PX154 - D4c - isotherm

Δ U = Q - W = 0

heat absorbed by the system does work that doesn't increase the system's temperature
work done: $W = \int_{V_{1}}^{V_{2}} p . d V$
- from here: $p = \frac{n R T}{V}$ :

\begin{aligned} W & = \int_{V_{1}}^{V_{2}} \frac{n R T}{V} . d V \\ ∴ W & = n R T \ln [\frac{V_{2}}{V_{1}}] \end{aligned}