Reversible adiabatic process insight How can a  reversible adiabatic process (theoretically) be brought about since the  system is insulated? A $\mathrm dP$ change in pressure will lead to a $\mathrm dT$ change in temperature thus disturbing the thermodynamic equilibrium.
Because there is a temperature difference between the system and the surrounding which isn't possible in an reversible process.
 A: I tried to explain this in connection with your other answer. But here's another try.
A reversible process is one in which no entropy is generated. Causes of entropy product include, but are not necessarily limited to, the following:

*

*Heat transfer occurs across a finite temperature difference.

This is what is meant by thermal disequilibrium. There is no thermal disequilibrium between two objects having different temperatures if there is no opportunity for heat to transfer between the two object. Insulating the system from the surroundings in an adiabatic process prevents the opportunity of heat transfer across a finite temperature difference.


*Work transfer involving a finite pressure difference.

For a reversible adiabatic process the difference in pressure is always infinitesimal so that the pressures can be considered the same, i.e., the system and surroundings are in mechanical equilibrium. This, plus the absence of any mechanical friction, makes the adiabatic process reversible.
Hope this helps.
A: When they say adiabatic, they mean perfectly insulated.
You can have a temperature difference between the system and the environment, but you just pretend that zero heat flows. That’s just a given. You are told to assume it.
Maybe that is not always realistic, especially when there are big temperature differences. But we assume it’s true to do the theoretical problem and learn. And sometimes is ok assumption in real life situations if close to true. But yes there is no perfect insulation. In reality, there would be heat lost through the insulation (and also into the insulation to set-up a temperature gradient, because the insulation is not zero mass, and is not zero “thermal mass”). Idealized case.
