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Which of the following circular rods (given radius r and length l), each made of the same material and whose ends are maintained at the same temperature will conduct most heat?
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- r = r0; l = l0
- r = 2r0; l = l0
- r = r0; l = 2l0
- r = 2r0; l = 2l0
Correct Option: B
| We know that Q = | ||
| R |
| Also, Thermal resistance R = | = | ||
| KA | Kπr² |
Heat flow will be maximum when thermal resistance is minimum.
From given option
(i) r = 2r0, l = 2l0
| ∴ R = | = | ||
| Kπ(2r0)² | 4Kπr0² |
(ii) r = 2r0, l = l0
| ∴ R = | = | ||
| Kπr0² | Kπr0² |
(iii) r = r0, l = 2l0
| ∴ R = | = | ||
| Kπr0² | Kπr0² |
(iv) r = r0, l = l0
r = 2r0, l = l0
| ∴ R = | = | ||
| Kπr0² | Kπr0² |
It is clear that for option (2) resistance is minimum, hence, heat flow will be maximum.
(i) Rate of heat flow is directly proportional to area
(ii) inversely proportional to length.
∴ Heat flow will be maximum when r is maximum and is minimum.
