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 $50K$ , 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 $H_A=H_B$
$\Rightarrow \frac{K_{A}A\left(T_A-T\right)}{\frac{L}{2}}=\frac{K_{B}A\left(T-T_B\right)}{\frac{L}{2}}$
$\Rightarrow 2K_B\left(T_A-T\right)=K_B\left(T-T_B\right)$
$\Rightarrow T_A-T=\frac{T-T_B}{2}=\frac{50}{2}=25K$