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An idealized representation of the air temperature as a function of distance from a singlepane window on a calm, winter day is shown in Fig. 23-28. The window dimensions are 60 cm × 60 cm × 0.50 cm. (a) At what rate does heat flow out through the window? (Hint: the temperature drop across the glass is very small.) (b) Estimate the difference in temperature between the inner and outer glass surfaces.

An idealized representation of the air temperature as a function of distance from a singlepane window on a calm, winter day is shown in Fig. 23-28. The window dimensions are 60 cm × 60 cm × 0.50 cm. (a) At what rate does heat flow out through the  window? (Hint: the temperature drop across the glass is very small.) (b) Estimate the difference in temperature between the inner and outer glass surfaces.   

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
6 years ago
232-669_1.PNG
The value that we arrived at is the rate that heat flows through the air across an area the size of the window on either side of the window. Therefore the rate of heat flows out through the window would be 1.8 W.
b) To find out the difference in temperature ΔT between the inner and outer glass surfaces, substitute 1.8 W for H, 0.50 cm for Δx, 1.0 W/m. K for k and (0.6 m)2 for A in the equation ΔT = H Δx/kA,
ΔT = H Δx/kA
= (1.8 W) (0.50 cm)/( 1.0 W/m. K)( (0.6 m)2)
= (1.8 W) (0.50 cm×10-2 m/1 cm )/( 1.0 W/m. K)( (0.6 m)2)
= 0.025 K
From the above observation we conclude that, the difference in temperature ΔT between the inner and outer glass surfaces would be 0.025 K.


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