Correction to my paper: On transfer functions and transients
Armen H. Zemanian · Quarterly of Applied Mathematics · 1959
we have -f p dV = AA = -AS AT,(3) Jc where C is a Carnot cycle which proceeds first along an adiabatic, then along an isothermal, then an adiabatic, and then along an isothermal to the starting point.We conclude that the family of isothermals T = Tx + nAT and the family of adiabatics S = Si + nAS, n = 0, ± 1, ±2, ±3, • • • drawn in the p, V plane map out equal areas AA in this plane.Thus, if for any gas the isothermals p = Pi(V) and the adiabatics p = p"(V) are determined by experiment, the "labels" S and T for the curves may then be determined for it is merely necessary to label as 0 the isothermal along which water freezes and as 100 the isothermal along which water boils at atmospheric pressure.The labels of the curves T = const, are then determined by Eq. ( 3) uniquely.Any pair of curves may be labeled S = I and S = 2 along any isothermal.The unit of entropy is related to the unit of mechanical energy by resorting again to Eq. ( 3).The labels for the intervening curves S = const, are also uniquely determined by Eq. ( 3).Entropy and absolute temperature S and T as thus determined for one gas must be consistent with S and T determined for any other gas due to the principle of conservation of energy.The extent to which the areas A A in the p, V plane are equal indicates the extent to which the postulated equation ( 2) is valid.