Glossary

is a fundamental property of matter, causing materials to change size as fluctuates. This phenomenon affects solids, liquids, and gases differently, with important implications for engineering and everyday life.

Understanding is crucial for designing everything from bridges to thermostats. We'll explore how to calculate expansion, its relationship to other thermodynamic properties, and its practical applications in various fields.

Thermal Expansion

Causes and effects of thermal expansion

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  • Caused by increased average of particles as temperature rises
    • Particles vibrate with greater amplitude leading to increased average separation between them (atoms in a solid, molecules in a liquid or gas)
    • This increased results in thermal expansion
  • Effects differ among solids, liquids, and gases
    • Solids
      • Expand in all dimensions (length, width, height)
      • Expansion typically small varies depending on material (metals expand more than ceramics)
    • Liquids
      • Expand primarily in as they lack a fixed shape
      • Expansion generally greater than solids (water expands about 4 times more than steel)
    • Gases
      • Expand significantly in volume compared to solids and liquids (about 1000 times more than solids)
      • Expansion directly proportional to temperature change at constant (doubling temperature doubles volume)

Calculations for temperature-induced changes

  • Linear thermal expansion (one-dimensional)
    • Change in length ΔL=αL0ΔT\Delta L = \alpha L_0 \Delta T
      • α\alpha: coefficient material-specific (aluminum α=24×10−6\alpha = 24 \times 10^{-6} /℃)
      • L0L_0: initial length
      • ΔT\Delta T: change in temperature
  • Volumetric thermal expansion (three-dimensional)
    • Change in volume ΔV=βV0ΔT\Delta V = \beta V_0 \Delta T
      • β\beta: coefficient material-specific (ethanol β=1100×10−6\beta = 1100 \times 10^{-6} /℃)
      • V0V_0: initial volume
    • For materials β≈3α\beta \approx 3\alpha (volume expands about 3 times as much as length)
  • Thermal expansion of liquids
    • : includes expansion of containing vessel (water level rises in a glass when heated)
    • : accounts only for liquid's expansion
      • ΔVabsolute=ΔVapparent−βvesselV0ΔT\Delta V_{absolute} = \Delta V_{apparent} - \beta_{vessel} V_0 \Delta T (subtracts expansion of the container itself)

Relationship between thermal expansion and thermodynamic properties

  • Temperature: A measure of the average kinetic energy of particles in a substance
  • Pressure: Force exerted by particles colliding with container walls, increases with temperature in a fixed volume
  • Volume: Increases with temperature as particles spread out, affecting the overall size of the substance

Applications of thermal expansion

  • Bimetallic strips in thermostats and fire alarms
    • Two metals with different expansion coefficients bonded together (brass α=19×10−6\alpha = 19 \times 10^{-6} /℃, α=1.2×10−6\alpha = 1.2 \times 10^{-6} /℃)
    • Strips bend when heated activating the device (electrical contact made or broken)
  • in bridges, railways, pipelines
    • Allow for expansion and contraction due to temperature changes (several centimeters over 100 m spans)
    • Prevent buckling, warping, damage to the structure (misaligned railroad tracks, burst pipes)
  • Challenges
    • and material fatigue
      • Repeated expansion and contraction can weaken materials over time (cracks in concrete, metal fatigue)
      • Proper material selection and design considerations crucial (expansion coefficients, operating temperature range)
    • Precision engineering and manufacturing
      • Thermal expansion can affect fit and tolerance of components (engine pistons, bearings)
      • Engineers must account for expansion when designing machines, engines, electronics (leaving gaps, using materials with similar α\alpha)
    • Extreme temperature environments
      • High temperatures in engines and industrial processes (turbines, furnaces operating above 1000 ℃)
      • Low temperatures in cryogenic systems and space applications (liquid nitrogen at -196 ℃, spacecraft exposed to near 0 K)
      • Materials with low expansion coefficients used in these cases (Invar α=1.2×10−6\alpha = 1.2 \times 10^{-6} /℃, silica glass α=0.4×10−6\alpha = 0.4 \times 10^{-6} /℃)

Key Terms to Review (33)

