Question

The coefficient of thermal conductivity of copper is nine times that of steel. In the composite cylindrical bar shown in the figure, what will be the temperature at the junction of copper and steel?

• A. $25^{\circ} C$
• B. $33^{\circ} C$
• C. $67^{\circ} C$
• D. $75^{\circ} C$

Answer 1

Answer: (D)

In steady state, the rate of flow of heat in both the conductors is same.
Let temperature of junction, when steady state is achieved be $ \theta $ ,
then rate of flow of heat is given by

$H=\frac{K_{c} A\left(\theta_{c}-\theta\right)}{l_{c}}$
$=\frac{K_{s} A\left(\theta-\theta_{s}\right)}{l_{s}}$
Where $K_{c}$ and $K_{s}$ are coefficient of thermal conductivities of copper and steel,
$A$ is area, $l_{c}, l_{s}$ lengths of copper and steel rods.
Given, $K_{c}=9 K_{s}$
$\therefore \frac{9 K_{s}\left(100^{\circ}-\theta\right)}{18}=\frac{K_{c}\left(\theta-0^{\circ}\right)}{6}$
$900-9 \theta=3 \theta $
$\Rightarrow 120=900$
$\Rightarrow \theta=75^{\circ} C$