A compressor driven by an electric motor is used to compress

A compressor driven by an electric motor is used to compress carbon dioxide (CO_2) CO_2 enters the compressor at 600 L/min with a temperature of 300 K and pressure of 95 kPa. At the exit of the compressor the CO_2, is at a temperature of 450 K and a pressure MPa. Heat is lost from the compressor during steady operation at a rate of 750 W. The electric motor driving the compressor has an electrical to mechanical efficiency of 89%. It is desired to determine the electrical power required to drive the compressor-electric motor system. Draw a system diagram showing the system boundary as well as indicating all heat transfer and work interactions. Outlining any necessary assumptions, develop an expression for the electrical power input required drive the compressor-electric-motor system based on a first law analysis. Determine the mass flow rate of CO_2 into the compressor. Utilizing the constant average specific heat assumption determine the required power input to the compressor.

Solution

An air compressor is a device that converts power (using an electric motor, diesel or gasoline engine, etc.) into potential energy stored in pressurized air (i.e., compressed air). By one of several methods, an air compressor forces more and more air into a storage tank, increasing the pressure. When tank pressure reaches its upper limit the air compressor shuts off. The compressed air, then, is held in the tank until called into use. The energy contained in the compressed air can be used for a variety of applications, utilizing the kinetic energy of the air as it is released and the tank depressurizes. When tank pressure reaches its lower limit, the air compressor turns on again and re-pressurizes the tank.