Question 108 of 126

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 figure.

ABCD

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Answer: (B)

We know that $\frac{\mathrm{dQ}}{\mathrm{dt}}=\mathrm{KA} \frac{\mathrm{d} \theta}{\mathrm{dx}}$
In steady state flow of heat
$$\begin{aligned} & \mathrm{d} \theta=\frac{\mathrm{dQ}}{\mathrm{dt}} \cdot \frac{1}{\mathrm{kA}} \cdot \mathrm{dx} \\ & \Rightarrow \theta_{\mathrm{H}}-\theta=\mathrm{k}^{\prime} \mathrm{x} \Rightarrow \theta=\theta_{\mathrm{H}}-\mathrm{k}^{\prime} \mathrm{x} \end{aligned}$$
Equation $\theta=\theta_H-k^{\prime} x$ represents a straight line.