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 $385 \mathrm{~J} \mathrm{~s}^{-1} \mathrm{~K}^{-1} \mathrm{~m}^{-1}$ and $50 \mathrm{~J} \mathrm{~s}^{-1} \mathrm{~m}^{-1}$…

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 $385 \mathrm{~J} \mathrm{~s}^{-1} \mathrm{~K}^{-1} \mathrm{~m}^{-1}$ and $50 \mathrm{~J} \mathrm{~s}^{-1} \mathrm{~m}^{-1}$ respectively. The free ends of copper and steel are held at $100^{\circ} \mathrm{C}$ and $0^{\circ} \mathrm{C}$ respectively. The temperature at the junction is, nearly:

Aicharya · Accepted Answer

As per question, we have;
$\begin{aligned}
& \theta=\text { ? } \\
& \text {As } \\
& \mathrm{K}=\frac{Q d}{\mathrm{~A} \Delta t}, \\
& \text {where, } \mathrm{K}=\text { thermal conductivity } \\
& Q=\text { amount of heat transferred } \\
& d=\text { distance between two planes } \\
& \mathrm{A}=\text { area of surface, and } \\
& \Delta \mathrm{T}=\text { difference in Temp. } \\
& \frac{\Delta \mathrm{Q}}{\Delta t}=\frac{385 \times \mathrm{A} \times\left(100^{\circ} \mathrm{C}-\theta\right)}{l} \\
& =\frac{50 \times \mathrm{A} \times\left(\theta-0^{\circ} \mathrm{C}\right)}{l} \\
& \Rightarrow 385\left(100^{\circ} \mathrm{C}-\theta\right)=50\left(\theta-0^{\circ} \mathrm{C}\right) \\
& \Rightarrow \theta=88.5^{\circ} \mathrm{C}
\end{aligned}$

Two rods one made of copper and other made of steel of the same length and same cross sectional area are…

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