Question 523: Thermodynamics & KTG

Question

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

Accepted Answer

The heat flow rate is given by
$${{dQ} \over {dt}} = {{kA\left( {{	heta _1} - 	heta } ight)} \over x}$$
$$ \Rightarrow {	heta _1} - 	heta $$
$$ = {x \over {kA}}{{dQ} \over {dt}} $$
$$\Rightarrow 	heta $$
$$ = {	heta _1} - {x \over {kA}}{{dQ} \over {dt}}$$
where $${	heta _1}$$ is the temperature of hot end and $$	heta $$ is temperature at a distance $$x$$ from hot end.
The above equation can be graphically represented by option $$(a).$$

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Thermodynamics & KTG

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?

Choose the correct answer: