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?
If you examine the interface of the two cubes, you will find no heat flow from cube to cube..Why?
So, find the heat flow on each cube, and add them.
To find the total rate of heat transfer through the cubes, we need to calculate the heat transfer through each cube separately and then add them together.
First, let's calculate the heat transfer through the cube of wood.
The rate of heat transfer through a solid can be calculated using the formula:
Q = k * A * (ΔT / d)
Where:
Q = rate of heat transfer
k = thermal conductivity of the material
A = surface area of the cube
ΔT = temperature difference
d = thickness of the cube
For the cube of wood:
k = thermal conductivity of wood (you can find this value in reference books or online)
A = surface area = length * width
ΔT = temperature difference between the two faces (32°C - 17°C = 15°C)
d = thickness = side length of the cube = 0.17 m
Once you have the value of k, you can plug in the values into the formula to find the rate of heat transfer (Q) for the cube of wood.
Now, let's calculate the heat transfer through the cube of concrete using the same formula.
For the cube of concrete:
k = thermal conductivity of concrete (you can find this value in reference books or online)
A = surface area = length * width
ΔT = temperature difference between the two faces (32°C - 17°C = 15°C)
d = thickness = side length of the cube = 0.17 m
Once you have the value of k, you can plug in the values into the formula to find the rate of heat transfer (Q) for the cube of concrete.
Finally, add the rates of heat transfer from both cubes together to get the total rate of heat transfer through the cubes.