Question

Three rods of same material, same area of cross-section but different lengths $10 \,cm , 20 \,cm$ and $30\, cm$ are connected at a point as shown. What is temperature of junction $O$ ?

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

Answer 1

Answer: (B)

Let temperature of junction be $=\theta$
Heat flowing to junction = heat out flowing
$\frac{K A}{30}(30-\theta)=\frac{K A}{20}(\theta-20)+\frac{K A}{10}(\theta-10)$
$\frac{(30-\theta)}{3}=\frac{(\theta-20)}{2}+\frac{(\theta-10)}{1}$
$\frac{(30-\theta)}{3}=\frac{\theta-20+2 \theta-20}{2}$
$60-2 \,\theta=9 \,\theta-120$
$\frac{180}{11}=\theta$
$16.36^{\circ} C =\theta$