Q. Two cylinders $P$ and $Q$ have the same length and diameter and are made of different materials having thermal conductivities in the ratio 2:3. These two cylinders are combined to make a cylinder. One end of $P$ is kept of $100℃$ and another end of $Q$ at $0℃$. The temperature at the interface of $P$ and $Q$ is
A) $30℃$
B) $40℃$
C) $50℃$
D) $60℃$
Explanation
(b) Temperature of interface $\theta = \frac{K_{1}\theta_{1} + K_{2}\theta_{2}}{K_{1} + K_{2}}$
Where $K_{1} = 2K$ and $K_{2} = 3K\ \left\lbrack \because\frac{K_{1}}{K_{2}} = \frac{2}{3} \right\rbrack$
$\Rightarrow \theta = \frac{2K \times 100 + 3K \times 0}{2K + 3K} = \frac{200K}{5K} = 40℃$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.