Q 11-10-093JEE MainJEE Main 2021 (26 Feb, Shift 1)Easy
The temperature $\theta$ at the junction of two insulating sheets, having thermal resistances $R_1$ and $R_2$ as well as top and bottom temperatures $\theta_1$ and $\theta_2$ (as shown in figure) is given by:
Answer: (C) $\frac{\theta_1 R_2 + \theta_2 R_1}{R_1 + R_2}$
In steady state the same heat current flows through both sheets:
$$\frac{\theta_2 - \theta}{R_2} = \frac{\theta - \theta_1}{R_1}$$
$$\theta_2 R_1 - \theta R_1 = \theta R_2 - \theta_1 R_2 \Rightarrow \theta = \frac{\theta_1 R_2 + \theta_2 R_1}{R_1 + R_2}$$
Solution by Sreeraj P, M.Sc Physics