Discussion
Heat is conducted through a uniform rod ABC of length 1 m keeping the end A at 100°C . If the temperature at the point B at a distance 0.4m from the end A is 80°C and that at the other end is 40°C, then the ratio of heat conducted through AB to that through BC is
Answer: A
The ratio is 3 : 4.
The rate of heat conduction through a section is \(H = kA\frac{\Delta T}{L}\), and the rod is uniform, so \(H\) is proportional to the temperature gradient:
\[ \begin{aligned} AB: \frac{100 - 80}{0.4} &= 50\ ^{\circ}\text{C m}^{-1} \\ BC: \frac{80 - 40}{0.6} &= \frac{200}{3}\ ^{\circ}\text{C m}^{-1} \\ \text{ratio} &= 50 : \tfrac{200}{3} = 3 : 4 \end{aligned} \]
Comparing temperature drops alone (20 : 40 = 1 : 2) ignores the different lengths, and 2 : 1 inverts that.
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