Question

Right now you live in a house that is pretty old and doesn’t have double- paned windows. Your heating bill in the winter and spring will be really big, and you think it might be due to the huge single-paned window in the living room. Your landlord has told you that he is willing to replace it with a double paned window but you have to cover the cost of the window. You want to do a quick calculation to see if you can recover the cost of the new window before you graduate (and hopefully move out). If electricity used for heating costs 6.90 cents per kWh, will you save enough money? Assume 120 days of winter, followed by 90 days of spring until your graduation.

The living room is 3.5 m by 4.2 m, and is 2.4 m tall. The exterior wall has the standard 20 cm of fiberglass insulation. The existing window is on the narrower wall at one end of the living room and is 130 cm wide, 75 cm tall, and 4 mm thick. The new window is a state-of-the-art double paned window, with two panels of 4 mm glass separated by a 2 mm air-filled gap. Use the following values of thermal conductivity:
kfiberglass=0.04 W m−1 K−1, kglass=0.96 W m−1 K−1, kair=0.024 W m−1 K−1.

And also assume the following values for the average temperature:

Thouse=20∘C inside the house (to be maintained)

Twinter=3∘C outside the house during winter

Tspring=8∘C outside the house during spring

Finally, you estimate that the house is heated for 12 hours per day on average.

1.Calculate the heat conduction rate of the single-paned window during spring and winter.

2. With multiple layers of material with separate thickness and thermal conductivity values, the heat conduction rate must be calculated using the total resistance R.

Using the description of the double pane window, calculate its total resistance R. Give your answer in W−1 m2 K, to four decimal places.

3. Calculate the heat conduction rate of the double pane window during spring and winter.

4.calculate the total energy saved during spring and winter by switching to the double pane window in kwh

5. Using the answers above, calculate the total savings in the heating bill. Assume that the efficiency of converting electrical energy to heat is 100%. Give your answer in dollars.

Answer 1