A non-ideal gas work process: A Van der Waals gas has an equation of state given

Question

A non-ideal gas work process: A Van der Waals gas has an equation of state given by ( p + a/v2)(v - b) = RT, where R is the gas constant and v is the Specific volume. Calculate the work 1W2 = 21 pdv for an ISOTHERMAL expansion process using oxygen as the working fluid. Use T= 500K, v1 = 1m3/kg and v2 = 2m3/kg. Also use a = 0.01 kPam6/kg2 and b = 0.01m3/kg. For the R value calculation see # 3 on the formula sheet and note that W = 32 kg/kmole for oxygen. Draw the process on a p-v diagram. Expansion process in a piston cylinder: Air, assumed to behave as an ideal gas (pv = RT), undergoes adiabatic expansion in

Explanation / Answer

For oxygen, R = 8.314/32 = 0.2598 kJ/kg-K

(P + a/v^2)(v - b) = RT

P = RT/(v-b) - a/v^2

W = [Integral P dv]v1v2

= [Integral (RT/(v-b) - a/v^2) dv]v1v2

= [RT ln (v-b) + a/v]v1v2

= [RT ln (v2-b) - RT ln(v1 - b) + a/v2 - a/v1]

= RT ln ((v2-b)/(v1-b)) + a/v2 - a/v1

= 0.2598*500 ln ((2-0.01)/(1-0.01)) + 0.01/2 - 0.01/1

= 90.689 kJ/kg

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