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 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.
A)53 cm
B)64 cm
C)71 cm
D)85 cm

Question

Quizplus · Accepted Answer

The rate of heat flow, or heat flux, is given by the equation:

q = kAΔT / x

where q is the heat flux, k is the thermal conductivity, A is the surface area, ΔT is the temperature difference, and x is the thickness of the material.

We want to find the thickness of the concrete wall that would give the same heat flux as the 8.0-cm thick wood wall. Let x1 be the thickness of the concrete wall and x2 be the thickness of the wood wall. Since the two walls have the same surface area and temperature difference, we can set their heat fluxes equal to each other:

k1AΔT / x1 = k2AΔT / x2

Simplifying and solving for x1, we get:

x1 = (k1 / k2) x2

Plugging in the values for k1, k2, and x2, we get:

x1 = (0.80 / 0.10) (8.0 cm)
x1 = 64 cm

Therefore, the thickness of the concrete wall would have to be 64 cm in order to have the same rate of heat flow as the 8.0-cm thick wood wall. The correct answer is B.

The Thermal Conductivity of a Certain Concrete Is 0