Question

Three bars of equal lengths and equal areas of cross-section are connected in series. Their thermal conductivities are in the ratio of $2:4:3$. If the open ends of the first and the last bars are at temperatures $200^{\circ }C$ and $18^{\circ }C$ respectively in the steady state, the temperature of the two junctions is

• A. $60^{\circ }C,50^{\circ }C$
• B. $116^{\circ }C,74^{\circ }C$
• C. $55^{\circ }C,65^{\circ }C$
• D. $160^{\circ }C,80^{\circ }C$

Answer 1

Answer: (B)

The rate of flow of heat is same

$H=(2K)A\frac{\left(200-{\theta }_1\right)}{L}$
$=(4K)A\frac{\left({\theta }_1-{\theta }_2\right)}{L}$
$=(3K)A\frac{{\theta }_2-18^{\circ }}{L}$
$\Rightarrow 2\left(200^{\circ }-{\theta }_1\right)=4\left({\theta }_1-{\theta }_2\right)$
$=3\left({\theta }_2-18^{\circ }\right)$
$\Rightarrow {\theta }_1=116^{\circ }C,{\theta }_2=74^{\circ }C$