8.3: Isothermal Expansion of an Ideal Gas

An ideal gas obeys the equation of state PV = RT (V = molar volume), so that, if a fixed mass of gas kept at constant temperature is compressed or allowed to expand, its pressure and volume will vary according to PV = constant. That is, Boyle's Law. We can calculate the work done by a mole of an ideal gas in a reversible isothermal expansion from volume V₁ to volume V₂ as follows.

\[ W=\int_{V_{1}}^{V_{2}} P d V=R T \int_{V_{1}}^{V_{2}} \frac{d V}{V}=R T \ln \left(V_{2} / V_{1}\right)\]