The wall of copper (thermal conductivity = 400 W/m*K) that needs to provide the same insulation as a 4-cm polystyrene board (thermal conductivity = 0.04 W/m*K) must have a thickness of 400 meters.
The insulation of a material is directly proportional to the R factor. The higher the R the higher is the insulation of the material.
The R factor is given by:
[tex] R = \frac{L}{k} [/tex] (1)
Where:
L: is the thickness
k: is the thermal conductivity
The thickness of the copper wall can be calculated with equation (1):
[tex] L_{copper} = R*k_{copper} [/tex]
Where:
[tex] k_{copper} [/tex]: is the thermal conductivity of copper = 400 W/(m*K)
Since the copper wall must provide the same insulation as a polystyrene board, we have:
[tex] L_{copper} = R*k_{copper} = \frac{L_{polystyrene}}{k_{polystyrene}}*k_{copper} = \frac{0.04 m}{0.04 W/(m*K)}*400 W/(m*K) = 400 m [/tex]
Therefore, the copper wall must have a thickness of 400 meters.
Learn more about thermal conductivity here:
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I hope it helps you!
