Q. Two bars of thermal conductivities $K$ and $3K$ and lengths $1cm$ and $2cm$ respectively have equal cross-sectional area, they are joined lengths wise as shown in the figure. If the temperature at the ends of this composite bar is $0℃$ and $100℃$ respectively (see figure), then the temperature $\phi$ of the interface is
A) $50℃$
B) $\frac{100}{3}℃$
C) $60℃$
D) $\frac{200}{3}℃$
Explanation
(c) Temperature of interface
$\theta = \frac{K_{1}\theta_{1}l_{2} + K_{2}\theta_{2}l_{1}}{K_{1}l_{2} + K_{2}l_{1}} = \frac{K \times 0 \times 2 + 3K \times 100 \times 1}{K \times 2 + 3K \times 1}$
$= \frac{300K}{5K} = 60℃$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.