Question

Two rectangular blocks $A$ and $B$ of different metals have the same length and same area of cross-section. They are kept in such a way that their cross-sectional areas are in contact. The temperature at one end of $A$ is $100 \, ^\circ C$ and that of $B$ at the other end is $0 \, ^\circ C$ . If the ratio of their thermal conductivity is $1:3$ , then under steady-state, the temperature of the junction in contact will be

• A. $25 \, ^\circ C$
• B. $50 \, ^\circ C$
• C. $75 \, ^\circ C$
• D. $100 \, ^\circ C$

Answer 1

Answer: (A)

It is given that $\frac{K_{1}}{K_{2}}=\frac{1}{3}$
Let $K_{1}=K \, \& \, K_{2}=3K$
The temperature of the junction in contact
$\theta =\frac{K_{1} \theta _{1} + K_{2} \theta _{2}}{K_{1} + K_{2}}$
$\theta =\frac{1 \times 100 + 3 \times 0}{1 + 3}=\frac{100}{4}$
$\theta =25^\circ C$