In an isothermal expansion of an ideal gas, there cannot be any change in the internal energy otherwise the temperature would change. So hence we know that all the heat goes into work.
Knowing that $PV=nRT$ as the equation of state and $T$ being constant in this process, we see that $P$ is inversely proportional to $V$.
Does that mean in order to feasibly realize an isothermal expansion we would need to do the following:
- Put the ideal gas in a cylinder with a piston and some amount of weight on it to reach some pressure.
- Find a heat reservoir equal to the temperature of the gas.
- Slowly lift weight off of the piston according to $P \propto 1/V$.
The last part is kind of the strange part. We have to lift some weight off otherwise the volume won't change. But why can't we quickly lift the weight off? So the external pressure changes from some large number to a very smaller number? Would that be approximately an adiabatic expansion?
Editted: Just want to confirm the necessity of the last part where we are slowly decreasing the force applied by the piston. Not sure how to do that practically, you would need some kind of electronically controlled device to slowly "lift the weights off".
Best Answer
The isothermal expansion is a theoretical ideal. An isothermal process requires the system is in perfect equilibrium with its surroundings at all times so it would have to be done infinitely slowly. As you say in your question, any process done at a finite speed is necessarily out of equilibrium.
However in real life provided heat flow is fast enough processes can be so close to isothermal that we can treat them as perfectly isothermal. That is, the error involved in assuming they are isothermal is negligibly small.