Question

Three rods of same material, same area of cross-section but different lengths $10\text{cm}$, $20\text{cm}$ and $30\text{cm}$ are connected at a point as shown in the figure. Find the temperature of junction ${}^{\prime }{\text{O}}^{\prime }$.

• A. ${19.2}^{\circ }\text{C}$
• B. ${16.4}^{\circ }\text{C}$
• C. ${11.5}^{\circ }\text{C}$
• D. ${22}^{\circ }\text{C}$

Answer 1

The correct option is B ${16.4}^{\circ }\text{C}$

Let temperature of the junction be $\theta$. Assume the heat flow in the rods is as follows:



Heat flowing into junction = heat flowing out of the junction.
$\Rightarrow \frac{KA}{30}(30-\theta )=\frac{KA}{20}(\theta -20)+\frac{KA}{10}(\theta -10)$
$\Rightarrow \frac{30-\theta }{3}=\frac{\theta -20}{2}+\frac{\theta -10}{1}$
$\Rightarrow \frac{30-\theta }{3}=\frac{\theta -20+2\theta -20}{2}$
$\Rightarrow 60-2\theta =9\theta -120$
$\Rightarrow \theta =\frac{180}{11}={16.36}^{\circ }\text{C}\approx {16.4}^{\circ }\text{C}$
Thus, option (b) is the correct answer.