The reversible work per mol done, Wrev, to expand a fuid from a molar volume

V1 to a molar volume V2 is given by

$\displaystyle W_{rev} = - \int^{V_{2}}_V_{{1}} P dV $

Where P the the pressure of the fluid at a volume V.

Calculate Wrev when

**a)** $\displaystyle PV = RT $ - - i.e. an ideal gas. Assume that the temperature, T, is constant

(i.e. an isothermal expansion).

**b)** $\displaystyle P = KV^{- \gamma} $ and K, $\displaystyle \gamma $ are constants. Adiabatic expansion of an ideal gas. For information's sake $\displaystyle \gamma = \frac{C_{p}}{C_{v}} $ where where Cp and Cv are the heat capacities at constant pressure and volume respectively.

**c)** $\displaystyle P = \frac{RT}{(V-b)} - \frac{a}{V^{2}} $ - van der Waals equation of state with a and b constants,

assume that the temperature T is constant.