Question

Three rods made of same material and having the same cross section and lengths have been joined as shown in the figure. The temperature at the junction of the rods will be :

• A. ${45}^{o}C$
• B. ${60}^{o}C$
• C. ${30}^{o}C$
• D. ${20}^{o}C$

Answer 1

The correct option is B ${60}^{o}C$

Let the temperature of the junction be $\theta$
So assume that total incoming heat at the junction will be equal to total outgoing heat.
So, $(T_1-\theta )=(\theta -T_2)+(\theta -T_3)$
$(0-\theta )=(\theta -90)+\left(\theta -90\right)$
$\theta ={60}^{0}C$

$\frac{KA(\theta -0)}{\ell }=\frac{KA(90-\theta )}{\ell }=\frac{KA(90-\theta )}{\ell }$