(Solved): A gas refrigeration cycle with a pressure ratio of 3 uses helium as the working fluid. The temperat ...

A gas refrigeration cycle with a pressure ratio of 3 uses helium as the working fluid. The temperature of the helium is \( -10^{\circ} \mathrm{C} \) at the compressor inlet and \( 50^{\circ} \mathrm{C} \) at the turbine inlet. Assuming isentropic efficiencies of \( 80 \% \) for both the turbine and the compressor, determine (a) the minimum temperature in the cycle (b) the COP (c) the mass flow rate of the helium for a refrigeration rate of \( 18 \mathrm{~kW} \).