Thermodynamic constraints on temperature distribution in a stationary system with heat engine or refrigerator

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Journal Article
Journal of Physics D: Applied Physics, 2006, 39 (19), pp. 4269 - 4277
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In this paper we consider a stationary thermodynamic system that includes a transformer of mechanical energy into heat energy or heat into mechanical energy. We derive conditions that determine temperature distribution (temperature field) inside such a system permitted by thermodynamics. We obtain conditions that divide feasible temperature fields into two classes - one where mechanical energy has to be spent and another where it is extracted. Closed-form expressions for the minimal supplied/maximal extracted power are derived. It is shown that for a linear heat transfer law and heat engine operating at maximal power the ratio of engine working body's temperatures during contact with reservoirs is equal to the square root of the ratio of reservoirs' temperatures irrespective of the system's structure and whether the engine is internally irreversible or not. Therefore, an engine's efficiency at maximal power does not depend on its internal structure. The problem of maintaining given temperatures in a subset of inter-connected chambers is considered. The conditions that determine optimal temperatures in the chambers where temperatures are not fixed which minimize energy are derived. © 2006 IOP Publishing Ltd.
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