The thermal conductivity of a certain concrete is 0.80 W/m ∙ K and the thermal conductivity of a certain wood is 0.10 W/m ∙ K.How thick would a solid concrete wall have to be in order to have the same rate of thermal energy flow through it as an 8.0-cm thick wall made of solid wood? Both walls have the same surface area and the same temperature difference across their faces.

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The rate of thermal energy flow ($Q/t$) through a material is given by the equation $Q/t = kA(T_2 - T_1)/d$, where $k$ is the thermal conductivity of the material, $A$ is the cross-sectional area of the material, $T_2 - T_1$ is the temperature difference across the material, and $d$ is the thickness of the material. For the two materials to have the same rate of thermal energy flow, we can set their equations equal to each other and solve for the unknown thickness of the concrete wall.Given that the thermal conductivity of concrete is 0.80 W/m∙K and the thermal conductivity of wood is 0.10 W/m∙K, and the thickness of the wood wall is 8.0 cm (or 0.08 m), we can set up the equation as follows:$$0.80 \times \frac{1}{d_{\text{concrete}}} = 0.10 \times \frac{1}{0.08}$$Solving for $d_{\text{concrete}}$, we get:$$d_{\text{concrete}} = 0.80 \times 0.08 / 0.10 = 0.64 \, \text{m}$$Therefore, the concrete wall needs to be 0.64 m or 64 cm thick to have the same rate of thermal energy flow as the 8.0-cm thick wood wall.

The Thermal Conductivity of a Certain Concrete Is 0