What is Adiabatic Process? The thermodynamic process in which there is no exchange of heat from the system to its surrounding neither during expansion nor during compression. The adiabatic process can be either reversible or irreversible. ... The system must be perfectly insulated from the surrounding.

Can a process be reversible and non adiabatic?

As long as the work is reversible (δW=−PdV), the process can be called reversible. For a reversible process, you have δQ=TdS but this is not a property of the heat exchange, only a consequence of the fact the entropy is increased by the heat only (no extra growth by some irreversible work).

What is the difference between reversible and irreversible adiabatic process?

The difference is that one expansion is quasi-static (the reversible one) while the other is spontaneous because of a dramatic change of the external constraints (the irreversible one). In the quasi-static case, you start off indeed in the state where gas pressure equates external pressure.