# Reversible processes in which mechanical or thermal equilibrium is not reached

The definition of a reversible thermodynamic process requires in any instant the mechanical equilibrium (equal pressures) and thermal equilibrium (equal temperatures) of the system in a quasi-static processr.

But there are cases of processes in which one of the two kinds of equilibrium cannot be reached.

Can these processes be considered "reversible" anyway?

I'll make two examples

1. Quasi-static process in a completely adiabatic tank with two different gases at different temperatures: mechanical equilibrium always present, but thermal equilibrium (between the two gases) not necessarily reached.

1. Isochoric quasi-static process of a gas in rigid and diatermic tank: thermal equilibrium always present, but mechanical equilibrium (between the gas and the environment) not necessarily reached.

• The internal wall in the first example is diathermal, right? What process is occurring in the second example? Since the tank is rigid and with diathermal walls, I don't see any evolution. – Diracology Jun 20 '16 at 16:13
• @Diracology No it is adiabatic too. I'm talking about a generic process, for istance some work or heat is supplied to the systems and the point is, as far as I can see, that thermal (in the first) and mechanical (in the second) equilibrium is not reached – Sørën Jun 20 '16 at 16:16
• But if the walls are all adiabatic, there is no heat exchanged by the systems. – Diracology Jun 20 '16 at 16:19
• @Diracology Yes sorry I meant work (and no heat) is exchanged with system $1.$ for istance moving the internal wall, and heat (no work) is exchanged with $2.$ for istance with an electric resistance dissipating power inside the box – Sørën Jun 20 '16 at 17:00
• I think you are thinking of the "adiabatic piston" problem. It has an enormous literature, just search google.com/?gws_rd=ssl#q=adiabatic+piston+problem and enjoy! – hyportnex Jun 20 '16 at 17:45

• Ok probably I missed this point, but in $1.$ if I choose as system the whole box (both the parts and so both gases), and as environment the external space (say at temperature $T_0$), then the middle wall is moved exchanging work in a quasi static way, the temperatures of the two gases at any equilibrium state would be different with each other and will differ from $T_0$, that is $T_1\neq T_2 \neq T_0$ in any intermediate state of the (reversible?) process. Would this scenario be a good one for my doubt? – Sørën Jun 20 '16 at 18:07