The ends of a long homogenous bar are maintained at different temperatures and there is no loss of heat from the lateral surface 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

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the temperature gradient is not constant

the cross-sectional area of the bar decreases as the distance from the hot end increases.

the bar has uniform crosssectional area

the cross-sectional area of the bar increases as the distance from the hot end increases

answer is A, D.

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Detailed Solution

In graph $\frac{d T}{d x}$ is not constant its magnitude is increasing . If $T_{0} i s t h e t e m p e r a t u r e o f t h e h o t t e r e n d, t h e n \frac{T_{0} - T_{x}}{x / k A} = Q = c o n s \tan t . S o T_{x} = T_{0} - \frac{Q x}{k A} \Rightarrow |\frac{d T_{x}}{d x}| = \frac{Q}{k A} A s |\frac{d T_{x}}{d x}| i n c r e a s e s, A d e c r e a s e s .$