A glass window pane has an area of 3.50 m2 and a thickness of 0.600 cm. If the temperature difference between its surfaces is 27.0°C, what is the rate of energy transfer by conduction through the window?
I tried using the formula P=ka[(th-Tc)/l] my answer was thirteen but this is not right, help please.
k = 1.05 W/(m C)
l = 6*10^-3 m
(Th - Tc) = 27 C
A = 3.50 m^2
Do the numbers again. You should not get 13 (Watts) It is much more than that. Did you remember to express the thickness l in meters? What did you use for k ?
21
To find the rate of energy transfer by conduction through the window, you can use the formula:
P = k * A * (ΔT / d)
Where:
P is the rate of energy transfer (in watts)
k is the thermal conductivity of the material (in watts per meter-kelvin)
A is the area of the window (in square meters)
ΔT is the temperature difference between the surfaces (in degrees Celsius)
d is the thickness of the window (in meters)
In this case:
A = 3.50 m^2 (given)
ΔT = 27.0°C (given)
d = 0.600 cm = 0.006 m (converted to meters)
Now you need the value for the thermal conductivity, k. This value varies depending on the type of glass used. You can find this value in textbooks, online references, or by contacting the manufacturer of the glass.
Once you have the value for k, substitute it and the other given values into the formula to find the rate of energy transfer by conduction through the window.
To calculate the rate of energy transfer by conduction through the window, we can use the formula:
P = k * A * (ΔT / L)
Where:
P is the power (rate of energy transfer) in watts (W).
k is the thermal conductivity of the material, which is 0.84 W/(m·K) for glass.
A is the cross-sectional area of the window, which is given as 3.50 m^2.
ΔT is the temperature difference in Kelvin (K), which is 27.0°C.
L is the thickness of the window, which is given as 0.600 cm.
First, let's convert the thickness to meters:
L = 0.600 cm = 0.006 m
Now, let's convert the temperature difference to Kelvin:
ΔT = 27.0°C = 27.0 + 273 = 300 K
Now we can substitute the values into the formula:
P = 0.84 * 3.50 * (300 / 0.006)
Simplifying the equation gives:
P = 14,700 W
Therefore, the rate of energy transfer by conduction through the window is 14,700 watts (or 14.7 kW).
Your previous answer of thirteen (13) was incorrect because there was a miscalculation in the formula. By correctly substituting the values and performing the calculation, we arrive at the correct answer of 14,700 watts.