Question

How do you calculate work for isothermal processes?

Answer 1

The basic premise is constant temperature. For ideal gases, the change in internal energy `U` is a function of ONLY temperature. From the first law of thermodynamics, we must have:

`overbrace(cancel(DeltaU))^("0 for "DeltaT = 0) = q + w`

And the work `w` done by or on the system is equal to the heat flow `q` into or out from the system, respectively:

`ul(w = -q)`

[This is the simplest case, and is shown here in further detail.](https://socratic.org/questions/what-is-reversible-isothermal-expansion)