$11-56$ Consider a two$-$stage cascade refrigeration system operating between the pressure limits

of $0\mathrm{.}8$ and $0\mathrm{.}14$ MPa $.$ Each stage operates on the ideal vapor$-$compression refrigeration cycle

with refrigerant$-134$a as the working fluid. Heat rejection from the lower cycle to the upper

cycle takes place in an adiabatic counter$-$flow heat exchanger where both streams enter at

about $0\mathrm{.}4$ MPa $.$ If the mass flow rate of the refrigerant through the upper cycle is $0\mathrm{.}24k\frac{g}{s},$

determine $($a$)$ the mass flow rate of the refrigerant through the lower cycle, $($b$)$ the rate of heat

removal from the refrigerated space and the power input to the compressor, and $($c$)$ the

coefficient of performance of this cascade refrigerator. Answers: $($a$)0\mathrm{.}195k\frac{g}{s},($b$)34\mathrm{.}2$ kW $,$

$7\mathrm{.}63kW,(c)4\mathrm{.}49$