Question

Two rods having thermal conductivities in the ratio of 5:3 and having equal length length and equal cross-section are joined by face to face. If the temperature of free end of first rod is ${100}^{o}C$ and temperature of free end of second rod is ${20}^{o}c$, then temperature of the junction, is-

• A. ${90}^{o}C$
• B. ${85}^{o}C$
• C. ${70}^{o}C$
• D. ${50}^{o}C$

Answer 1

The correct option is C ${70}^{o}C$

Let the thermal conductivity of first rod be $5K$

Let the thermal conductivity of second rod be $3k$

now, sum of heat current flowing through the junction =0

$\begin{array}{c}\frac{5KA\left(100-T\right)}{x}+\frac{3KA\left(20-T\right)}{x}=0\\ 500-5T+60-3T=0\\ 8T=560\\ \therefore T={70}^{0}C\end{array}$