On a cold night a house is losing heat at a rate of 15 kW A

On a cold night a house is losing heat at a rate of 15 kW. A reversible heat pump maintains the house at 20 C while the outside temperature is 0 C.

Part A

Determine the heating cost for the night (8 hours). Assume the price of electricity to be 17 cents/kWh .

Express the cost per night in dollars to three significant figures.

Part B

Also determine the heating cost if resistance heating were used instead. Assume the price of electricity to be 17cents/kWh .

Express the cost per night in dollars to two significant figures.

>> Reversible Heat Pump

>> Q\" = Heat Lose by the House = 15 kW

As, to maintain house temperature, at 20 C, pump has to provide 15 kW heat to house, which it is loosing to surroundings.

=> Q1 = Heat Supplied by Pump to house = 15 kW

>> T1 = Source temperature = 20 C = 293 K

>> T2 = SInk Temperature = 0 C = 273 K

Now, COP = T1/(T1 - T2) = Q1/W

=> 293/(93 - 273) = 15/W

=> 14.65 = 15/W

=> W = 1.024 kW

>> As, in night, Total No of Hours are = 8 hours

So, Total No of Units Consumed = 1.024*8 = 8.19 kWh

>> Now, Price of Electricity = 17 cents/kWh

So, Total Heating Cost = 8.19*17 = 139.23 cents

=> Required Cost = $ 1.392

>> Part B

>> Now, Total Power Required = 15 kW

So, Total No of Units are = 15*8 = 120 kWh

So, Total Cost = 120*17 cents = $ 20.40 .....ANSWER....