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

Answer:

a)$Q_H=16.4kW$

b) $w=5.467$

c)  $w=1.2345$

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

$COP=\frac{Q_H}{w}$

Therefore

$w=\frac{Q_H}{COP}$

$w=16.4/3$

$w=5.467$

c)

Generally the equation for coefficient of performance is mathematically given by

$COP_r=\frac{TH}{TH-TC}$

$COP_r=\frac{20+273}{(20+273)-(2+273)}$

$COP_r=16.2$

Therefore

$w=1.2345$

$w=20/16.2$

$w=1.2345$