Question

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

Answer 1

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

Step-by-step explanation

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

`R=(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=(1)/(2)k_B`

Therefore, the rate of heat trnsfer for Wall ABis:

`R_B=(k_BA_B\Delta T)/(d_B)`

and for Wall A is:

`\begin{gathered} R_A=(k_AA_A\Delta T)/(d_A) \\ R_A=(((1)/(2)k_B)(4A_B)\Delta T)/(2d_B)=(4k_BA_B\Delta T)/(4d_B) \\ R_A=(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.