$(15$ pt$)$ In a heat pump system which is used to meet the heating demand of a residential building, R$-134$a is used as the refrigerant. The building is losing heat at a rate of $50,000k\frac{J}{h}.$ The heat pump is using underground water at $6C$ as the heat source. The refrigerant enters the compressor at $260$ kPa and $0C,$ and it leaves at $0\mathrm{.}8$ MPa and $60C.$ The refrigerant exits the condenser at $30C$ and at $0\mathrm{.}8$ MPa $.$ Determine:

a$)$ the power input to the heat pump,

b$)$ the rate of heat absorption from the water,

c$)$ the increase in electric power input if an clectric resistance heater is used instead of a heat pump $($in kW$).$

Also, draw the T$-$s diagram of this heat pump.