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

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

AIEEEAIEEE 2009Thermal Properties of Matter

Solution:

We know that $\frac{dQ}{dt}=KA \frac{d\theta}{dx}$
In steady state flow of heat
$d\theta =\frac{dQ}{dt}. \frac{1}{kA}.dx$
$\Rightarrow \theta_{H}-\theta=k 'x \Rightarrow \theta =\theta_{H}-k 'x$
Equation $θ = θ_{H} - k ′ x$ represents a straight line.