A heat pump is operating between a low temperature reservoir of 270 K and a high temperature reservoir of 340 K. The heat pump receives heat at 255 K from the low temperature reservoir and rejects heat at 355 K to the high temperature reservoir. The heating coefficient of performance of the heat pump is 3.2. The heat transfer rate from the low temperature reservoir is 30 kW. The dead state temperature is 270 K. Determine the,

a. Power input to the heat pump (kW)

b. Heat transfer rate to the high-temperature reservoir (kW)

c. Exergy destruction rate associated with the low temperature heat transfer (kW)

d. Exergy destruction rate of the heat pump (kW)

e. Exergy destruction rate associated with the high temperature heat transfer (kW)

f. Exergetic efficiency of the heat pump itself