A cube of wood and a cube of concrete, each 0.17 m on a side, are placed side by side. One of the long faces of the rectangular prism formed by the two cubes is held at 17°C, and the opposite long face is held at 32°C. What is the total rate of heat transfer through the cubes?
To find the total rate of heat transfer through the cubes, you need to determine the rate of heat transfer through each cube and then sum them up.
The rate of heat transfer through a material can be calculated using the formula:
Q = k * A * (ΔT / d)
Where:
Q: Rate of heat transfer (in watts)
k: Thermal conductivity of the material (in watts per meter per degree Celsius)
A: Surface area (in square meters)
ΔT: Temperature difference (in degrees Celsius)
d: Thickness or distance (in meters)
First, we need to find the thermal conductivity of wood and concrete. Let's assume the thermal conductivity of wood (k_wood) is 0.12 W/(m·°C) and the thermal conductivity of concrete (k_concrete) is 1.2 W/(m·°C).
The surface area (A) for each cube can be calculated as the area of one face multiplied by the number of faces. For a cube, there are 6 faces.
A = 6 * (side length)^2
Substituting the values for the side length (0.17 m), we can find the surface area for each cube.
Next, we need to calculate the temperature difference (ΔT) between the two long faces of the rectangular prism formed by the cubes. In this case, it is (32°C - 17°C) = 15°C.
Finally, we need to determine the thickness or distance (d) of the cubes. Since we are only given the side length, which is the same for both cubes, we can assume the thickness of each cube is equal to its side length (0.17 m).
Now, we have all the required values to calculate the rate of heat transfer through each cube using the formula mentioned earlier. Then, we can sum up the rates of heat transfer through both cubes to find the total rate of heat transfer.
Total Rate of Heat Transfer = Rate of Heat Transfer through Wood Cube + Rate of Heat Transfer through Concrete Cube