Abstract: This paper studied the effect of the finite constructional parameter on a class of endoreversible Carnot heat pumas with pitons. We used an ideal gas working substance and the crank linked up with the Pump rotated uniformly.The fundamental optimal relation of the pumps was derived, and some significant discussions were made. Some more instructive new conclusions for the real heat pumps were obtained.

Key words: finite time thermodynamics, constructional parameter, Carnot heat pump