As energy efficient devices become more necessary, it is desired to increase the efficiency of air conditioning systems. Current systems use on/off control, where the unit primarily operates in the long lasting start up transients. A proposed solution is an air conditioning unit that runs continuously with active computer control implemented to maximize efficiency. The objective of this thesis is to develop a mathematical model for a specific air conditioning unit and to compare this model to measurements made on the specific unit. This model can then be used to develop a multi-input multi-output control law in the future. In this thesis, a linearized moving interface lumped parameter model is presented, and the derivation verified with great detail. The model predicts transient perturbations from a steady state operating point. The air conditioner tested in this work required several modifications including the addition of sensors and controllers. A description of the system is provided. Methods used to determine all of the parameters for the model are given with explanation. The model is simulated with computer software and compared with experimental data. Simulations predict the final value of superheat and pressures in the evaporator and condenser well for step changes in the compressor speed and expansion valve opening.