Question

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

• A.
• B.
• C.
• D.

Answer 1

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:
$\frac{dQ}{dt}=-kA\frac{d\theta }{dX}$
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
$-\frac{d\theta }{dX}=C$
$\Rightarrow \int d\theta =-\int Cdx$
$\Rightarrow \theta =-CX+D$
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.