Question:
The coefficient of linear expansion of a metal rod is $12 \times 10^{-6} / ^{\circ}C$ , its value in per its value in per $^{\circ}F$
The coefficient of linear expansion of a metal rod is $12 \times 10^{-6} / ^{\circ}C$ , its value in per its value in per $^{\circ}F$
Updated On: Jun 20, 2024
- $\frac{20}{3} \times 10^{-6}/^{\circ}F$
- $\frac{15}{4} \times 10^{-6}/^{\circ}F$
- $21.6\times 10^{-6}/^{\circ}F$
- $12\times 10^{-6}/^{\circ}F$
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The Correct Option is A
Solution and Explanation
Coefficient of thermal expansion = Change in length / (original length $X$
change in temperature)
So, $\alpha_{ c } / \alpha_{ F }=$ Change in temp in Fahrenheit / change in temp in centigrade
Or $\alpha_{ F }=\alpha_{ C }\left(\right.$ change in $T _{ C } /$ change in $\left.T _{ F }\right)$
$
=\alpha_{ C }\left(\text { change in } T _{ C } /(9 / 5) \text { change in } T _{ C }\right)
$
$=\alpha_{ C } \times(5 / 9)$
$=(20 / 3) \times 10^{-6}$
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Concepts Used:
Thermal Expansion
Thermal expansion is the tendency of matter to change its shape, area, and volume in response to a change in temperature. Temperature is a monotonic function of the average molecular kinetic energy of a substance.
The expansion of the solid material is taken to be the linear expansion coefficient, as the expansion takes place in terms of height, thickness and length. The gaseous and liquid expansion takes the volume expansion coefficient. Normally, if the material is fluid, we can explain the changes in terms of volume change.
The bonding force among the molecules and atoms differs from material to material. These characteristics of the compounds and elements are known as the expansion coefficient.
