Consider a two-stage cascade refrigeration system operating between the pressure limits of 2 MPa and 0.05 MPa. Each stage operates on an ideal vapor-compression refrigeration cycle with R-134a as the working fluid. Heat rejection from the lower cycle to the upper cycle takes place in an adiabatic counterflow heat exchanger where both streams enter at 0.5 MPa. If the mass flow rate of the refrigerant through the upper cycle is 0.25 kg/s, determine (a) the mass flow rate of the refrigerant through the lower cycle, (b) the rate of heat removal from the refrigerated space, (c) the power input to the compressor in the lower cycle and (d) the coefficient of performance (COPR) of this cascade refrigerator. What-if Scenario: What would the COP be if the heat exchanger pressure were (e) 0.4 MPa or (f) 0.7 MPa?