Question

Figure shows a copper rod joined to a steel rod. The rods have equal length and equal crosssectional area. The free end of the copper rod is kept at $0^{\circ} C$ and that of steel rod is kept at $100^{\circ} C$. Find the temperature of the junction of the rod. Conductivity of copper $=390 W / m ^{\circ} C$. Conductivity of steel $=46 W / m ^{\circ} C$

• A. $18.01^\circ C$
• B. $26^\circ C$
• C. $10.6^\circ C$
• D. $20^\circ C$

Answer 1

Answer: (C)

$10.6^\circ C$

Answer 2

Heat current in first rod (copper) $=\frac{390 \times A(0-\theta)}{\ell}$ Here $\theta$ is temperature of the junction and $A \& \ell$ are area and length of copper rod. Heat current in second rod (steel) $=\frac{46 \times A(\theta-100)}{\ell}$ In series combination, heat current remains same. So, $\frac{390 \times A(0-\theta)}{\ell}=\frac{46 \times A(\theta-100)}{\ell}$ $-390 \theta==46 \theta-4600$ $436 \theta=4600$ $\Rightarrow 4600$ $\Rightarrow \theta=10.6^{\circ} C$