Consider a regenerative gas refrigeration cycle using helium as the working fluid. Helium enters the compressor at 100 kPa and -10°C and is compressed to 300 kPa. Helium is then cooled to 20°C by water. It then enters the regenerator where it is cooled further before it enters the turbine. Helium leaves the refrigerated space at -25°C and enters the regenerator. Assuming both the turbine and the compressor to be isentropic, determine
(a) the temperature of the helium at the turbine inlet,
(b) the coefficient of performance of the cycle, and
(c) the net power input required for a mass flow rate of 0.45 kg/s.