The van der Waals equation of state, an approximate representation of the behavior of gases at high pressure, is given by

Where a and b are constants having different values for different gases. (In the special case of a = b = 0, this is the ideal-gas equation.)
(a) Calculate the work done by a gas with this equation of state in an isothermal expansion from VI to V2€¢ Show that your answer agrees with the ideal-gas result found in Example 19.1 (Section 19.2) when you set a = b = 0.
(b) For ethane gas (C2H6), a = 0.554 J €¢ m3/mol2 and b = 6.38 X 10-5 m3/mol. Calculate the work W done by 1.80 mol of ethane when it expands from 2.00 X 10-5 m3 to 4.00 X 10-5 m3at a constant temperature of 300 K. Do the calculation using (i) the van der Waals equation of state and (ii) the ideal-gas equation of state.
(c) How large is the difference between the two results for W in part (b)? For which equation of state is W larger? Use the interpretation of the terms a and b given in Section 18.1 to explain why this should be so. Are the differences between the two equations of state important in this case?

an? - nb) = nRT y