A gas refrigeration system using air as the working fluid has a pressure ratio of 4. Air enters the compressor at -7°C. The high-pressure air is cooled to 27°C by rejecting heat to the surroundings. It is further cooled to -15°C by regenerative cooling before it enters the turbine. Assuming both the turbine and the compressor to be isentropic and using constant specific heats at room temperature, determine,
(a) The lowest temperature that can be obtained by this cycle,
(b) The coefficient of performance of the cycle, and
(c) The mass flow rate of air for a refrigeration rate of 12 kW.