The enthalpy is h = u + p v , and the product p v is just p v = R T v / ( v − − b ) − − a / v . Then h is simply h − − C u = R T [ c + v / ( v − − b ) ] − − 2 a / v This is the enthalpic equation of state for a perfect vdW fluid, or in reduced form h r − − C u = [ c + 3 v r / ( 3 v r − − 1 ) ] T r − − 9 / ( 4 v r ) where h r = h / ( R T c c )