Question

What is the temperature of the steel copper junction in the steady state of the system shown in the figure?



Length of the steel rod $=15 cm$, length of the copper rod $=10 cm$, temperature of the furnace $=300^{\circ} C$, temperature of the other end is $0^{\circ} C$. The area of cross-section of steel rod is twice that of copper rod. (Thermal conductivity of steel $=50.2 Js ^{-1} m ^{-1} K ^{-1}$ and of copper $\left.=385 Js ^{-1} m ^{-1} K ^{-1}\right)$

• A. $36.6^{\circ} C$
• B. $44.4^{\circ} C$
• C. $92.5^{\circ} C$
• D. $118.6^{\circ} C$

Answer 1

Answer: (B)

$1=$ steel, $2=$ copper
$\frac{K_{1} A_{1}(300-T)}{L_{1}}=\frac{K_{2} A_{2}(T-0)}{L_{2}}$
$\frac{(50.2)\left(2 A_{2}\right)(300-T)}{15}=\frac{385 A_{2} \cdot T}{10} $
$\Rightarrow T=44.4^{\circ} C$