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Question

A long metallic bar is carrying heat from one of its ends to the other end under steady state. The variation of temperature θ along the length X of the bar from its hot end is best described by which of the following figures?

A
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B
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C
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D
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Solution

The correct option is B
In the question, we are given that a metallic bar is carrying heat from one of its ends to the other. So, we can write the rate of flow of heat by the formula:
dQdt=kAdθdX
Now, in the question, we are told that the metallic box carrying the heat is under a steady state. So the thermal gradient of the rod will be constant.
Therefore, we can write
dθdX=C
dθ=Cdx
θ=CX+D
So, we can see that the graph will be a straight line and slope will be negative for this plot.
Hence, option (b) is correct answer.

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