The Second Law of Thermodynamics and Optimal Bounds for the Efficiency of Cyclic Processes

Abstract

The paper shows the equivalence of Clausius' inequality to a certain bound on the efficiency of any general cyclic process, as well as the equivalence of the entropy inequality to a certain bound on the work performed in any general process. These bounds are expressed in terms of a geometrical characteristic of the functions accounting the absorption and emission of heat in terms of the temperatures at which the exchange takes place, namely the "baricenters" or "first moments" of these functions. Further, with the aid of general heat transfer inequalities between the system and its environment the analysis is extended to take into account the temperatures of the environment. All known bounds on efficiency and on work are shown to be consequences of the main result; in fact, they are seen to be estimates cruder than those here presented, which, in this sense, may be called optimal.