Using the van der Waals equation of state expressed in "reduced variables," namely,
(PR + (3/V2R)) (VR - 1/3) = 8/3 TR,
Where PR = P/Pc, VR = v/vc, and TR = T/Tc, calculate values for the following critical-point exponents: (a) δ; (b) ϒ,. From the molar internal energy for the van der Waals gas, given by
u = cT - (a/V),
(c) calculate the critical-point exponent α.