# Thermal Equilibrium and adiabatic walls - Zemansky

In Zemansky's "Heat and Thermodynamics" it is stated that:

A thermodynamic system is in thermal equilibrium with its sorroundings iff it is in mechanical and chemical equilibria with its sorroundings, it is delimited by diathermic walls and its macroscopic coordinates do not change with time (hence they may be called thermodynamic coordinates).

A thermodynamic system is in thermodynamic equilibrium with its sorroundings iff it is in mechanical, chemical and thermal equilibria with its sorroundings.

Now, I have two questions concerning these definitions:

1. Is there any difference between thermal and thermodynamic equilibria? (it seems like there should be, at least that is what I have read in the dedicated wikipedia page: https://en.wikipedia.org/wiki/Thermal_equilibrium);

2. If diathermic walls are needed in the definition of thermal equilibrium, how is it possible to use the same concept with systems that are delimited by adiabatic walls? (indeed, Zemansky speaks of such systema as if they can be in an equilibrium state).

As always, any comment or answer is much appreciated and let me know if I can explain myself clearer!

You have two concepts here:

"In thermodynamic equilibrium."

and

"In thermodynamic equilibrium with its surroundings."

In both cases the system is in internal equilibrium. In the second case it is also able to exchange energy and volume (and maybe material too) with its surroundings, and it is in dynamic equilibrium at the same temperature and pressure (and possibly chemical potential) as the surroundings. The phrases in brackets apply to an open system (one able to exchange matter with its surroundings). If you have a closed system then you need not require chemical equilibrium with the surroundings in order to say it is in thermodynamic equilibrium with its surroundings, so on this point Zemansky is less than clear I think.

Finally, the term "thermal equilibrium" always includes internal equilibrium, but as regards surroundings it is sometimes employed as a synonym for "thermodynamic equilibrium" and sometimes it just refers to a system that is at the same temperature as another. This is usually not ambiguous in practice.

As I understand it:

Mechanical equilibrium: Equal pressures (forces).

Chemical equilibrium: Equal chemical potentials (fugacities)

Thermal equilibrium: Equal temperatures

Thermodynamic equilibrium: The state in which all three types of equilibria are satisfied.

• I like the way you presented it, however I would like to stick to the text I am using as much as I can and I would like to know wether the author was precise or not in his definitions of these concepts. In the latter case I wouldn't mind adopting your definitions. Commented Oct 9, 2022 at 13:12

For an adiabatic system to be in thermodynamic equilibrium, there can be no spatial variations within the system in temperature, pressure, or chemical potential.

• Doesn't that also apply to a non adiabatic system? Commented Oct 12, 2022 at 13:22
• @ BobD Yes it does. Commented Oct 12, 2022 at 16:45