The vehicle air-conditioning system has significant impact on fuel economy and range of electric vehicles. Improving the fuel economy of vehicles therefore demand for energy efficient climate control systems. Also the emissions regulations motivate the reduced use of fuel for vehicle's cabin climate control. Solar heat gain of the passenger compartment by greenhouse effect is generally treated as the peak thermal load of the climate control system. Although the use of advanced glazing is considered first to reduce solar heat gain other means such as ventilation of parked car and recirculation of cabin air also have impetus for reducing the climate control loads. However experimental based recirculation control strategies may lead to - 1) increased humidity levels, increasing the risk of windshield fogging, especially during cabin heating operation, 2) unpleasant odors due to biological aerosols and harmful volatile organic compounds and 3) insufficient oxygen and high CO2 levels inside the cabin. The analytical method is proposed to determine compressor work for a given cabin cooling requirement defined by the evaporator outlet air temperature and a mixing ratio and for known coefficient of performance of the compressor, the mass flow of evaporator air and the enthalpies of air from outside and inside of the passenger compartment. The compressor work is obtained as a linear function of mixing ratio for the unsaturated evaporator outlet air and a quadratic function for the saturated evaporator outlet air. The solution of these expressions is found to re-emphasize the fact that the least-enthalpy of air at the evaporator inlet requires minimum compressor work for cooling of the air. The applicability of a proposed method is demonstrated by using the closed loop simulation results obtained with the help of a thermal simulation tool - eThermal under various vehicle operating conditions. Particularly, reduced compressor power for cabin cooling while maintaining thermal comfort and safety of the vehicle occupants is observed. Correlations for calculating coefficient of performance of a compressor are also provided.