A single stage, vapour compression refrigeration system based on propane $($R$-290)$ uses a

liquid$-$to$-$suction$-$heat exchanger $($LSHX$)$ that has an effectiveness of $0\mathrm{.}8.$ The system

operates at an evaporating temperature of $7C$ and a condensing temperature of $54C.$ The

refrigerant condition at the exit of condenser is saturated liquid, while it is saturated vapour at

evaporator exit. The saturated properties of propane at condensing and evaporating

temperature are given below. The compression process is reversible, adiabatic and the

temperature of the refrigerant at the exit of compressor is $92\mathrm{.}8C.$ Estimate the COP of the

system with LSHX taking average specific heat $(c_p)$ of vapour at evaporator and condensing

pressures as $1\mathrm{.}86k\frac{J}{k}g.K$ and $2\mathrm{.}40k\frac{J}{k}g.K,$ respectively.