Thermal Expansion
Thermal expansion is the tendency of matter to increase in length, area, or volume when its temperature rises, due to the increased average separation between particles as they vibrate more vigorously. Most solids, liquids, and gases expand on heating, with gases expanding far more than liquids or solids. Thermal expansion has important engineering implications — railway tracks have expansion gaps, bridges have expansion joints, and thermometers exploit the expansion of mercury or alcohol — while water's anomalous contraction on cooling from 4 °C to 0 °C is critical to aquatic life in cold climates.
Key Formula
ΔL = L₀ × α × ΔT
LaTeX: \Delta L = L_0 \alpha \Delta T
| Symbol | Meaning | Unit |
|---|---|---|
| ΔL | Change in length | m |
| L₀ | Original length | m |
| α | Coefficient of linear thermal expansion | K⁻¹ (or °C⁻¹) |
| ΔT | Change in temperature | K or °C |
Worked Example
Problem
A steel railway track is 25 m long at 20 °C. How much does it expand when heated to 50 °C? (α for steel = 12 × 10⁻⁶ K⁻¹)
Solution
Step 1: Identify variables: L₀ = 25 m, α = 12 × 10⁻⁶ K⁻¹, ΔT = 50 - 20 = 30 K. Step 2: Apply ΔL = L₀ × α × ΔT. ΔL = 25 × 12 × 10⁻⁶ × 30 = 25 × 3.6 × 10⁻⁴ = 9 × 10⁻³ m.
Answer
ΔL = 0.009 m = 9 mm
Coefficients of Linear Thermal Expansion for Common Materials
| Material | α (×10⁻⁶ K⁻¹) | Application | Expansion per 1 m per 100 K (mm) |
|---|---|---|---|
| Invar (Ni-Fe alloy) | 1.2 | Precision instruments, clocks | 0.12 |
| Glass (borosilicate) | 3.3 | Lab glassware, cookware | 0.33 |
| Concrete | 12 | Buildings, roads | 1.2 |
| Steel | 12 | Bridges, railways | 1.2 |
| Aluminium | 23 | Aircraft, engine parts | 2.3 |
| Copper | 17 | Pipes, electrical conductors | 1.7 |
Interactive Tools
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Related Terms
Temperature
Temperature is a scalar physical quantity that measures the average kinetic energy of the particles in a substance, indicating how hot or cold the substance is. It is a fundamental thermodynamic property that determines the direction of heat flow between objects in thermal contact — heat always flows from a higher-temperature body to a lower-temperature body. Temperature is measured using thermometers and is expressed in units of Kelvin (SI), Celsius, or Fahrenheit, and it plays a central role in all thermodynamic processes including phase transitions, chemical reactions, and heat engines.
Ideal Gas Law
The Ideal Gas Law is an equation of state for a hypothetical ideal gas, combining the empirical gas laws of Boyle, Charles, and Gay-Lussac into a single relationship between the pressure, volume, amount, and absolute temperature of a gas. It assumes gas molecules have negligible volume and no intermolecular forces, making it an excellent approximation for real gases at low pressures and high temperatures. It is foundational to thermodynamics, chemistry, and engineering, used in everything from weather balloon calculations to industrial gas storage and the analysis of respiratory physiology.
Charles's Law
Charles's Law states that for a fixed amount of an ideal gas at constant pressure, the volume of the gas is directly proportional to its absolute (Kelvin) temperature — when temperature doubles (in Kelvin), volume doubles. This is an isobaric (constant pressure) process, and the ratio V/T remains constant. The law explains why a balloon expands when warmed, why hot air rises in atmospheric convection, and why gas-filled containers must be stored away from heat sources to prevent rupture.
From Latin "thermalis" (relating to heat, from Greek "therme") and "expansio" (a spreading out, from "expandere" — to spread). The systematic study of thermal expansion was conducted by French scientist Guillaume Amontons and later refined by Lavoisier and Laplace in the 18th century.