Question

Two metal rods X and Y having equal cross-sectional areas are joined end to end to form a composite bar, one end of which is heated. After some time has elapsed, the temperature gradient along each rod is found to be uniform, but greater in X than that in Y. Which of the following can be inferred

• A. Both the rods are well lagged
• B. The heat current is the same in both the rods
• C. Both the rods are of equal lengths
• D. X is better conductor of heat than Y

Answer 1

Answer: (A), (B)

(A) and (B)

Answer 2

A uniform temperature gradient along a rod implies no heat loss to the surroundings, hence the rods are well-lagged. In a series arrangement of rods, the heat current is the same through each rod. Fourier's Law ($H = -kA \frac{dT}{dx}$) with same H and A implies that a greater temperature gradient means lower thermal conductivity. Therefore, X is a poorer conductor than Y.