Question:
Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is ' $\alpha^{\prime}$. The metal sheet is heated uniformly, by a small temperature $\Delta T ,$ so that its new temperature is $T +\Delta T$. Calculate the increase in the volume of the metal box.
Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is ' $\alpha^{\prime}$. The metal sheet is heated uniformly, by a small temperature $\Delta T ,$ so that its new temperature is $T +\Delta T$. Calculate the increase in the volume of the metal box.
Updated On: Aug 14, 2024
- $3 a ^{3} \alpha \Delta T$
- $4 a ^{3} \alpha \Delta T$
- $4 \pi a ^{3} \alpha \Delta T$
- $\frac{4}{3} \pi a ^{3} \alpha \Delta T$
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The Correct Option is A
Solution and Explanation
The correct option is(A): \(3 a ^{3} \alpha \Delta T\).
\(\Delta V = V \gamma \Delta T\)
\(\Delta V =3 a ^{3} \alpha \Delta T\)
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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.
