Question

Three rods made of the same material and having the same cross-section have joined as shown in the fig. Each rod is of same length. The left and right ends are kept at ${10}^0$ C and ${90}^0$ C respectively. The temperature of the junction of the three rods will be :

• A. ${70}^{0}C$
• B. ${60}^0$
• C. ${30}^0$
• D. ${\frac{190}{3}}^{0}C$

Answer 1

Answer: (D)

${\frac{190}{3}}^{0}C$

Let the temp at the intersection of the three rods is $T$.
Since at steady state rate of heat transfer is same,

$KA\frac{(90-T)}{x}+KA\frac{(90-T)}{x}=KA\frac{(T-10)}{x}$

$\Rightarrow 2(90-T)=T-10$

$\Rightarrow T={\frac{190}{3}}^{0}C$