Two materials having coefficients of thermal... | Thermal Properties | JEE Main 2019

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JEE MAIN 2019

09-04-2019 S2

Question

Two materials having coefficients of thermal conductivity ' 3 K ' and ' K ' and thickness ' d ' and ' 3 d ', respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are ' $\theta_2$ ' and ' $\theta_1$ ' respectively, $\left(\theta_2>\theta_1\right)$. The temperature at the interface is:

Select the correct option:

A

$\frac{\theta_1}{6}+\frac{5 \theta_2}{6}$

B

$\frac{\theta_1}{10}+\frac{9 \theta_2}{10}$

C

$\frac{\theta_1}{3}+\frac{2 \theta_2}{3}$

D

$\frac{\theta_2+\theta_1}{2}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$\begin{aligned} & H=\frac{3 K A}{d}\left(\theta_2-\theta\right)=\frac{K A}{3 d}\left(\theta-\theta_1\right) \\ & \Rightarrow \quad \theta=\frac{9 \theta_2}{10}+\frac{\theta_1}{10}\end{aligned}$

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