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

Answer:

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 $T_{h}$ = 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 = $\frac{T_{h} }{T_{h}- T_{c} }$ = $\frac{521.3}{521.3- T_{c} }$

8.7 = $\frac{521.3}{521.3- T_{c} }$

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