discussing what would happen in a process if dissipation were absent. It is defined as a motion in equilibrium state space, and hence presupposes that the system always remains in equilibrium.
However, empirically, fast processes generate far more excess entropy (the source of the dissipation) than slow ones, so one can treat a slow process approximately as a reversible one.
In a nonequilibrium state, the extensive variables are still well-defined, while the intensive variables (temperature, pressure, chemical potential) typically aren't. On the other hand, most nonequilibrium processes in ordinary life are well-described by local equilibrium; which means that every small region is approximately in equilibrium, and then temperature, pressure, and chemical potential can be assigned definite values. As a result one gets a temperature field, a pressure field, etc. (This is what you feel when you move through a room from the heating to a open window.)