Optimal process durations of expansion of a heated gas with linear phenomenological transfer law

Abstract

An optimal motion of a piston is examined. The piston is fitted inside one cylinder, which contains ideal gas. The gas contacts a heat bath and is heated with given rate f (t) in finite time. The heat transfer between heat bath and gas obeys the linear phenomenological heat transfer law (LPHTL) 1 q (T )    . Optimal expansion problem of the heated gas is solved step by step. There exist an OMP for any given final time, an optimal process duration of expansion (OPDE) for maximum power output (MPO), and an OPDE for maximum work output (MWO) for fixed power output. Both the OPDE for MPO and the OPDE for MWO with fixed power output is obtained. The best performance of the system is obtained using finite time thermodynamics. Numerical calculations are performed. The results show that the leaking energy and the energy from the heat source change into work output of the expansion process. Both the MPO and MWO with fixed power increase with the increase of heat conductance K . The results obtained can provide some guidelines for real systems operating with LPHTL.