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The rate of heat conduction out of a window on a winter day is rapid enough to chill the air next to it. To see just how rapidly the windows transfer heat by conduction, calculate the rate of conduction in watts through a 3.00-m^2 window that is 0.635 cm thick (1/4 in) if the temperatures of the inner and outer surfaces are 5.00ºC and −10.0ºC, respectively. This rapid rate will not be maintained—the inner surface will cool, and even result in frost formation. (answer in ×10^{3} W)

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Answer:

[tex]5.9527559\times 10^3\ W[/tex]

Explanation:

Q = Heat

t = Thickness = d = 0.635 cm

[tex]k_g[/tex] = Heat conduction coefficient of glass = 0.84 W/m °C (general value)

[tex]\Delta T[/tex] = Change in temperature

A = Area = 3 m²

Power is given by

[tex]P=\frac{dQ}{dt}=\frac{kA\Delta T}{d}\\\Rightarrow P=\frac{k_gA\Delta T}{d}\\\Rightarrow P=\frac{0.84\times 3(5-(-10))}{0.00635}\\\Rightarrow P=5.9527559\times 10^3\ W[/tex]

The rate of conduction in watts through the window is [tex]5.9527559\times 10^3\ W[/tex]

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