Question

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 :

• A. $\frac{\theta_{2} R _{2}-\theta_{1} R _{1}}{ R _{2}- R _{1}}$
• B. $\frac{\theta_{1} R _{2}-\theta_{2} R _{1}}{ R _{2}- R _{1}}$
• C. $\frac{\theta_{1} R _{2}+\theta_{2} R _{1}}{ R _{1}+ R _{2}}$
• D. $\frac{\theta_{1} R _{1}+\theta_{2} R _{2}}{ R _{1}+ R _{2}}$

Answer 1

Answer: (C)

Heat flow rate will be same through bot
$\therefore \frac{\theta_{1}-\theta}{ R _{1}}=\frac{\theta-\theta_{2}}{ R _{2}}$
$R _{2} \theta_{1}- R _{2} \theta= R _{1} \theta- R _{1} \theta_{2}$
$\theta=\frac{ R _{2} \theta_{1}+ R _{1} \theta_{2}}{ R _{1}+ R _{2}}$