 Thus, a heat engine operating between "T"1 and "T"3 must have the same efficiency as one consisting of two cycles, one between "T"1 and "T"2, and the second between "T"2 and "T"3.This can only be the case if

which implies

Since the first function is independent of "T"2, this temperature must cancel on the right side, meaning "f"("T"1, "T"3) is of the form "g"("T"1)/"g"("T"3) (i.e.= = = , where "g" is a function of a single temperature.