A new ground$-$source heat pump is used to provide heating in a residential building. The working fluid, R$-134$a$,$ enters the evaporator with a quality of $22\%$ at $3\mathrm{.}4$ bar and leaves at $3\mathrm{.}2$ bar superheated by $5\backslash$deg C$.$ The compressor has an isentropic efficiency of $88\%.$ A well$-$insulated water$-$cooled condenser is used to transfer heat from the refrigerant to the building. The refrigerant enters the condenser at $13\mathrm{.}0$ bar and leaves at $12\mathrm{.}0$ bar, subcooled by $4\mathrm{.}3\backslash$deg C$.$ The cooling water enters the condenser at $10\backslash$deg C and $4\mathrm{.}0$ bar with a mass flow rate of $0\mathrm{.}5$ kg$/$s and leaves at $25\backslash$deg C with negligible pressure drop. For this heat pump system:a$)$ Draw and label a schematic diagram and the T$-$s diagramb$)$ Calculate the mass flow rate of the refrigerant, in kg$/$sc$)$ Determine the heating load provided by the heat pump, in kWd$)$ Calculate the COP of the heat pump