Question

Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K₁ and K₂. The thermal conductivity of the composite rod will be

• A. \(\frac {K_1+K_2}{2}\)
• B. \(\frac {3(K_1+K_2)}{2}\)
• C. \(K_1+K_2\)
• D. \(3(K_1+K_2)\)

Answer 1

The Correct Option is A

To determine the thermal conductivity of the composite rod made of two rods A and B of different materials, we consider the configuration as two rods in parallel because both are welded together and will conduct heat simultaneously. The concept of effective thermal conductivity for composite materials in parallel can be applied here.

When two materials are arranged in parallel with thermal conductivities \( K_1 \) and \( K_2 \), the effective thermal conductivity \( K_{\text{eff}} \) of the composite is given by:

K_{\text{eff}} = \frac{K_1 + K_2}{2}

Here, the assumption is that both rods have the same cross-sectional area, and they receive the same temperature difference across their length. This results in the average of the two conductivities as the effective conductivity for the composite in a parallel configuration.

Thus, the effective thermal conductivity of the composite rod is:

\(\frac{K_1 + K_2}{2}\)

This makes option \(\frac{K_1 + K_2}{2}\) correct.