Question

Three rods of the same dimensions have thermal conductivities $3K,2K$ and $K$ . They are arranged as shown, with their ends at $100^\circ C,50^\circ C$ and $0^\circ C$ .
The temperature of their junction is :-

• A. $75^\circ C$
• B. $\frac{200}{3}^\circ C$
• C. $40^\circ C$
• D. $\frac{100}{3}^\circ C$

Answer 1

Answer: (B)

$R \propto \frac{1}{ Thermal conductivity }$
$R_{1}=\frac{R}{3},R_{2}=\frac{R}{2},R_{3}=R$
$i=i_{1}+i_{2}$
$\frac{100 - \theta }{R / 3}=\frac{\theta - 50}{R / 2}+\frac{\theta - 0}{R}$
$300-3\theta =2\theta -100+\theta $
$6\theta =400\Rightarrow \theta =\frac{200}{3}\_{}^{^\circ }C$