Question

Two ends of a conducting rod of varying cross-sections are maintained at $200^{\circ }C$ and $0^{\circ }C$ respectively. In steady-state

• A. temperature difference across $AB$ and $CD$ are equal
• B. temperature difference across $AB$ is greater than that of across $CD$
• C. temperature difference across $AB$ is less than that of across $CD$
• D. temperature difference may be equal or different depending on the thermal conductivity of the rod

Answer 1

Answer: (C)

Rate of flow of heat $\frac{\text{dQ}}{\text{dt}}$ or H is equal throughout the rod.
Temperature difference = (H) X (thermal resistance)
or Temperature difference $\left(\mu \right)\propto$ thermal resistance $\left(R\right)$
where $\text{R}=\frac{l}{\text{KA}}\text{ or }\text{R}\propto \frac{1}{\text{A}}$
Area across $CD$ is less. Therefore, temperature difference across $CD$ will be more.