A heat pump operates on a Carnot heat pump cycle with a COP of 8.7. It keeps a space at 248C by consum-ing 2.15 kW of power. Determine the temperature of the reservoir from which the heat is absorbed and the heat-ing load provided by the heat pump.

Heat of the reservoir is 461.38 K or 188.1 °C

The heating load is 18.705 kW

Explanation:

COP = 8.7

working temperature = 248 °C = 248 + 273.3 = 521.3 K

work power W = 2.15 kW

reservoir temperature = ?

heating load Q = ?

We know that

COP = Q/W

Q = COP x W = 8.7 x 2.15 = 18.705 kW

Also,

COP = =

8.7 =

4535.31 - 8.7  = 521.3

4535.31 - 521.3 = 8.7  

4014.01 = 8.7  

 = 4014.01/8.7 = 461.38 K

or 461.38 -273.3 = 188.1 °C

a coal burning power plant

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west