Assume that house Is maintained at a comfortable temperature by means of an elec
ID: 1717898 • Letter: A
Question
Assume that house Is maintained at a comfortable temperature by means of an electrical resistor heater during winter The heater is operated at a constant current (I) under an applied voltage of 110 V. For simplicity, let us assume that the heater operates at a steady state, with 85% of conversion efficiency from the electrical energy to the Internal energy of air In your house. (4p) Please find I If you pay $11.8/day for heating, with electricity cost $0.11/kWh. (4p) Also, please calculate the heat produced by such a heater during a week.Explanation / Answer
a)
Total payable amount = 11.8 dollars/day
Electricity cost = 0.11 dollars/kW-hour
We can write
Total Payable amount = Electricity cost*Power consumed*24 (24 for conversion of hours into days)
11.8 = 0.11*Power consumed*24
Power consumed = 4.47 kW
Power consumed can also written as
Power consumed = VI = 110*I = 4.47*1000 W
I = 40.64 A
b)
Power consumed per day = 4.47 kW
Since Heater is 85% efficient
Heat power required = 4.47/0.85 = 5.26 kW
Heat produced during a week = 5.26*7*24*60*60
(1 week = 7 days = 7*24*60*60 seconds)
Heat produced during a week =3181 MJ (mega Joules)