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From Wikipedia, https://en.wikipedia.org/wiki/Thermodynamic_equilibrium

The second paragraph states that "Systems can be in one kind of mutual equilibrium, though not in others" . Could someone give an example to clarify this? Does this mean that two systems separated by a movable wall that allows the exchange of thermal energy cannot reach both mechanical and thermal equilibrium?

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  • $\begingroup$ for example, gas in two compartments separated by a fixed position diathermal wall can be in thermal equilibrium (heat is exchanged) but at different pressures. $\endgroup$
    – hyportnex
    Aug 31, 2019 at 20:54
  • $\begingroup$ the case of an adiabatic but movable wall is an old chestnut with much controversy behind it, see Callen $\endgroup$
    – hyportnex
    Aug 31, 2019 at 20:55

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One kind of equilibrium is thermal equilibrium which generally means there are no temperature differences between a system and the surroundings driving heat transfer between the two. The system and the surroundings are in mutual thermal equilibrium.. But the system and surroundings may not be in mechanical equilibrium due to pressure differences between them. They would not be in mutual mechanical equilibrium. When they say mutual thermodynamic equilibrium it covers all forms of mutual equilibrium (thermal and dynamic).

I think that’s what they’re trying to say.

Hope this helps

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