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 $384W{m}^{-1}{K}^{-1}$ and that of iron is $48W{m}^{-1}{K}^{-1}$ ]

• 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.
$\frac{100-\theta }{R_1}=\frac{\theta -0}{R_2}$
$\Rightarrow K_{1}A\left(\frac{100-\theta }{L_1}\right)=K_{2}A\left(\frac{\theta -0}{L_2}\right)$
$\Rightarrow \left(100-\theta \right)\frac{K_1}{L_1}=\theta \frac{K_2}{L_2}$
$=>\left(100-\theta \right)\frac{384}{0.75}=\theta \frac{48}{1.25}$
$\Rightarrow \theta =93^{\circ }C$