NEET-XII-Physics
28: Heat Transfer
- #11The ends of a metre stick are maintained at 100°C and 0°C. One end of a rod is maintained at 25°C. Where should its other end be touched on the metre stick so that there is no heat current in the rod in steady state?Ans :
One end of the rod is at a temperature of 25°C. So, if no heat current flows through the rod in steady state, then the other end of the rod should also be at a temperature of 25°C.
Let the point at which the other end of the rod is touched be C.
No heat flows through the rod when the temperature at point C is also 25°C.
Heat current through AC = Heat current through CB
`` \Rightarrow \frac{{\left(\,\mathrm{\,\Delta \,}T\right)}_{\,\mathrm{\,AC\,}}}{{\displaystyle \frac{x}{\,\mathrm{\,kA\,}}}}=\frac{{\left(\,\mathrm{\,\Delta \,}T\right)}_{\,\mathrm{\,CB\,}}}{{\displaystyle \frac{100-x}{\,\mathrm{\,kA\,}}}}``
`` \frac{\left(100-25\right)}{x}=\frac{25-0}{100-x}``
`` \frac{3}{x}=\frac{1}{100-x}``
`` 300-3x=x``
`` 300=4x``
`` x=75\,\mathrm{\,cm\,}``
Thus, it should be touched at 75 cm from 100°C end.
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