Question:
The ratio of the coefficient of thermal conductivity of two different materials is $ 5:3. $ If the thermal resistance of the rods of same thickness of these materials is same, then the ratio of the length of these rods will be
The ratio of the coefficient of thermal conductivity of two different materials is $ 5:3. $ If the thermal resistance of the rods of same thickness of these materials is same, then the ratio of the length of these rods will be
Updated On: Jun 23, 2024
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The Correct Option is B
Solution and Explanation
The thermal resistance of a rod of length $l$, area of cross-section $A$ and thermal conductivity $K$, is
$R=\frac{l}{K A}$
Given, thermal resistance of rods is equal therefore, also $A_{1}=A_{2}$
$\frac{l_{1}}{K_{1}\, A_{1}}=\frac{l_{2}}{K_{2} \,A_{2}}$
$\Rightarrow \frac{l_{1}}{K_{1}}=\frac{l_{1}}{K_{2}}$
$\Rightarrow \frac{l_{1}}{l_{2}}=\frac{K_{1}}{K_{2}}=\frac{5}{3}$
$R=\frac{l}{K A}$
Given, thermal resistance of rods is equal therefore, also $A_{1}=A_{2}$
$\frac{l_{1}}{K_{1}\, A_{1}}=\frac{l_{2}}{K_{2} \,A_{2}}$
$\Rightarrow \frac{l_{1}}{K_{1}}=\frac{l_{1}}{K_{2}}$
$\Rightarrow \frac{l_{1}}{l_{2}}=\frac{K_{1}}{K_{2}}=\frac{5}{3}$
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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.
