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Temperature changes cause materials to expand or contract, affecting their dimensions and properties. This phenomenon, known as thermal expansion, is crucial in engineering and everyday life, from designing bridges to creating thermometers.

Thermal expansion occurs because increased temperature boosts atomic kinetic energy, causing particles to move more vigorously. This leads to greater average separation between particles, resulting in overall expansion. Different materials expand at varying rates, influencing their behavior under temperature changes.

Thermal Expansion

Thermal expansion effects

  • Matter changes dimensions when temperature changes
    • Solids expand when heated and contract when cooled (railroad tracks)
    • Liquids expand when heated and contract when cooled (mercury thermometer)
  • Increased temperature leads to increased average kinetic energy of atoms or molecules
    • Particles move more vigorously, maintaining greater average separation, causing expansion (vibrating atoms in a crystal lattice)
  • Degree of expansion varies based on material properties
    • Different materials have different coefficients of thermal expansion (aluminum vs. glass)
  • Thermal expansion causes changes in dimensions, volume, and density
    • Linear expansion affects length (metal rod)
    • Area expansion affects surface area (metal sheet)
    • Volume expansion affects volume (water in a tank)
  • Thermal expansion can lead to changes in density as the mass remains constant while volume changes

Linear expansion calculations

  • Calculate linear expansion using: $\Delta L = \alpha L_0 \Delta T$
    • $\Delta L$ = change in length
    • $\alpha$ = coefficient of linear expansion, a material property ($\text{K}^{-1}$ or $^\circ\text{C}^{-1}$)
    • $L_0$ = initial length
    • $\Delta T$ = change in temperature
  • Coefficient of linear expansion measures expansion per unit length per degree of temperature change
    • Example: $\alpha = 2 \times 10^{-5} \text{K}^{-1}$ for steel
  • Calculate new length after thermal expansion: $L_f = L_0 + \Delta L$
    • $L_f$ = final length after expansion
    • Example: $L_f = 1 \text{m} + (2 \times 10^{-5} \text{K}^{-1})(1 \text{m})(10 \text{K}) = 1.0002 \text{m}$

Volume expansion determination

  • Calculate volume expansion using: $\Delta V = \beta V_0 \Delta T$
    • $\Delta V$ = change in volume
    • $\beta$ = coefficient of volume expansion, a material property
    • $V_0$ = initial volume
    • $\Delta T$ = change in temperature
  • Coefficient of volume expansion is approximately three times coefficient of linear expansion for most materials: $\beta \approx 3\alpha$
    • Example: $\beta \approx 3(2 \times 10^{-5} \text{K}^{-1}) = 6 \times 10^{-5} \text{K}^{-1}$ for steel
  • Calculate new volume after thermal expansion: $V_f = V_0 + \Delta V$
    • $V_f$ = final volume after expansion
    • Example: $V_f = 1 \text{m}^3 + (6 \times 10^{-5} \text{K}^{-1})(1 \text{m}^3)(10 \text{K}) = 1.0006 \text{m}^3$

Thermal stress analysis

  • Thermal stress occurs when an object is constrained while undergoing thermal expansion or contraction
    • Constraint prevents free expansion or contraction, leading to internal stresses (railroad tracks buckling on a hot day)
  • Thermal stress can cause deformation, buckling, or breakage if stress exceeds material's strength
    • Example: glass shattering when subjected to rapid temperature change
  • Magnitude of thermal stress depends on material properties
    • Coefficient of thermal expansion
    • Elastic modulus (measure of material's stiffness)
  • Calculate thermal stress using: $\sigma = E\alpha\Delta T$
    • $\sigma$ = thermal stress
    • $E$ = elastic modulus
    • $\alpha$ = coefficient of linear expansion
    • $\Delta T$ = change in temperature
  • Minimize thermal stress by:
    1. Using materials with similar coefficients of thermal expansion in applications with expected temperature changes (bimetallic strip in a thermostat)
    2. Allowing for expansion joints or gaps to reduce thermal stress in structures (bridge expansion joints)

Thermal Equilibrium and Energy Transfer

  • Thermal equilibrium occurs when two objects reach the same temperature through heat transfer
  • The process of reaching thermal equilibrium involves the transfer of kinetic energy between particles
  • As objects expand or contract due to temperature changes, they work towards achieving thermal equilibrium with their surroundings