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 3.00 m2 window that is 0.600 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.
To calculate the rate of conduction through a window, we can use the formula:
Q = k * A * (ΔT / d)
Where:
Q = heat conduction rate (in watts)
k = thermal conductivity of the window material
A = area of the window
ΔT = temperature difference between the inner and outer surfaces of the window
d = thickness of the window
First, we need to convert the thickness of the window from centimeters to meters:
d = 0.600 cm = 0.006 m
Next, let's find the thermal conductivity of the window material. Assuming it is a typical glass window, we can use a value of 0.78 W/(m·K) for thermal conductivity.
Now, let's calculate the temperature difference:
ΔT = (-10.0°C) - (5.00°C) = -15.00°C
Finally, we can plug the values into the formula to calculate the rate of conduction:
Q = (0.78 W/(m·K)) * (3.00 m^2) * (-15.00°C / 0.006 m)
Q = -930 W
Therefore, the rate of heat conduction through the window is -930 watts. Since the heat is flowing from the warmer inner surface to the colder outer surface, the negative sign indicates that heat is being lost from the inside to the outside, contributing to the chilling of the air next to the window.
To calculate the rate of conduction, we need to use the equation for heat conduction:
Q = k * A * (ΔT / d)
Where:
Q is the rate of heat conduction (in watts)
k is the thermal conductivity of the material (in watts per meter per degree Celsius)
A is the area of the window (in square meters)
ΔT is the temperature difference between the inner and outer surfaces (in degrees Celsius)
d is the thickness of the window (in meters)
First, let's convert the thickness of the window from centimeters to meters:
d = 0.600 cm * (1 m / 100 cm) = 0.006 m
Now, we can substitute the given values into the equation:
Q = k * A * (ΔT / d)
To determine the thermal conductivity, we need to know the material of the window. Different materials have different thermal conductivities. Let's assume a value of k = 1.00 W/(m·°C) for this calculation.
Q = (1.00 W/(m·°C)) * (3.00 m^2) * (5.00°C - (-10.0°C)) / (0.006 m)
Q = (1.00 W/(m·°C)) * (3.00 m^2) * (15.00°C) / (0.006 m)
Q = 7500 W
Therefore, the rate of conduction through the window is 7500 watts (or 7.5 kilowatts).