A long rod has one end at \( 0^{\circ} \mathrm{C} \) and other end at a high temperature. The co...

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A long rod has one end at \( 0^{\circ} \mathrm{C} \) and other end at a high temperature. The coefficient of thermal conductivity varies with distance from the low temperature end as \( k=k_{0}(1+ \) \( a x \) ), where \( k_{0}=10^{2} \) S.I. unit and \( \alpha=1 \mathrm{~m}^{-1} \). At what distance from the first end the temperature will be \( 100^{\circ} \mathrm{C} \) ? [The area of cross-section is \( 1 \mathrm{~cm}^{2} \) and rate of heat conduction is \( 1 \mathrm{~W} \).]
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