A vapour$-$compression system having Freon $12$ as the working fluid is to be used as a heat pump to extract $23\mathrm{.}5$ kw from the ambient air outside a house at a temperature of o$\text{'}$c in order to transfer it to the air circulating inside of the house at $25\backslash$deg c$.$ There is a difference of $10\text{'}$c between the evaporator temperature and the outside air temperature as well as a difference of $7\mathrm{.}5\text{'}$c between the condenser temperature and the inside air temperature. For the purposes of the analysis, assume that the vapour entering the compressor is saturated, that the efficiency of the compression process is $88\%$ and that the liquid at the inlet of the expansion valve is saturated. Determine the coefficient of performance and use of the heat pump if the saving to be realized from the electricity is available at $4\mathrm{.}5$ cents per kilowatt hour. Indicate the process in the T$-$S Diagram.