Question

A large cylindrical rod of length L is made by joining two identical rods of copper and steel of length $\left(\frac{L}{2}\right)$ each. The rods are completely insulated from the surroundings. If the free end of copper rod is maintained at $100^{°}C$ and that of steel at $0^{°}C$ then the temperature of junction is (Thermal conductivity of copper is 9 times that of steel)

• A. $90^{°}C$
• B. $50^{°}C$
• C. $10^{°}C$
• D. $67^{°}C$

Answer 1

Answer: (A)

Let conductivity of steel $K_{steel}=k$ then from question
Conductivity of copper $K_{copper}=9k$
${\theta }_{copper}=100^{°}C$
${\theta }_{steel}=0^{°}C$
$l_{steel}=l_{copper}=\frac{L}{2}$
From formula temperature of junction;
$\theta =\frac{K_{copper}{\theta }_{copper}{l}_{steel}+k_{steel}{\theta }_{steel}{l}_{copper}}{K_{copper}{l}_{steel}+K_{steel}{l}_{copper}}$
$=\frac{9k\times 100\times \frac{L}{2}+k\times 0\times \frac{L}{2}}{9k\times \frac{L}{2}+k\times \frac{L}{2}}$
$=\frac{\frac{900}{2}kL}{\frac{10kL}{2}}=90^{°}C$