Question

A partition wall has two layers of different materials $A$ and $B$ in contact with each other. They have the same thickness but the thermal conductivity of layer $A$ is twice that of $B$ . At steady state, if the temperature difference across the layer $B$ is $50 \, K$ , then the corresponding temperature difference across the layer $A$ is

• A. $\text{50 K}$
• B. $\text{12} \text{.5 K}$
• C. $\text{25 K}$
• D. $\text{60 K}$

Answer 1

Answer: (C)

Let $T$ be the junction temperature
Here, $K_{A}=2K_{B}, \, T-T_{B}=50K$
At the steady state $H_{A}=H_{B}$
$\Rightarrow \frac{K_{A} A \left(T_{A} - T\right)}{\frac{L}{2}} = \frac{K_{B} A \left(T - T_{B}\right)}{\frac{L}{2}}$
$\Rightarrow \, \, 2K_{B} \, \left(T_{A} - T\right)=K_{B} \, \left(T - T_{B}\right)$
$\Rightarrow \, \, T_{A}-T=\frac{T - T_{B}}{2}=\frac{50}{2}=25 \, K$