Question

A heating system must maintain the interior of a building at TH = 20 °C when the outside temperature is TC = 2 °C. If the rate of heat transfer from the building through its walls and roof is 16.4 kW, determine the electrical power required, in kW, to heat the building using (a) electrical-resistance heating, (b) a heat pump whose coefficient of performance is 3.0, (c) a reversible heat pump operating between hot and cold reservoirs at 20 °C and 2 °C, respectively.

Answer 1

a)
`Q_H=16.4kW`

b)
`w=5.467`

c)
`w=1.2345`

Step-by-step explanation:

From the question we are told that:

Interior temperature
`TH = 20 °C`

outside temperature is
`TC = 2 °C`

Rate
`H=16.4kW`

a)

Generally electric resistance heating is the heat transfer from interior building

Therefore

`Q_H=R`

`Q_H=16.4kW`

b)

COP =3

Generally the equation for coefficient of performance is mathematically given by

`COP=(Q_H)/(w)`

Therefore

`w=(Q_H)/(COP)`

`w=16.4/3`

`w=5.467`

c)

Generally the equation for coefficient of performance is mathematically given by

`COP_r=(TH)/(TH-TC)`

`COP_r=(20+273)/((20+273)-(2+273))`

`COP_r=16.2`

Therefore

`w=1.2345`

`w=20/16.2`

`w=1.2345`