A two$-$stage compression refrigeration system operates with refrigerant$-134$a

between the pressure limits of $1$ and $0\mathrm{.}14$ MPa $.$ The refrigerant leaves the

condenser as a saturated liquid and is throttled to a flash chamber operating at

$0\mathrm{.}5$ MPa $.$ The refrigerant leaving the low$-$pressure compressor at $0\mathrm{.}5$ MPa is

also routed to the flash chamber.

The vapor in the flash chamber is then compressed to the condenser pressure

by the high$-$pressure compressor, and the liquid is throttled to the evaporator

pressure. Assuming the refrigerant leaves the evaporator as a saturated vapor,

and both compressors are isentropic$,$

Determine:

$($a$)$ the fraction of the refrigerant that evaporates as it is throttled to the

flash chamber,

$($b$)$ the rate of heat removed from the refrigerated space for a mass flow

rate of $0\mathrm{.}25$kg$//$s through the condenser,

$($c$)$ the coefficient of performance.

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