A mathematical model is developed, based on a control volume for suction, pressure, and discharge volume.

The basic equations, the equations of continuity, energy, and motion, are integrated over these control volumes and are reduced to the lumped parameter system using the Leibninz formula for differentiating a volume integral.

The reed valve, used for a discharge valve, is also considered a lumped parameter system: the mathematical model of the valve is treated as a massspring system with damping.

The simultaneous differential equations for these models are solved numerically by the Kutta-Merson method, and the results for a real gas, refrigerant 12, are in close agreement with experimental results.

Units: SI