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 V1 to volume V2 as follows.
W=∫V2V1PdV=RT∫V2V1dVV=RTln(V2/V1)