Question

To maintain a dwelling steadily at 68°F on a day when the outside temperature is 32°F, heating must be provided at an average rate of 740 Btu/min. Compare the electrical power required, in kW, to deliver the heating 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 68°F and 32°F,

Answer 1

a) 13.01 kw

b) 4.336 kw

c) 0.8875 kw

Step-by-step explanation:

Given:

Heating rate
`Q_H` = 740 Btu/min

`T_H` = 60°F = 293.15 K

`T_L` = 32° = 273.15 K

Performance-Coeff. = 3.0

a)

Electrical-Resistance Heating

`W_(elect)` =
`Q_H`

`W_(elect)` = 740 x (60 min / 1hr) x (1 kw / 341 Btu/min)

`W_(elect)` = 13.01 kw

b)

a Heat Pump

`P_(HP)` =
`(Q_(H))/(Performance-Coeff.)`

`P_(HP)` = 13.01 kw / 3.0

`P_(HP)` = 4.336 kw

c)

Performance coefficient of reversible Heat Pump

Since;
`Q_H` = 13.01 kw

and
`(Performance-Coeff)_(R.HP) = (T_H)/(T_H - T_L)` ==>
`(293.15)/(293.15 - 273.15)` ==> 14.66

Performance-Coeff =
`Q_H` /
`W_(elect)`

∴
`(W_(elec))_(R.Heat Pump) = (Q_H)/(Perf. Coeff.)`

`(W_(elec))_(R.Heat Pump) = (13.01)/(14.66)`

`(W_(elec))_(R.Heat Pump)` = 0.8875 kw