Question

A copper rod of length $75cm$ and an iron rod of length $125cm$ are joined together end to end. Both are of circular cross-section with diameter $2cm$ . The free ends of the copper and iron rods are maintained at $100^\circ C$ and $0^\circ C$ respectively and the curved surfaces of the bars are insulated thermally. The temperature of the copper-iron junction is [Thermal conductivity of copper is $384Wm^{- 1}K^{- 1}$ and that of iron is $48Wm^{- 1 }K^{- 1}$ ]

• A. $100^\circ C$
• B. $0^\circ C$
• C. $93^\circ C$
• D. $50^\circ C$

Answer 1

Answer: (C)

Heat current will be same in both rods.
$\frac{100 - \theta }{R_{1}}=\frac{\theta - 0}{R_{2}}$
$\Rightarrow K_{1}A\left(\frac{100 - \theta }{L_{1}}\right)=K_{2}A\left(\frac{\theta - 0}{L_{2}}\right)$
$\Rightarrow \left(100 - \theta \right)\frac{K_{1}}{L_{1}}=\theta \frac{K_{2}}{L_{2}}$
$=>\left(100 - \theta \right)\frac{384}{0 .75}=\theta \frac{48}{1 .25}$
$\Rightarrow \, \theta =93^\circ C$