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 , where R is the gas constant and v is the specific volume. Calculate the work 1W2 = 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 = 0.01 m3/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 a piston cylinder from the initial condition T1 = 2000K, p1 = 4 MPa, undergoes

Explanation / Answer

p = RT/(v - b) - a/V2

W = V1V2 [RT/(V - b) - a/V] dV = RT ln(V - b) + a/V |V1V2 = RT ln[(V2 - b)/(V1 - b)] + a(1/V2 - 1/V1)

= 8.31*500 ln[1.99/0.99] + 0.01(0.5 - 1) = 2900

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