The thermal conductivity of a certain concrete is 0.80 $\mathrm { W } / \mathrm { m } , \mathrm { K }$ and the thermal conductivity of a certain wood is 0.10 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K }$ How thick would a solid concrete wall have to be in order to have the same rate of heat 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.

Question

The thermal conductivity of a certain concrete is  0.80  $\mathrm { W } / \mathrm { m } , \mathrm { K }$ and the thermal conductivity of a certain wood is  0.10  $\mathrm { W } / \mathrm { m } \cdot \mathrm { K }$ How thick would a solid concrete wall have to be in order to have the same rate of heat 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.

Quizplus · Accepted Answer

The rate of heat flow ($Q/t$) through a material is given by the equation $Q/t = kA(T_1 - T_2)/d$, where $k$ is the thermal conductivity, $A$ is the area, $T_1 - T_2$ is the temperature difference, and $d$ is the thickness. Since the area and temperature difference are the same for both materials, and we want the rate of heat flow to be the same, we can set up the equation $k_{concrete}d_{concrete} = k_{wood}d_{wood}$. Plugging in the given values, $0.80d_{concrete} = 0.10 \times 8.0$. Solving for $d_{concrete}$ gives $d_{concrete} = 64$ cm.

The Thermal Conductivity of a Certain Concrete Is 0 W/m,K\mathrm { W } / \mathrm { m } , \mathrm { K }W/m,K

The Thermal Conductivity of a Certain Concrete Is 0 $\mathrm { W } / \mathrm { m } , \mathrm { K }$