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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

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Solution

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 dTdx is changing and hence the magnitude of the temperature gradient is not a constant.

Also we know that for conduction

q=−kAdTdx

Since the slope is negative and the magnitude of the slope increases from the hot end or we can say −dTdx increases.

Hence for a constant q, the area of cross section A has to decrease from the hot end.

In graph dTdx is changing and hence the magnitude of the temperature gradient is not a constant.

Also we know that for conduction

q=−kAdTdx

Since the slope is negative and the magnitude of the slope increases from the hot end or we can say −dTdx increases.

Hence for a constant q, the area of cross section A has to decrease from the hot end.

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