1. The problem statement, all variables and given/known data In calculus, the work done when a gas expands from volume V1 to volume V2 is given by W = ∫V2V1 P dV Use this expression to show that the work done by n moles of gas at temperature T during an isothermal expansion from volume V1 to V2 is W = nRT ln(V2/V1) 2. Relevant equations Q = ΔU + W PV = nRT 3. The attempt at a solution W = [VP]V2V1 = PV2 - PV1 = PΔV But I think it should be ΔPΔV since this is an isothermal expansion. W = PΔV is for isobaric since P is constant. Then I can't even guess where the ln comes from.