Question

A heat pump is to be used to heat a house during the winter, as shown in Fig. 6–52. The house is to be maintained at 21 ℃ at all times. The house is estimated to be losing heat at a rate of 135,000 kJ/h when the outside temperature drops to -5 ℃. Determine the minimum power required to drive this heat pump.

Answer 1

`3.32\ \text{kW}`

Step-by-step explanation:

`T_c` = Outside temperature =
`-5^(\circ)\text{C}`

`T_h` = Temperature of room =
`21^(\circ)\text{C}`

`Q_h` = Heat loss = 135000 kJ/h =
`(135000)/(3600)=37.5\ \text{kW}`

Coefficient of performance of heat pump

`\text{COP}=(1)/(1-(T_c)/(T_h))\\\Rightarrow \text{COP}=(1)/(1-(273.15-5)/(273.15+21))\\\Rightarrow \text{COP}=11.3`

Input power

`W_i=\frac{Q_h}{\text{COP}}\\\Rightarrow W_i=(37.5)/(11.3)\\\Rightarrow W_i=3.32\ \text{kW}`

The minimum power required to drive this heat pump is
`3.32\ \text{kW}`.