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Work done by an ideal gas in an isothermal (constant-temperature) process (15-6)

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Ideal gas constant
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Review

On a pV diagram, the area under the curve represents the work W done by the gas; Figure 15-7b shows this area for an isothermal expansion. Unlike the isobaric case shown in Figure 15-6, the area under the curve is not a rectangle, so we cannot find W simply by multiplying the pressure and the change in volume. Using calculus, it can be shown that the work that the gas does as the volume changes is