The kinetic energy of gas molecules or atoms is: (3/2)kTN/M where k is Boltzman constant, T is absolute temperature, N is avogadros number and M is molecular weight. The formula is derived from http://en.wikipedia.org/wiki/Kinetic_theory. Assume that the gas is steam with M = 18 kg/mol at 373K, it is equivalent to approximately 260 J/kg but suppose i cool the steam up to 40C based on Cdt + Lf (C is specific heat, dt is change in temperature and Lf is latent heat of vaporization), it becomes an overunity of 10420 more effective. From what assumption or derivation im wrong? or if i'm right where does the excess energy came from?