Question

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 3.5 m2 window that is 0.635 cm thick (1/4in) if the temperatures of the inner and outer surfaces are 7∘C and −8∘C, respectively. This rapid rate will not be maintained -the inner surface will cool, and even result in frost formation. The coefficient of heat conduction for glass k=0.84 J/(sm∘C). Q/t=

Answer 1

The rate of conduction through the window is 35.7 watts.

Step-by-step explanation:

To calculate the rate of conduction in watts through the window, we can use the formula:

Q/t = kAΔT/d

Where:

• Q/t is the rate of conduction in watts
• k is the coefficient of heat conduction for glass (0.84 J/(sm∘C))
• A is the area of the window (3.5 m2)
• ΔT is the temperature difference between the inner and outer surfaces (7∘C - (-8∘C) = 15∘C)
• d is the thickness of the window (0.635 cm = 0.00635 m)

Substituting the given values into the formula:

Q/t = (0.84 J/(sm∘C)) * (3.5 m2) * (15∘C) / (0.00635 m)

Simplifying the equation:

Q/t = 35.7 J/s = 35.7 W

Therefore, the rate of conduction through the window is 35.7 watts.