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

Question

Temperature against distance from hot end; downward concave curve, increasing gradient magnitude

TestHub · Accepted Answer

At steady state, the heat-flow rate is the same through each section.
$\dot{Q} = - k A \frac{d T}{d x} = constant$
The graph has a changing slope, so the temperature gradient is not constant (A).
Since the magnitude of the gradient increases towards the cold end, area A decreases along the bar (D).

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