Question

A heat pump with a 2 kW motor is used to heat a building at 30 deg C. The building loses heat at a rate of 0.5 kW per degree difference to the colder ambient at T amb. The heat pump has a coefficient of performance that is 50 % of a carnot heat pump. What is the maximum ambient temperature for which the heat pump is sufficient?

Answer 1

T=5.3° C

Step-by-step explanation:

Given that

Power input to the pump = 2 KW

Building loses heat rate = 0.5 KW/C

So rate of heat transfer = 0.5(273+30-T)

rate of heat transfer = 0.5(303-T)

T=Ambient temperature

Building temperature = 30° C

We know that ,heat pump is used to heat the building.

COP of pump = 0.5 COP of Carnot heat pump

`COP\ of\ Carnot\ heat\ pump=(273+30)/(303-T)`

`COP\ of\ Carnot\ heat\ pump=(303)/(303-T)`

`COP\ of\ pump=(303-T)/(Power)`

`COP\ of\ pump=0.5* (303-T)/(2)` -----1

And also

`COP\ of\ pump=(1)/(2)* (303)/(303-T)` ----2

So from now equation 1 and 2

`(303-T)/(4)=(1)/(2)* (303)/(303-T)`

So T= 278.38 K=5.3° C

T=5.3° C

Ambient temperature =5.3° C.