Question:
Heat is flowing through two cylindrical rods of the same material. The diameters of the rods are in the ratio 1 : 2 and the lengths in the ratio 2 : 1. If the temperature difference between the ends is same, then ratio of the rate of flow of heat through them will be
Heat is flowing through two cylindrical rods of the same material. The diameters of the rods are in the ratio 1 : 2 and the lengths in the ratio 2 : 1. If the temperature difference between the ends is same, then ratio of the rate of flow of heat through them will be
Updated On: Jun 23, 2024
- 2:1
- 8:1
- 1:1
- 1:8
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The Correct Option is D
Solution and Explanation
Ratio of diameters of rod = 1 : 2 and ratio of their lengths 2:1.
The rate of flow of heat, \((R) = \frac{ KA \Delta T}{l} \propto \frac{A}{l}\)
\(\therefore \, \, \, \, \, \frac{R_1}{R_2}= \frac{ A_1}{A_2} \times \frac{l_2}{l_1} = \bigg( \frac{1}{2} \bigg)^2 \times \frac{1}{2} = \frac{1}{8}\)
or \(R_1 : R_2 = 1:8\)
Therefore, the correct option is (D) : 1:8
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Concepts Used:
Heat Transfer
What is Heat Transfer?
It is defined as the movement of heat across the border of the system due to a difference in temperature between system and its surroundings.
How is Heat Transferred?
Heat can travel from one place to another in several ways. The different modes of heat transfer include:
- Conduction - Heat flows from things with higher temp to objects with lower temp.
- Convection - Movement of liquid molecules from higher temp regions to lower temp regions.
- Radiation - Radiant heat is present in every other way in our daily lives. Thermal radiations are also known to as radiant heat. Thermal radiation is generated by the emission of electromagnetic waves.
