# Heat pumps and coeffiecent of performance

1. Feb 24, 2007

### rmorelan

Hi everyone, I was hoping to ask a thermodynamics problem, specificially one about heat pumps and coeffiecent of performance. I am wondering if I am missing something.

I am given that heat pump is heat a building. Inside temperature is to be maintained at 22 degree celcius, outside is -5.0 celcius. The coefficent of performance is 3.8, and the the pump delivers 7.6MJ of heat each hour to the building. I need to find out at what rate work needs to be applied to run the pump.

2. Relevant equations

Now I believe the equation of the the coeffiecient of performance (CP) is equal to:

cp = |Q|/W

Now this is where I am confused, as I don't understand what (if anything) I am supposed to do with the temperatures given. I know cp, and I know Q, so I can solve for W needed to run the pump can't I? I would need to convert the heat produced to be in SI in order to get Watts as a result of course.

rob

2. Feb 25, 2007

### Hootenanny

Staff Emeritus
If we treat the heat pump as a Carnot heat pump we can say that;

$$\frac{Q_2}{Q_1} = \frac{T_2}{T_2}$$

Hence;

$$\eta^{HP}_{C} = \frac{Q_1}{W} = \frac{Q_1}{Q_1-Q_2} = \frac{T_1}{T_1-T_2}$$

Where T1 and T2 are the temperatures of the hot and cold reservoirs respectively.