Question

PLEASEEE HELP The outer walls of your house have an R-value of 84.0 K m² / W, and a total area of 2000 m². Lets assume that, from the beginning of December to the end of February, the temperature outside the house is 0°C while you set your thermostat to maintain a constant temperature of 22°C inside the house.

(a) How much energy is conducted through the walls of your house in this three-month period? Assume it is not a leap year. _____J

(b) How much energy would be conducted through the walls if you lowered the thermostat so as to maintain a constant temperature of 20°C? _____J

(c) Every kW-h (kilowatt-hour) of energy costs 20 cents. First, convert 1 kW-h to joules, and then determine how much money you would save by keeping your thermostat at 20°C for the three months. ____$

Answer 1

$\Delta$T = temperature difference = 22 - 0 = 22

A = area = 2000 m²

R = 84.0 K m² / W

t = time = 90 days = 90 x 24 x 3600 = 7776000

a)

energy = (1/R) A $\Delta$T t = (1/84) (2000) (22) (7776000) = 4.07 x 10⁹ J

b)

$\Delta$T = temperature difference = 20 - 0 = 20

energy = (1/R) A $\Delta$T t = (1/84) (2000) (20) (7776000) = 3.7 x 10⁹ J

c)

1 kWh = 1000 x 3600 = 3.6 x 10⁶ J

3.6 x 10⁶ J of energy costs = 20 cents

1 J of energy costs = 20 / (3.6 x 10⁶ )

Total cost for 4.07 x 10⁹ J of energy = 4.07 x 10⁹ (20 / (3.6 x 10⁶ )) = 22611.11 cents

Total cost for 3.7 x 10⁹ J of energy = 3.7 x 10⁹ (20 / (3.6 x 10⁶ )) = 20555.56 cents

savings = 22611.11 - 20555.56 = 2055.6 cents = 20.56 $