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?
AIEEE 2009, Medium
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The heat flow rate is given by
$\frac{{dQ}}{{dt}} = \frac{{kA\left( {{\theta _1} - \theta } \right)}}{x}$
$ \Rightarrow {\theta _1} - \theta = \frac{x}{{kA}}\frac{{dQ}}{{dt}} \Rightarrow \theta = {\theta _1} - \frac{x}{{kA}}\frac{{dQ}}{{dt}}$
Where $\theta _1$ is the temperature of hot and $\theta $ is temperature at a distance $x$ from hot end.
The above equation can be graphically represented by option $(a)$.
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