An air conditioner using refrigerant$-134$a as the working fluid and operating on the ideal vapor$-$compression refrigeration cycle is to maintain a space at $22C$ while operating its condenser at $1000$ kPa $.$ Determine the COP of the system when a temperature difference of $2C$ is allowed for the transfer of heat in the evaporator.

Hints for analysis: Assume the compression process is isentropic$,$ the refrigerant enters the compressor as a saturated vapor at the evaporator pressure, and leaves the condenser as saturated liquid at the condenser pressure. Because of the stated temperature requirements, the temperature leaving the evaporator will be $222=20C.$

$CO{P}_{AC}=10\mathrm{.}8$

$CO{P}_{AC}=9\mathrm{.}6$

$CO{P}_{AC}=13\mathrm{.}4$

$CO{P}_{AC}=6\mathrm{.}5$

$7\mathrm{.}13$ kW

${10\mathrm{.}55}^{\text{'}}kW$

$8\mathrm{.}95$ kW

$7\mathrm{.}48$ kW

Total power input to the cascade cycle $($kW$)$

$2\mathrm{.}25$ kW

$1\mathrm{.}60$ kW

$1\mathrm{.}36$ kW

$0\mathrm{.}50$ kW

Determine'the coefficient of performance of the combined cycle

$1\mathrm{.}25$

$5\mathrm{.}5$

$4\mathrm{.}46$

$2\mathrm{.}95$