The thermal conductivity of concrete is 0.80 W/m-C° and the thermal conductivity of wood is 0.10 W/m-C°. How thick would a solid concrete wall have to be in order to have the same rate of flow through it as an 8.0 cm thick wall made of solid wood? (Assume both walls have the same surface area.)
it would have to be 8 times as thick
64 cm (pretty thick :)
thank you so much damon
You are welcome.
Well, let's see. We want to find out how thick the concrete wall needs to be in order to have the same rate of heat flow as the wooden wall, right? So, let's call the thickness of the concrete wall "x".
Now, we know that the thermal conductivity of concrete is 0.80 W/m-C° and the thermal conductivity of wood is 0.10 W/m-C°.
The rate of heat flow is directly proportional to the thermal conductivity and inversely proportional to the thickness of the material. So, we can set up the following equation:
(0.80 W/m-C°) / x = (0.10 W/m-C°) / 8.0 cm
Now, we need to convert the thickness of the wooden wall from centimeters to meters. Since 1 meter is equal to 100 centimeters, the thickness of the wooden wall in meters would be 8.0 cm / 100 = 0.08 m.
Substituting the values into the equation, we get:
(0.80 W/m-C°) / x = (0.10 W/m-C°) / 0.08 m
Cross-multiplying, we get:
0.80 W/m-C° * 0.08 m = (0.10 W/m-C°) * x
0.064 W = 0.10 W/m-C° * x
Dividing both sides by 0.10 W/m-C°, we get:
0.064 W / 0.10 W/m-C° = x
0.64 m = x
So, the concrete wall would need to be 0.64 meters thick in order to have the same rate of heat flow as the 8.0 cm thick wooden wall.
To find the thickness of a solid concrete wall that would have the same rate of flow as an 8.0 cm thick wall made of solid wood, we can use the formula for thermal conductivity:
Q = (k * A * ΔT) / L
Where:
Q is the rate of heat flow through the material
k is the thermal conductivity of the material
A is the surface area of the material
ΔT is the temperature difference across the material
L is the thickness of the material
Since we want the rate of flow to be the same for both walls, we can equate the formulas for the concrete wall and the wood wall:
(k_concrete * A * ΔT) / L_concrete = (k_wood * A * ΔT) / L_wood
Given:
k_concrete = 0.80 W/m-C°
k_wood = 0.10 W/m-C°
L_wood = 8.0 cm = 0.08 m (converting from cm to m)
A (surface area) is the same for both walls (assumed)
We can rearrange the equation and solve for L_concrete:
L_concrete = (k_wood * L_wood * A) / k_concrete
Substituting the given values, we have:
L_concrete = (0.10 W/m-C° * 0.08 m * A) / 0.80 W/m-C°
Since the surface area (A) is the same for both walls, it cancels out:
L_concrete = (0.10 * 0.08) / 0.80
L_concrete = 0.008 m
Therefore, the thickness of the solid concrete wall would have to be 0.008 meters (or 8 mm) in order to have the same rate of flow as the 8.0 cm thick wall made of solid wood.