On the efficiency of thermal engines with power output: Consideration of inertial effects

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Abstract
We consider an idealized heat engine with nonzero power output, which receives heat from and rejects heat to reservoirs by linear heat conduction and produces work in the surroundings by providing kinetic and potential energy to a mass in the gravitational field. The working fluid of the engine is in internal equilibrium. For this engine we write the equations of motion including inertial effects, i.e., we include Newton’s equation for conservation of momentum. We define variables, controls, parameters, and boundary conditions in these equations in connection with the optimization of some performance (cost) functional. The conceptual neglect of inertial effects, as has been done previously, is shown to change the set of variables and controls, thus changing the optimization problem. Furthermore, the neglect of these terms leads to requirements of energy balance which must be incorporated as boundary conditions. We do not solve any optimization problem explicitely but show that appropriate inclusion of inertial effects in such engines precludes in the optimal cycle the existence of isothermal branches which are not preceded and followed by acceleration and deceleration branches.