Speed dependence of the efficiency of heat engines

We have studied the efficiency and power output of a simple model of an irreversible heat engine as a function of cyclic operating frequency. The model adopted is defined by a reversibly cycled working substance coupled to heat source and sink by thermally conducting walls. The maximum operating frequency corresponding to zero external power output is associated with the traversal of a limit cycle in the working substance. Closed form expressions for the maximum operating frequencies are derived for the special cases of isothermal and polytropic limit cycles.