Question

The ends of a long homogenous bar are maintained at different temperatures and there is no loss of heat from the sides of the bar due to conduction or radiation. The graph of temperature against distance of the bar when it has attained steady state is shown here. The graph shows

• A. the temperature gradient is not constant
• B. the bar has uniform cross-sectional area
• C. the cross-sectional area of the bar increases as the distance from the hot end increases
• D. the cross-sectional area of the bar decreases as the distance from the hot end increases

Answer 1

Answer: (A), (D)

The correct options are
A the temperature gradient is not constant
D the cross-sectional area of the bar decreases as the distance from the hot end increases

In graph $\frac{dT}{dx}$ is changing and hence the magnitude of the temperature gradient is not a constant.
Also we know that for conduction
$q=-kA\frac{dT}{dx}$
Since the slope is negative and the magnitude of the slope increases from the hot end or we can say $-\frac{dT}{dx}$ increases.
Hence for a constant $q$, the area of cross section $A$ has to decrease from the hot end.