To heat a house, a heat pump(HP) is used during the winter time. The COP of that heat pump is 1.4 and the HP is to produce 70,000 Btu/hr of heat to the house. How much power is needed for the heat pump to operate properly?

 To heat a house, a heat pump(HP) is used during the winter time. The COP of that heat pump is 1.4 and the HP is to produce 75,000 Btu/hr of heat to the house. How much power is needed for the heat pump to operate properly?

To heat a house, a heat pump(HP) is used during the winter time. The COP of that heat pump is 1.4 and the HP is to produce 70,000 Btu/hr of heat to the house. How much power is needed for the heat pump to operate properly?

 

coefficient of performance of heat pump , COP = 1.4

heat supply by heat pump to room , `Q_{2}`  =  70000 Btu/hr

 

so, we know that 

 

coefficient of performance of heat pump , COP = `\frac{heatSupplied}{powerInput}`

 

                                                                      COP = `\frac{Q_{2}}{W}`

`

                                                                      1.4 = `\frac{70000}{W}`

 

                                                                     W =  `\frac{70000}{1.4}`

                                                                    W = 50000 Btu/hr

Hence, power is needed for the heat pump to operate properly is 50000 Btu/hr