Thermal Expansion

1. Expansion in Solids

Thermal expansion occurs when a substance expands upon heating due to the increased kinetic energy of its molecules. In solids, expansion occurs in three dimensions: length, area, and volume.

Linear Expansivity (α)

Linear expansivity is the fractional increase in length per unit length per Kelvin (or degree Celsius) rise in temperature. The formula is:

α = (L₂ - L₁) / (L₁ * Δθ)

Where L₁ is initial length, L₂ is final length, and Δθ is the change in temperature. The unit is K⁻¹ or °C⁻¹.

Area (Superficial) and Volume (Cubic) Expansivities

• Area Expansivity (β): The increase in area per unit area per degree rise in temperature. Relationship: β = 2α.
• Volume Expansivity (γ): The increase in volume per unit volume per degree rise in temperature. Relationship: γ = 3α.

Effects and Applications

• Railway Tracks: Gaps are left between rails to allow for expansion in hot weather, preventing buckling.
• Bimetallic Strips: Two metals with different expansivities bonded together. Used in thermostats (irons, water heaters) because the strip bends when heated.
• Bridges: Steel girders are often placed on rollers to allow for seasonal expansion and contraction.
• Building Strips: Expansion joints are placed in concrete roads and walls to prevent cracking.

2. Expansion in Liquids

Liquids do not have a fixed shape, so we only consider volume expansivity. However, when a liquid is heated, its container also expands.

Real and Apparent Expansivities

• Apparent Expansivity (γₐ): The observed expansion of the liquid without accounting for the expansion of the container.
• Real (Absolute) Expansivity (γᵣ): The actual expansion of the liquid.
• Formula: γᵣ = γₐ + γ꜀ (where γ꜀ is the volume expansivity of the container).

3. Anomalous Expansion of Water

Most substances expand when heated, but water behaves strangely between 0°C and 4°C. When water is heated from 0°C to 4°C, it contracts (volume decreases, density increases). Above 4°C, it expands normally. This means water has its maximum density at 4°C. This phenomenon is vital for aquatic life as it ensures that the bottom of frozen lakes remains at 4°C, allowing fish to survive.