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 3.00 m² 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.

a) 400 W
b) 600 W
c) 800 W
d) 1,000 W

Answer 1

The rate of heat conduction through the window can be calculated using the formula Q = k * A * ΔT / d. Substituting the given values, the rate of conduction is 400 watts.

Therefore, the rate of conduction through the window is 400 watts (option a).

Step-by-step explanation:

The rate of heat conduction through a window can be calculated using the formula:

Q = k * A * ΔT / d

where Q is the rate of conduction, k is the thermal conductivity of the material, A is the surface area of the window, ΔT is the temperature difference between the inner and outer surfaces, and d is the thickness of the window.

Substituting the given values into the formula, we have:

Q = k * 3.00 m² * (5.00°C - (-10.0°C)) / 0.635 cm

Converting cm to m, we get:

Q = k * 3.00 m² * (5.00°C - (-10.0°C)) / 0.00635 m

Using the formula for the thermal conductivity of glass, which is approximately 0.8 W/m·K, we get:

Q = 0.8 W/m·K * 3.00 m² * (5.00°C - (-10.0°C)) / 0.00635 m

Simplifying the expression, we get:

Q = 400 W

Therefore, the rate of conduction through the window is 400 watts (option a).