Problem $2.$ A vapor$-$compression refrigeration cycle with refrigerant$-134$a as the working fluid is used to maintain a space at $-13C$ by rejecting heat to ambient air at $27C.$ R$-134$a enters the compressor at $100$kPa superheated by $6\mathrm{.}4C$ at a rate of $0\mathrm{.}05k\frac{g}{s}.$ The isentropic efficiency of the compressor is $85$ percent. The refrigerant leaves the condenser at $39\mathrm{.}4C$ as a saturated liquid. Determine the rate of cooling provided and the COP of the system,