Question

A wall has two layers A and B, each made of different materials. The thickness of both the layers is the same. The thermal conductivity of A, $K_A=3K_B$. The temperature across the wall is ${20}^{\circ }$ C. In thermal equilibrium

• A. the temperature difference across $A={15}^{\circ }$C
• B. rate of heat transfer across A is more than across B
• C. rate of heat transfer across both is same
• D. temperature difference across A is $5^{\circ }$ C

Answer 1

Answer: (C), (D)

The correct options are
C rate of heat transfer across both is same
D temperature difference across A is $5^{\circ }$ C

$K_A=3K_{B}and{\theta }_1-{\theta }_2={20}^{\circ }C\therefore \frac{K_A({\theta }_1-\theta )}{l}=\frac{K_B(\theta -{\theta }_2)}{l}\Rightarrow 3K_B({\theta }_1-\theta )=K_B(\theta -{\theta }_2)\Rightarrow 3{\theta }_1-3\theta =\theta -{\theta }_2\Rightarrow 3{\theta }_1+{\theta }_2=4\theta$
And ${\theta }_1-{\theta }_2=20\therefore 4{\theta }_1=4\theta +20\Rightarrow {\theta }_1-\theta =\frac{20}{4}=5^{\circ }C$
Also, in thermal equilibrium, rate of heat transfer across both is same.