Question

A heat pump is used to maintain a house at 22°C by extracting heat from the outside air on a day when the outside air temperature is 2°C. The house is estimated to lose heat at a rate of 110,000 kJ/h, and the heat pump consumes 5 kW of electrical power when running. Is this heat pump powerful enough to do the job?

Answer 1

Answer:

It is enough

Explanation:

To develop the problem it is necessary to take into account the concepts related to the coefficient of performance of a pump.

The two ways in which the performance coefficient can be expressed are given by:

$COP_p = \frac{T_H}{T_H-T_L}$

Where,

$T_H =$High Temperature

$T_L =$ Low Temperature

And the other way is,

$COP_p = \frac{\dot{Q}}{W}$

Where $\dot{Q}$ is heat rate and W the power consumed.

We have all our terms in Celsius, so we calculate the temperature in Kelvin

$T_H = 22+273 = 295K$

$T_L = 2+273 = 275k$

The rate at which heat is lost is:

$\dot{Q} = 110000kJ/h$

The power consumed by the heat pump is

$\dot{W} = 5kW$

And the coefficient of performance is

$COP_p = \frac{T_H}{T_H-T_L}$

$COP_p = \frac{295}{295-275}$

$COP_p = 14.75$

With this value we can calculate the Power required,

$COP_p = \frac{\dot{Q}}{W}$

$14.75 = \frac{110000}{W}$

$W = \frac{110000}{3600*14.75}$

$W = 2.07kW$

The power consumed is consumed is 5kW which is more than 2.07kW so this heat pump powerful enough.