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Chapter 14: Thermal Physics

14.A: Thermal Expansion

Thermal Energy
The total kinetic energy of the particles within a system.
Thermal Expansion
A condition in which a material increases in size when thermal energy is added.
Thermodynamics
The study of thermal energy and its movement within systems.
Coefficient of Linear Expansion (α)
A constant that quantifies how much a material expands per degree of temperature change, measured in °C-1.

Basics of Thermal Expansion

  • Hotter atoms have more kinetic energy and vibrate faster, causing materials to expand.
  • Vibrating atoms occupy more space at higher temperatures, leading to expansion in all directions.
  • Examples include:
    • Railroad tracks and sidewalks designed with expansion gaps.
    • Bridges with expansion joints to accommodate temperature changes.

Linear Thermal Expansion

Formula

Δl = α li ΔT

Variables
  • Δl: Change in length (m).
  • α: Coefficient of linear expansion (°C-1).
  • li: Original length (m).
  • ΔT: Temperature change (°C).

Examples of Thermal Expansion

  1. Linear Expansion of a Steel Bridge:
    • Initial length: 200.00 m
    • Temperature change: 50.0 °C
    • α for steel: 11.7 × 10-6 °C-1
    • Δl = (11.7 × 10-6)(200.00)(50.0) = 0.117 m
  2. Volumetric Expansion:
    • ΔV = βViΔT, where β = 3α.
    • Used for objects with irregular shapes.

Applications of Thermal Expansion

  • Bimetallic strips in thermostats to sense temperature changes.
  • Design of engine components to account for thermal expansion.
  • Expansion joints in bridges and buildings to prevent structural damage.

Questions for Students

  1. Define thermal energy and explain how it differs from temperature.
  2. What is the significance of the coefficient of linear expansion (α)?
  3. Calculate the change in length of a 300 m steel rail for a temperature increase of 40 °C (α = 11.7 × 10-6 °C-1).
  4. Describe how bridges are designed to accommodate thermal expansion.
  5. Why do liquids generally expand more than solids?