Q.
The coefficient of thermal conductivity of copper is nine times that of steel. In the composite cylindrical bar show in figure, what will be the temperature at the junction of copper ad steel?
A) 75$℃$
B) 67$℃$
C) 33$℃$
D) 25$℃$
Explanation
(a) Let the temperature of junction be $\theta.$
$\left( \frac{\mathrm{\Delta}Q}{d_{1}} \right)_{copper}\ = \left( \frac{\mathrm{\Delta}Q}{\mathrm{\Delta}T} \right)_{steel}$
$K_{1}A = \ \frac{(100 - \theta)}{18} = \frac{K_{2}A(\theta - 0)}{6}$
$9K_{2}\frac{(100 - \theta)}{3} = K_{2}\theta$
3$\theta = 900 - 9\theta$
12$\theta = 900$
$\theta = 75℃$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.