JEE MAIN - Physics (2009 - No. 22)
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?
Explanation
The heat flow rate is given by
$${{dQ} \over {dt}} = {{kA\left( {{\theta _1} - \theta } \right)} \over x}$$
$$ \Rightarrow {\theta _1} - \theta $$ $$ = {x \over {kA}}{{dQ} \over {dt}} $$
$$\Rightarrow \theta $$ $$ = {\theta _1} - {x \over {kA}}{{dQ} \over {dt}}$$
where $${\theta _1}$$ is the temperature of hot end and $$\theta $$ is temperature at a distance $$x$$ from hot end.
The above equation can be graphically represented by option $$(a).$$
$${{dQ} \over {dt}} = {{kA\left( {{\theta _1} - \theta } \right)} \over x}$$
$$ \Rightarrow {\theta _1} - \theta $$ $$ = {x \over {kA}}{{dQ} \over {dt}} $$
$$\Rightarrow \theta $$ $$ = {\theta _1} - {x \over {kA}}{{dQ} \over {dt}}$$
where $${\theta _1}$$ is the temperature of hot end 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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