Finite time optimizations of a Newton’s law Carnot cycle

Abstract

We treat the problem of optimal finite time operations of a heat engine using an arbitrary working fluid and working between two constant temperature heat reservoirs. We work in a simplified framework (’’Newton’s law thermodynamics’’) which considers only losses associated with the heat exchange processes. We find the operations which maximize power, efficiency, effectiveness, and profit and those which minimize the loss of available work and the production of entropy. We find that all these optimal operations take place with the working fluid exchanging heat at a constant rate with each reservoir (implying a constant rate of entropy production) and undergoing adiabatic processes instantaneously. We define ’’Carnot space’’ to be the set of all operations of the engine which consist of constant rate heat exchanges and instantaneous adiabats. All optimal operations are points in this space which is shown (within the model) to be three dimensional. The different optimal operations with different connotations of ’’optimal’’ as described above are compared within this framework. To further study the economic implication of this model we also view the operation of the engine as an economic production process with work as its output. We obtain a simple analytical form of the production function and see repeatedly that maximum profit operation is a compromise between operation which maximizes the power and operation which minimizes the loss of available work. The path of maximum profit is obtained as a function of the costs of power and of availability.