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A system of volume V contains a mass m of gas at pressure p and temperature T. The macroscopic properties of the system obey the following relationship:

\(\left(p + \frac a{V^2}\right) (V - b) = mRT\)

Where a, b, and R are constants.

Obtain an expression for the displacement work done by the system during a constant-temperature expansion from volume V1 to volume V2. Calculate the work done by a system which contains 10 kg of this gas expanding from 1 m3 to 10 m3 at a temperature of 293 K. Use the values a = 15.7 x 10 Nm4, b = 1.07 x 10-2 m3 and R = 0.278 kJ/kg-K.

1 Answer

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As it is constant temp-expansion then

\(\left(p + \frac a{V^2}\right) (V - b) \) = constant (mRT) (k) as T = constant

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