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Surely equilibrium thermodynamics
cannot be said to fail when applied to real thermodynamic processes.
If it isn't of any use in those cases then what is it good for?
Equilibrium thermodynamics does fail when applied to real
thermodynamic processes, but to different degrees. Relatively slow
processes (slow compared to the relaxation time of the system) are
described very well by equilibrium thermodynamics.
Thermodynamic equilibrium states subsume static equilibrium states.
A box of gas in an unchanging state of thermodynamic equilibrium is
in static equilibrium by conventional definition.
I'm curious, then. How do you define "dynamic equilibrium"? Is a
reversible chemical reaction at equilibrium static or dynamic?