Is the Heat Pump and Motor Setup Efficient?

[lostinsauce]

Not sure if I am doing this correct and do not have answer available...
A heat pump takes on 30,000BTU/hr of heat and uses 5030 watts. However its COP as an air conditioner is 2.19. How efficient is the pump and motor setup?

I am assuming the following:
Qh=30000 BTU/hr=11.79 hp
WKin=5030 W=5.03kW/0.746kW=6.74 hp * 2545 BTU/hr = 17,153 BTU/hr

COPhp= Qh/WKin=11.79/6.74= 1.75

So is that the efficiency or should I solve for Qc as such:
Qc= Qh - WKin= 30000 BTU/hr - 17153 BTU/hr= 12,847 BTU/hr

And then use Carnot's efficiency equation? But Qc or Qh are rates and not Th or Tl...any help would be appreciated.

 

[Andrew Mason]

Not sure if I am doing this correct and do not have answer available...
A heat pump takes on 30,000BTU/hr of heat and uses 5030 watts. However its COP as an air conditioner is 2.19. How efficient is the pump and motor setup?

I am assuming the following:
Qh=30000 BTU/hr=11.79 hp
WKin=5030 W=5.03kW/0.746kW=6.74 hp * 2545 BTU/hr = 17,153 BTU/hr

COPhp= Qh/WKin=11.79/6.74= 1.75

So is that the efficiency or should I solve for Qc as such:
Qc= Qh - WKin= 30000 BTU/hr - 17153 BTU/hr= 12,847 BTU/hr

And then use Carnot's efficiency equation? But Qc or Qh are rates and not Th or Tl...any help would be appreciated.

The units are distracting. I am not sure why you are using HP but I will convert to MKS (watts). 1 BTU/hr = .2931 W. 30000 BTU/hr = 8793 watts.

First of all, there is some ambiguity in the statement of the problem. What does it mean the the heat pump "takes on 30,000 BTU/hr of heat"?. Is this the heat removed from the cold reservoir or is it the heat delivered to the warm reservoir? I will assume it is the heat removed, ie. Qc.

Second, you have to be clear on what the question is asking. It is not asking for the COP of the heat pump. It is asking for the efficiency of the motor - ie. how much mechanical work it does for each unit of energy supplied. The 5.03 kW is the (electrical) power consumption of the motor. You have to find rate of mechanical work supplied to the pump by the motor. hint: It will be less than 5.03 kW.

AM