The mechanical equilibrium is a state in which the pressure (and elastic stress) inside a gas is evenly distributed. Do we make such an assumption while deriving the equation of state in thermodynamics?
I know that for ideal gas equation and van der Waal gas equation, mechanical equilibrium is assumed. But is this true for all the other more accurate equations of states?
If so, then is this not a very unrealistic way of modelling real gases? I mean, for a general gas, the force between particles can be assumed to be anything, in which case, the pressure of the gas away from the center will drop. Moreover, for a general gas, even the temperature will tend to decrease with increase in the distance away from the center, like in a star.
So if mechanical equilibrium is assumed while deriving the equations of state, then how can such assumption be physically justified?