Question

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.

Answer 1

Heat of the reservoir is 461.38 K or 188.1 °C

The heating load is 18.705 kW

Step-by-step explanation:

COP = 8.7

working temperature
`T_(h)` = 248 °C = 248 + 273.3 = 521.3 K

work power W = 2.15 kW

reservoir temperature
`T_(c)` = ?

heating load Q = ?

We know that

COP = Q/W

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

Also,

COP =
`(T_(h) )/(T_(h)- T_(c) )` =
`(521.3)/(521.3- T_(c) )`

8.7 =
`(521.3)/(521.3- T_(c) )`

4535.31 - 8.7
`T_(c)` = 521.3

4535.31 - 521.3 = 8.7
`T_(c)`

4014.01 = 8.7
`T_(c)`

`T_(c)` = 4014.01/8.7 = 461.38 K

or 461.38 -273.3 = 188.1 °C