Question

You are considering buying some new windows for your house, where you have single paned glass windows where the glass is 1/8 " thick. You normally like to keep your house at 75 ^oF, even when the outside temperature is 105 ^oF in Tucson, AZ. You are planning on replacing a window that is 3 feet tall and 18 inches wide in your bathroom with double paned glass that is the same thickness glass on each side, but that has argon as the gas in between the two panes, where the argon space is 1/4" thick.

a) What is the fractional reduction in heat losses if you do this?

b) Imagine you just used glass that was 1/4" thick with no argon in between. What is the fractional reduction in heat losses if you do this instead?

c) Chlorine would be an even better gas to use for some technical reasons. Why, giving a citation? Give two counter reasons on why you would not use chlorine for this application.

Answer 1

Rate of heat transfer q = KA Delta T/Delta x A = (3) (1.5) = 45 ft^2 = 0.41826 m^2 Delta T = (105 - 75) = 30 degree F = 16.666 degree c Delta x = 1/8 inch = 0.125 inch = 0.3175 cm = 3.175 times 10^- 3 m thermal conductivity of window glass k_g = 1 W/m.kel q = k A Delta T/Delta x = (1) (0.41816) (16.666)/3 .175 times 10^- 3 q = 2197.28 w if argon is in between 2 glasses Delta x_Argon = 1/4 inch = 0.25 inch = 0.635 cm = 6.35 times 10^- 3 m k_Ar = 17.9 mw/m kel \r\n R_1 = Delta x_1/k_g A = 3.175 times 10^- 3/(1) (0.41806) = 7.5946 times 10^- 3 R_2 = Delta x_Ar/k_ar A = 6.35 times 10^- 3/(17.9 times 10^- 3 (0.41806) = 0.84855 R_3 = Delta x_2/k_g A = 3.175 times 10^- 3/(1) (0.41806) = 7.5946 times 10^- 3 q_new = Delta T/R_1 + R_2 + R_3 = 16.666/2 (7.5946 times 10^- 3 + 0.84855 q_new = 19.2949 w frictional decrease in heat transfer