We operate the engine between a hot and a cold reservoir kept at temperatures T h and T c. All net changes accompanying the operation of the engine thus occur in the universe. To be useful as a continuous source of power it must be capable of being operated in cycles, so that at the end of every cycle the engine gets back to the same state from which it started. 1.10.3 Operation of a Heat EngineĬonsider now the operation of a heat engine. No process for which S decreases can occur in an (adiabatically) isolated system conversely, any process for which S increases in such a system will be spontaneous.įor a system A which exchanges heat with surroundings B we consider an enlarged system in which the original system and all of its surroundings form a composite isolated system for which dS tot = dS A + dS B ≥ 0. Note once more that the state function S serves as a means of monitoring whether a given process in an (adiabatically) isolated system is indeed possible. If an irreversible process proceeds at all, it must go in the spontaneous direction that increases the entropy when quiescence sets in the entropy will be at a maximum consistent with the imposed constraints. Note again the very nature of an irreversible process: one can never reverse the process and return to the starting point without incurring other changes in the universe also, one cannot influence any event in an isolated system. Which is known as the Clausius inequality. Which of these alternatives do we choose? No other changes have occurred in the universe. That is to say: in executing a cycle we have expended (i.e., put into the system) an amount of heat đ iQ 1→2 + đ rQ 2→1 > 0 and have obtained from the system (i.e., the system has performed) an exactly equal amount of work đ iW 1→2 + đ rW 2→1 0 and we have obtained from the system (i.e., the system has transferred to its surroundings) an exactly equal amount of heat đ iQ 1→2 + đ rQ 2→1 < 0. (1.10.1), the work involved in completing the cycle by going from 1 to 2 and back to 1 is given by đ rW 1→2 – đ iW 1→2 = –(đ iW 1→2 + đ rW 2→l) > 0. Suppose first that đ iQ 1→2 – đ rQ 1→2 ≡ đ iQ 1→2 + đ rQ 2→1 > 0 then, by Eq. Thus, the algebraic sums in (1.10.1) must be either positive or negative. This, however, would lead to a contradiction of terms. If they did the reversible and irreversible paths would have to coincide, because đ Q and đ W depend on the chosen paths. Note that the energy differentials have canceled out being functions of state, they are the same for both processes.
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