Use the exact values you enter in previous answer(s) to make later calculation(s

Question

Use the exact values you enter in previous answer(s) to make later calculation(s). Energy-efficient windows are constructed with two panes glass separated by an air (see figure below). In a typical window of this type, the air makes difference in the rate of heat flow. The heat-flow rate is much smaller for an energy-efficient window than for a single pane of glass because the thermal conductivity of the air gap is much less than that of a glass pane. (a) To compare heat flow for the different types of windows, first calculate the heat-flow rate for a single-pane window. Assume the glass is 3.3 mm thick, it has an area of 0.52 m^2, and the temperatures on the two sides of the glass differ by 31 degree C. W (b) Now consider an energy-efficient window consisting of two sheets of glass as in part (a), separated by an air gap that is 1.0 cm thick. Assuming the same temperature difference as in part (a), what is the heat flow rate in this case? For simplicity, assume all the temperature difference is across the air gap and none is across the two panes of glass. W (c) How thick would a single pane of glass have to be to give the same rate of heat flow as through the energy-efficient window (as calculated in part (b)), assuming the same temperature difference? mm

Explanation / Answer

thermal conductivity of air = 0.024 W / m K

and of glass = 0.96 W / m K

and heat flow rate = k A deltaT / a

(A) heat flow rate = (0.96 ) (0.52) (31) / (3.3 x 10^-3)

= 4689.4 W

(B) heat flow rate = (0.024) (0.52) (31) / (1 x 10^-2)

= 38.7 W

(C) 38.7 = (0.96) (0.52) (31) / (a)

a = 0.4 m Or 40 cm Or 400 mm

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