Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Thermodynamics → Heat and work ↓


Thermal expansion


Thermal expansion is a fundamental concept in the field of thermodynamics that describes how the size or volume of an object changes when exposed to changes in temperature. This phenomenon is important in understanding how a substance behaves when it is heated or cooled. When the temperature of a substance increases, its particles move more and thus the substance generally expands. Conversely, when the temperature is lowered, the particles slow down and the substance contracts.

Basics of thermal expansion

At the atomic and molecular level, matter consists of particles that are constantly in motion. These particles vibrate and collide with one another. Temperature is essentially a measure of the average kinetic energy of these particles. When the temperature of a substance increases, the kinetic energy of its particles also increases. This increased speed causes the particles to require more space, resulting in the expansion of the substance. Conversely, when the temperature is lowered, the movement of the particles slows down and the substance contracts.

Linear expansion

Linear expansion refers to the change in one dimension (length) of an object due to a temperature change. When discussing linear expansion, engineers and scientists often use the coefficient of linear expansion, represented by the symbol α. This coefficient is a material-specific constant that indicates how much a material expands per degree temperature rise.

The equation governing linear expansion is:

ΔL = αL₀ΔT
  • ΔL is the change in length.
  • L₀ is the original length of the material.
  • ΔT is the change in temperature.
  • α is the coefficient of linear expansion.

For example, consider a metal rod with an original length of 2 m at 20 °C. If the coefficient of linear expansion of the material of the rod is 12 x 10^-6 / °C and the temperature is increased to 100 °C, the change in its length can be calculated as:

ΔL = αL₀ΔT = (12 x 10^-6 / °C) * 2 m * (100°C - 20°C) = 0.00192 m

Hence, the rod will expand by 0.00192 m (or 1.92 mm) with increase in temperature.

Area expansion

Area expansion considers how the surface area of a two-dimensional object changes with temperature. This kind of expansion is important in contexts where flat objects such as metal sheets and thin plates are used.

The field expansion can be described by the formula:

ΔA = βA₀ΔT
  • ΔA is the change in area.
  • A₀ is the fundamental region.
  • ΔT is the change in temperature.
  • β is the field expansion coefficient, which is approximately equal to 2α for most materials.

Suppose the area of a metal plate at 25°C is 1 square meter and the coefficient of linear expansion for the material is 10 x 10^-6 / °C If the temperature changes to 75°C, the expansion in area can be calculated as:

β = 2α = 2 * (10 x 10^-6 / °C) = 20 x 10^-6 / °C ΔA = βA₀ΔT = (20 x 10^-6) * 1 m² * (75°C - 25°C) = 0.001 m²

This area expands to 0.001 square metres (or 1,000 square metres) as the temperature increases.

Volumetric expansion

Volume expansion addresses the changes in the volume of an object with temperature changes and is important in applications involving liquids or solids with significant three-dimensional proportions. The volume expansion formula is:

ΔV = γV₀ΔT
  • ΔV is the change in volume.
  • V₀ is the original volume.
  • ΔT is the change in temperature.
  • γ is the coefficient of volume expansion, which is about 3α for most materials.

Consider a sealed jug filled with 3 liters of water at 20°C. If the water is heated to 80°C, and the coefficient of volume expansion of water is 210 x 10^-6 / °C, the change in volume can be determined by:

ΔV = γV₀ΔT = (210 x 10^-6 / °C) * 3 L * (80°C - 20°C) = 0.0378 L

Therefore, the water expands by approximately 0.0378 liters (or 37.8 mL) as the temperature increases.

Visualization of thermal expansion

Visualizing thermal expansion helps to understand this concept more effectively. Imagine a thick metal ring. When the ring is heated uniformly, each part of the ring expands, so the ring becomes larger overall. The following example shows a simplified view of a circle expanding when heated.

original size Extended Size

In this diagram, the circle on the left shows the original shape, and the circle on the right shows the expanded shape after heating. The visualization clearly shows how the dimensions increase proportionally.

Text example: train tracks

A practical example of thermal expansion is the design of railway tracks. Metal rails are usually made from steel which expands and contracts with seasonal temperature changes. To account for thermal expansion, small gaps are left between sections of the rails so that they do not warp or twist. Let us understand this through an example.

Assume that each track segment has an initial length of 12 m at 15°C. Given a linear expansion coefficient of 11 x 10^-6 / °C for steel, if the temperature is increased to 35°C, the increase in length will be:

ΔL = αL₀ΔT = (11 x 10^-6 / °C) * 12 m * (35°C - 15°C) = 0.00264 m

Each section becomes 0.00264 m (or 2.64 mm) longer as the temperature increases. Designers must consider this expansion and provide adequate gaps between the rails to avoid structural damage.

Applications and implications

Thermal expansion, although often subtle, has many engineering applications and consequences. Bridges require expansion joints to prevent failure of structural integrity as materials expand and contract. Buildings can move subtly with changes in temperature, requiring careful planning in architectural design to accommodate this movement.

Another important application of thermal expansion is the liquid thermometer in glass. The liquid inside (usually mercury or colored alcohol) expands and contracts with changes in the outside temperature, moving up or down on the thermometer scale to indicate temperature.

Understanding thermal expansion is also essential in electronics. Circuit boards heat up during operation, so it is important to consider thermal expansion to prevent breakage or connection problems.

Conclusion

In short, thermal expansion is an important physics concept that describes how objects react to temperature changes. It manifests through linear, area, and volume expansion. These principles are important in a variety of real-world applications, from railways to aerospace engineering. Understanding thermal expansion helps engineers design structures that remain safe and functional despite changes in environmental temperature.


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Thermal expansion

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