Question

What is the temperature of junction point between $B$ and $C$?

• A. ${57.14}^{o}C$
• B. ${55.5}^{o}C$
• C. ${68.1}^{0}C$
• D. ${30.5}^{0}C$

Answer 1

Answer: (A)

${57.14}^{o}C$

Let ${\theta }_1$ be the temperature of junction between A and B.

Let ${\theta }_2$ be the temperature of junction between B and C.

At steady state the heat conducted layer to layer is same.

$\therefore \frac{2KA}{L}\ast (100-{\theta }_1)=\frac{KA}{L}\ast ({\theta }_1-{\theta }_2)=\frac{KA}{2L}\ast ({\theta }_2-0)$

$\therefore 2\left(\right(100-{\theta }_1)=({\theta }_1-{\theta }_2)=\frac{{\theta }_2}{2}$

$\Rightarrow 2{\theta }_1=3{\theta }_2$

$\Rightarrow {\theta }_1=\frac{3}{2}{\theta }_2$

Taking $2(100-{\theta }_1)=\frac{{\theta }_2}{2}$ and substituting ${\theta }_1=\frac{3}{2}{\theta }_2$

We get,

$2(200-3{\theta }_2)={\theta }_2$

$\therefore 400=7{\theta }_2$

$\therefore {\theta }_2={57.14}^{0}C$