Q81 / 90 · JEE Main 2009 · Physics

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.

  • A
    Figure
  • Correct answer
    B
    Figure
  • C
    Figure
  • D
    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.

Hence, the correct answer is option: 'B'.

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