# Validity of the adiabatic equation in irreversible processes

I read here that the ideal gas equation and all state equations are valid only at thermodynamic equilibrium. In irreversible processes, the system is not at thermodynamic equilibrium. Also, for reversible processes, I know that the process has to be incredibly slow. However, I was taught that the adiabatic equation $$P_1V_1^\gamma = P_2V_2^\gamma$$ is valid for all adiabatic processes, and that adiabatic processes can be carried out quickly (irreversibly) or slowly (reversibly). Is this true, or am I misunderstanding any of it?

Related to my question, this question states as fact that "adiabatic expansions and compressions involving ideal gases are reversible and follow $$PV^\gamma$$ constant, provided the process is quick enough." However, it was my understanding, as I mentioned, that quick processes are irreversible. So some clarification about speed and reversibility of processes would be helpful.

• Slow enough to be considered reversible, fast enough to be considered adiabatic. E.g. pressure change in free air leads to adiabatic compresion/expansion of air. But if too slow, there would be heat transfer with surrounding. Dec 10, 2021 at 13:08
• And if there were perfectly insulating walls, wouldn't a faster process be unnecessary? As we're considering ideal gases, wouldn't this ideal scenario mean that adiabatic processes could happen slowly? Dec 10, 2021 at 13:19
• Sure, an isolated system can perform an adiabatic process in infinite time. For real cases one must evaluate if idealizing assumptions are true. As no process can take infinite time, truly reversible processes do not exist. but many processes can be considered reversible with negligible error. Dec 10, 2021 at 13:22
• Your "adiabatic equation" is valid only for adiabatic reversible processes of ideal gases. Adiabatic expansions and compressions involving ideal gases are reversible and follow this equation only if the process is slow enough. Rapid adiabatic expansions and compressions are irreversible and do not obey that equation. Dec 10, 2021 at 13:49