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29 July, 01:00

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 windows conduct heat, calculate the rate of conduction in watts through a 2.82 m2 window that is 0.675 cm thick if the temperatures of the inner and outer surfaces are 5.00°C and - 10.0°C, respectively. This rapid rate will not be maintained - the inner surface will cool, and frost may even form. The thermal conductivity of glass is 0.84 J / (s · m · °C).

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  1. 29 July, 01:15
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    Q = - 5264 W = - 5.26 KW

    Here, negative sign indicates the outflow of heat

    Explanation:

    Fourier's Law of heat conduction, gives the following formula:

    Q = - KAΔT/t

    where,

    Q = Rate of Heat Conduction out of window = ?

    K = Thermal Conductivity of Glass = 0.84 W/m.°C

    A = Surface Area of window = 2.82 m²

    ΔT = Difference in Temperature of both sides of surface

    ΔT = Inner Surface Temperature - Outer Surface Temperature = 5°C - ( - 10°C)

    ΔT = 15°C

    t = thickness of window = 0.675 cm = 0.00675 m

    Therefore,

    Q = - (0.84 W/m.°C) (2.82 m²) (15°C) / 0.00675 m

    Q = - 5264 W = - 5.26 KW

    Here, negative sign indicates the outflow of heat.
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