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## Homework Statement

In calculus, the work done when a gas expands from volume V

_{1}to volume V

_{2}is given by

W = ∫

^{V2}

_{V1}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 V

_{1}to V

_{2}is

W = nRT ln(V

_{2}/V

_{1})

## Homework Equations

Q = ΔU + W

PV = nRT

## The Attempt at a Solution

W = [VP]

^{V2}

_{V1}= PV

_{2}- PV

_{1}= 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.