HW#$7-7(15$ pt$)$ A refrigerator uses R$-134$a as the working fluid and operates on the vapor$-$compression refrigeration cycle. The evaporator and condenser pressures are $200$kPa and $1400$ kPa $,$ respectively. The isentropic efficiency of the compressor is $88\%.$ The refrigerant enters the compressor at $0\mathrm{.}025k\frac{g}{s},$ superheated by $10\mathrm{.}1C($i$.$e$.,T_1=T_{\text{s}\text{a}\text{t}}+10\mathrm{.}1C)$ and leaves the condenser subcooled by $4\mathrm{.}4C($i$.$e$.,T_3=T_{\text{s}\text{a}\text{t}}-4\mathrm{.}4C).$ Determine $($a$)($i$)$ the rate of cooling provided by the evaporator, $($ii$)$ the power input, and $($iii$)$ the COP. Determine $($b$)$ the same parameters if the cycle operated on the ideal vapor$-$compression refrigeration cycle between the same pressure limits $($no subcooling, no superheating & isentropic compressor$).$