MIND GROW Magazine

Properties of Matter – Stage 1 (Page 8)

Thermal Stress, Thermal Strain & Thermal Expansion (JEE Core)

1. Thermal Expansion

When temperature of a material changes, its dimensions change. This phenomenon is called thermal expansion.

Occurs due to increase in molecular vibration
Important in bridges, rails, machinery

2. Types of Thermal Expansion

Type	Coefficient	Formula
Linear Expansion	α	ΔL = LαΔT
Area Expansion	β	ΔA = AβΔT
Volume Expansion	γ	ΔV = VγΔT

3. Relation Between Expansion Coefficients

β = 2α

γ = 3α

IIT Tip:
These relations hold only for isotropic solids.

4. Thermal Strain

Thermal strain is the strain produced due to temperature change.

Thermal Strain = αΔT

Independent of original length
Purely temperature dependent

5. Thermal Stress

If expansion or contraction of a body is prevented, stress develops in the body called thermal stress.

Thermal Stress = Y × α × ΔT

JEE Favourite Condition:
Rod fixed at both ends → maximum thermal stress

6. Important Special Cases

Free expansion: No stress developed
Fully constrained: Maximum stress
Partially constrained: Reduced stress

σ = Y(αΔT − actual strain)

7. Numerical Shortcut (JEE)

One-Line Formula:
If expansion is fully prevented:
σ = YαΔT

Units Check:
α → per °C
Y → N/m²
σ → N/m²

Stage 1 – Page 8 Summary

Thermal expansion types
Coefficient relations
Thermal strain & stress
Fully vs free expansion cases

Stage 1 – Page 8 Completed ✅
Next: Poisson’s Ratio & Elastic Constants – Page 9

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