Abstract: In this paper,the power and efficiency of the finite time steady-state heat engine operating between two reservoirs with finite heat-capacity rate are studied.The optimum power and efficiency of the finite time endoreversible Carnot heat engine under two kinds of restraining conditions and operating in two cyclic modes are derived analytically, and some new performance limits of the finite time thermodynamics are discussed.

Key words: endoreversible Carnot cycle, finite time thermodynamics, finite heat reservoir, steady-state engine