Q. Two rectangular blocks $A$ and $B$ of different metals have same length and same area of cross-section. They are kept in such a way that their cross-sectional area touch each other. The temperature at one end of $A$ is $100℃$ and that of $B$ at the other end is $0℃$. If the ratio of their thermal conductivity is 1 : 3, then under steady state, the temperature of the junction in contact will be
A) $25℃$
B) $50℃$
C) $75℃$
D) $100℃$
Explanation
(a) It is given that $\frac{K_{1}}{K_{2}} = \frac{1}{3} \Rightarrow K_{1} = K$ then $K_{2} = 3K$ the temperature of the junction in contact
$\theta = \frac{K_{1}\theta_{1} + K_{2}\theta_{2}}{K_{1} + K_{2}} = \frac{1 \times 100 + 3 \times 0}{1 + 3} = \frac{100}{4} = 25℃$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.