Question

Three rods made of the same material and having the same cross-section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at $0^{o}C$ and ${90}^{o}C$ respectively. The temperature of the junction of the three rods is

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

Answer 1

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

$i_1,i_2,i_3$ are heat currents

Identical $\to$ same length, same area

$i=\frac{△Q}{\frac{l}{kA}}$

Let $x$ be junction of temperature

$i_1+i_2+i_3=0\Rightarrow x-0+x-90+x-90=03x=180x=60$