Q.If α, β and γ are coefficients of linear, areal and volume expansion of a solid then (A) α:β:γ = 1:3:2 (B) α:β:γ = 1:2:3 (C) α:β:γ = 2:3:1 (D) α:β:γ = 3:1:2

Thermal Expansion: Why Things Grow When Heated

You already know that matter is made of atoms or molecules. In a solid, these particles are locked into a lattice, but they are not still — they vibrate around fixed positions. When you heat a substance, you give its particles more energy. They vibrate faster and with larger amplitude. That larger vibration pushes the particles slightly farther apart from each other. The result? The whole object gets bigger. That is thermal expansion.

The key intuition: heat increases atomic vibration, which increases the average distance between atoms, which makes the object expand in every direction.

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The Precise Physics

For small temperature changes, the expansion is directly proportional to the temperature change. This is an excellent approximation for most engineering and exam problems.

Linear expansion (change in one dimension — length):

$\Delta L = \alpha L_0 \Delta T$

where $\alpha$ is the coefficient of linear expansion, $L_0$ is the original length, and $\Delta T$ is the temperature change.

Area expansion (change in two dimensions):

$\Delta A = \beta A_0 \Delta T$

where $\beta$ is the coefficient of area expansion. …