# Theoretic restrictions for isothermal processes

As far as I understand, in thermodynamics an isothermal process is a process (a state change) during which the temperature of the system remains constant.

If I consider an ideal gas, the work obtained from (or put into) the system during an isothermal expansion (or compression) from volume $V_1$ to volume $V_2$ is $W = n R T \ln \frac{V_2}{V_1}$.

Considering this equation alone, I'm puzzled, as $\ln$ as a function is unbounded. This equation alone means that by letting my gas expand to arbitrarily large volume, I can get out arbitrarily large amounts of work. As this obviously cannot be the case, there must be something that forbids the assumption of expansion to arbitrarily large volume. What is this something?

Please understand I see there would be technical obstacles (e. g. how would you build a machine that can handle arbitrarily large volumes?) but I am not interested in these. I'm asking for a theoretical reason that restricts expansion, or a characterisation of the set of possible isothermal processes of a system (an ideal gas) in a given state.

• As long as you keep adding heat, the volume can continue to increase, albeit at lower pressure. So you can continue to do work as long as you add more heat. – Chet Miller Jun 24 '18 at 16:33
• I see. Is it correct to expand this argument to saying that isothermal expansion of an ideal gas is possible only by adding heat? So that an isothermal expansion of an isolated system is impossible? (Is it correct to say that for an ideal gas, constant temperature means constant internal energy, so the energy for any work done must come from the outside?) – MHvM Jun 24 '18 at 16:50
• Yes. That is correct (neglecting changes in potential and kinetic energy). – Chet Miller Jun 24 '18 at 19:41