A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation…
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.
Solution
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
