1. The problem statement, all variables and given/known data 2. Relevant equations Using the Carnahan and Starling equation, estimate the coefficient of volumetric expansion, α, and the coefficient of compressibility, β, defined as α ≡ 1/V * (δV/δT) [holding P constant] and β ≡ -1/V * (δV/δP) [holding T constant] (I've used δ here for partial differentials) for the hard sphere fluid at a packing fraction η = 0.40. 3. The attempt at a solution I've tried using Z = PV/nkT and then the CS expression for Z: Z = (1+η+η²-η³) / (1-η)³ however we find α = 1/T and β = 1/P which seems far too easy. Could someone please offer a suggestion of which direction I should be looking in? Any help would be greatly appreciated!!