# 8.3: Isothermal Expansion of an Ideal Gas

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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 *V _{1}* to volume

*V*as follows.

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