A concrete wall is 15.0 cm thick and has an area of 10.0 m². A layer of wood that is 2.50 cm thick is placed over the wall to reduce the loss of heat by thermal conduction. The thermal conductivity of concrete is 1.70 W/m °C and the thermal conductivity of wood is 0.0400 W/m °C. What is the effective thermal conductivity of the wood-on-concrete system?

Question

Quizplus · Accepted Answer

The effective thermal conductivity of a composite system can be found by considering the resistances to heat flow of each layer in series. The total thermal resistance ($R_{total}$) is the sum of the individual resistances ($R_{concrete}$ and $R_{wood}$), where $R = \frac{L}{kA}$, with $L$ being the thickness, $k$ the thermal conductivity, and $A$ the area. Since the area cancels out and we're looking for an effective thermal conductivity ($k_{eff}$) over the total thickness ($L_{total}$), we rearrange the formula to $k_{eff} = \frac{L_{total}}{R_{total} \cdot A}$. Given the significantly lower thermal conductivity of wood compared to concrete and its addition to the system, the effective thermal conductivity will decrease but not drastically, making option A the most plausible choice without performing detailed calculations.

A Concrete Wall Is 15