Thermodynamics Final answer is giving, show me how to get to it. If you get prop

Question

Thermodynamics

Final answer is giving, show me how to get to it.

If you get property values from a table, give the name of the table.

A heat pump provides 1,000 kW of heat to a house, maintaining its temperature at 20°C. The cold air outside the house, which is at 0°C, is used by the heat pump as its low-temperature reservoir. The heat pump operates at steady state. The actual COPHP of the heat pump is known to be 90 of the maximum COPHP possible. a. Determine the actual power input to the heat pump, in kW. CAns: W 75.8 kW) b. At what rate is heat removed from the cold air outside, in kW? CAns: QLE924.2 kW)

Explanation / Answer

Ans a) Let QH be the heat provided by the heat pump

Given QH = 1000kW

Let Ta be the temperature of the house =200C

                                                          =20+273K =293K

Let TL be the low temperature = 00C = 273K

Now It is given that

Actual COPHP = 90/100 possible COPHP

Actual COPHP =0.9 possible COPHP

Now Possible COPHP = 1/Ta/TL -1

                                 = 1/293/273 -1

                                 = 14.65

Actual COPHP = 0.9 x 14.65

                      =13.185

Now Let W be the actual power input to the heat pump

W= QH / Actual COPHP

    = 1000/13.185

    =75.84kW

Ans b) Let QL be the rate at which heat is removed from cold air outside

QL = QH - W

      =1000 - 75.84

      = 924.2kW

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