The entropy is given by the entropic equation of state: s − − C s = ∫ ∫ c v ( T ) d T T + ∫ ∫ ∂ ∂ p ∂ ∂ T d v Using c v = c R as before, and integrating the second term using ∂ ∂ T p = R / ( v − − b ) we obtain simply s − − C s = R ln ⁡ ⁡ [ T c ( v − − b ) ] This is the entropic equation of state for a perfect vdW fluid, or in reduced form s r − − C s = ln ⁡ ⁡ [ T r c ( 3 v r − − 1 ) ]