Question

Two rods one made of copper and other made of steel of the same length and same cross sectional area are joined together. The thermal conductivity of copper and steel are $385 \, J\, s ^{-1} \, K ^{-1} \, m ^{-1}$ and $50\, J\, s ^{-1} \, K ^{-1}\, m ^{-1}$ respectively. The free ends of copper and steel are held at $100^{\circ} C$ and $0^{\circ} C$ respectively. The temperature at the junction is, nearly:

• A. $12^{\circ} C$
• B. $50^{\circ} C$
• C. $73^{\circ} C$
• D. $88.5^{\circ} C$

Answer 1

Answer: (D)

$\frac{\Delta \theta}{\Delta t }=\frac{385 A (100-\theta)}{\ell}=\frac{50 A (\theta-0)}{\ell}$
$\Rightarrow 77(100-\theta)=10 \theta$
$\Rightarrow 7700-77 \theta=10 \theta$
$\Rightarrow 87 \theta=7700$
$\Rightarrow \theta=\frac{7700}{87}=88.5^{\circ} C$