Question

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

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

Answer 1

The correct option is A ${75}^{\circ }\text{C}$

We know that in series combination, heat flux remains constant.
Let the temperature of junction be $\theta$.
${\left(\frac{\Delta Q}{\Delta t}\right)}_{copper}={\left(\frac{\Delta Q}{\Delta t}\right)}_{steel}$

$\Rightarrow k_{1}A\frac{(100-\theta )}{18}=\frac{k_{2}A(\theta -0)}{6}$
$(\because k_1=9k_2)$
$\Rightarrow 9k_2\frac{(100-\theta )}{3}=k_2\theta$

or $900-9\theta =3\theta$
or $900=12\theta$
or $\theta ={75}^{\circ }\text{C}$