In view of the limitations of certain modeling techniques, it appears that the most practical way of studying the interaction of the instantaneous performance characteristics of the various components is a full-fledged mathematical simulation model. In a mathematical simulation model the instantaneous processes are described locally in terms of pertinent variables such as temperatures, pressures, mass flow rates, etc., which in turn have been calculated from piston motions, heat transfer rates, and frictional pressure drops; which in turn are dependent on temperatures, pressures, mass flows, etc. The result is a system consisting of a large number of dependent differential and algebraic equations that have to be solved simultaneously. Mathematical simulation models permit not only studies of the interaction of the various components of a system, but also the interactions of the performance of the various parts of any one of these components. The study of the performance of one of these components, the compressor, by mathematical simulation models, is the topic of the present paper.