1. Tardigrade
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  3. Physics
  4. A rod is of 40 cm in length and has a temperature difference of 80° C at its two ends. Another rod b is of length 60 cm and has a temperature difference 90° C but has the same area of cross-section. If the rate of flow of heat is the same, then the ratio of their thermal conductivities will be

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Q. A rod is of 40 cm in length and has a temperature difference of $80^{\circ} C$ at its two ends. Another rod $b$ is of length 60 cm and has a temperature difference $90^{\circ} C$ but has the same area of cross-section. If the rate of flow of heat is the same, then the ratio of their thermal conductivities will be

Thermal Properties of Matter

Solution:

$ H=\frac{K_{1} A \Delta T_{1}}{l_{1}}=\frac{K_{2} \cdot A \cdot \Delta T_{2}}{l_{2}}$
$\Rightarrow \frac{K_{1} \Delta T_{1}}{l_{1}}=\frac{K_{2} \cdot \Delta T_{2}}{l_{2}}$
$ \frac{K_{1}\left(80^{\circ} C \right)}{40 cm }=\frac{K_{2}\left(90^{\circ} C \right)}{60 cm }$
$\Rightarrow \frac{K_{1}}{K_{2}}=\frac{40 cm \times 90^{\circ} C }{60 cm \times 80^{\circ} C }=\frac{3}{4}$