Question

Hello I could use some help answering this question I don’t quite understand ! :)

Answer 1

ANSWER

C. The rate of heat transfer for both walls is the same

EXPLANATION

The rate of heat transfer for a material is given by:

$R=\frac{kA\Delta T}{d}$

where k = thermal conductivity

A = surface area of the material

ΔT = change in temperature

d = thickness of the material

Wall A has 4 timesthe area of Wall B and is also twice as thicjk as wall B. This implies that:

$\begin{gathered} A_A=4A_B \\ d_A=2d_B \end{gathered}$

We also have that the thermal conductivity of Wall A is half that of Wall B:

$k_A=\frac{1}{2}k_B$

Therefore, the rate of heat trnsfer for Wall ABis:

$R_B=\frac{k_BA_B\Delta T}{d_B}$

and for Wall A is:

$\begin{gathered} R_A=\frac{k_AA_A\Delta T}{d_A} \\ R_A=\frac{(\frac{1}{2}k_B)(4A_B)\Delta T}{2d_B}=\frac{4k_BA_B\Delta T}{4d_B} \\ R_A=\frac{k_BA_B\Delta T}{d_B} \end{gathered}$

Note: ΔT is the same for both walls

Hence, we see that the rate ofheat rtransfer for both walls is the same.

The correct option is option C.