A gas refrigeration system using air as the working fluid has a pressure ratio of 5. Air

Question:

A gas refrigeration system using air as the working fluid has a pressure ratio of 5. Air enters the compressor at 0oC. The high-pressure air is cooled to 35oC by rejecting heat to the surroundings. The refrigerant leaves the turbine at - 80oC and then it absorbs heat from the refrigerated space before entering the regenerator. The mass flow rate of air is 0.4 kg/s. Assuming isentropic efficiencies of 80 percent for the compressor and 85 percent for the turbine and using constant specific heats at room temperature, determine
(a) The effectiveness of the regenerator.
(b) The rate of heat removal from the refrigerated space.
(c) The COP of the cycle. Also, determine
(d) The refrigeration load and the COP if this system operated on the simple gas refrigeration cycle. Use the same compressor inlet temperature as given, the same turbine inlet temperature as calculated, and the same compressor and turbine efficiencies.