Absolute expansion: Absolute expansion refers to the total increase in the size of an object or material when it is heated, measured without considering any external constraints. This concept is crucial in understanding how materials respond to temperature changes, emphasizing that all matter expands to some degree as it gains heat. The idea of absolute expansion is foundational to predicting how different materials behave in varying thermal environments.
Absolute temperature scale: An absolute temperature scale is a thermodynamic temperature scale that uses absolute zero as its null point. The two most common absolute temperature scales are Kelvin and Rankine.
Apparent Expansion: Apparent expansion refers to the observed increase in the size or volume of an object or material due to changes in temperature. This phenomenon is a result of the thermal expansion of the object, where the atoms or molecules within the material vibrate more as they gain thermal energy, causing the overall dimensions to increase.
Bimetallic Strip: A bimetallic strip is a device composed of two different metals bonded together. The different thermal expansion coefficients of the metals cause the strip to bend or flex when exposed to changes in temperature, making it a useful component in various temperature-sensitive applications.
Charles's Law: Charles's law is a fundamental principle in thermodynamics that describes the relationship between the volume and absolute temperature of a gas, given that the pressure and amount of gas remain constant. It states that the volume of a gas is directly proportional to its absolute temperature, provided that the pressure and the amount of gas remain unchanged.
Coefficient of linear expansion: The coefficient of linear expansion quantifies how much a material's length changes per degree change in temperature. It is typically denoted by the symbol $\alpha$ and has units of $\text{1/°C}$ or $\text{1/K}$.
Coefficient of Linear Expansion: The coefficient of linear expansion is a measure of the fractional change in the length of a material per unit change in temperature. It quantifies the thermal expansion behavior of a substance along a single dimension, typically length.
Coefficient of volume expansion: The coefficient of volume expansion is a material-specific constant that quantifies the fractional change in volume per degree change in temperature. It is typically denoted by $\beta$ and measured in $\text{K}^{-1}$.
Density of water: The density of water is the mass per unit volume of water, typically measured in kilograms per cubic meter (kg/m³). It varies with temperature and pressure, being approximately 1000 kg/m³ at standard conditions (4°C and 1 atm).
Expansion Joint: An expansion joint is a gap or space that is intentionally designed and incorporated into structures, such as buildings, bridges, and pipelines, to allow for thermal expansion and contraction. These joints accommodate the natural movement and deformation of materials caused by changes in temperature, preventing damage and ensuring the structural integrity of the overall system.
Expansion joints: Expansion joints are structural components designed to absorb the dimensional changes that occur due to thermal expansion and contraction in materials. They prevent stress and damage in structures by allowing movement without compromising integrity.
Freezing of water: Freezing of water is the phase transition of water from a liquid to a solid state at 0°C (32°F) under standard atmospheric pressure. This process involves the formation of ice as water molecules arrange into a crystalline structure.
Gay-Lussac's Law: Gay-Lussac's law is a fundamental principle in thermodynamics that describes the relationship between the pressure and absolute temperature of a gas, while the volume and amount of gas remain constant.
Invar: Invar is a nickel-iron alloy that has an extremely low coefficient of thermal expansion, making it resistant to changes in length or volume due to temperature variations. This unique property of Invar has made it an important material in various applications where dimensional stability is crucial.
Isothermal expansion: Isothermal expansion is a thermodynamic process in which a gas expands at a constant temperature. During this process, the internal energy of the gas remains unchanged while work is done by the gas.
Isotropic: Isotropic refers to a property that is the same in all directions. It describes a material or system that exhibits uniform and consistent behavior regardless of the direction of measurement or applied force.
James Prescott Joule: James Prescott Joule was a British physicist who made significant contributions to the understanding of the relationship between heat and mechanical work, leading to the establishment of the principle of the conservation of energy. His work was crucial in the development of the concept of thermal expansion.
Kinetic Energy: Kinetic energy is the energy of motion possessed by an object due to its movement. It is the energy that an object has by virtue of being in motion and is directly proportional to the mass of the object and the square of its velocity.
Linear Expansion: Linear expansion is the increase in the length of a solid material when its temperature is raised. This phenomenon occurs due to the vibration and increased spacing between the atoms or molecules that make up the material.
Mercury thermometer: A mercury thermometer is a temperature measuring device that uses mercury, a liquid metal, which expands and contracts in response to temperature changes. As the temperature rises, the mercury expands and moves up a calibrated glass tube, indicating the temperature on a scale marked on the tube. This principle of thermal expansion is fundamental to how mercury thermometers function and directly relates to various temperature scales used in scientific measurements.
Molecular Motion: Molecular motion refers to the constant, random movement of individual molecules within a substance due to their thermal energy. This motion is a fundamental property of matter that is directly related to the temperature of the substance and plays a crucial role in various physical processes, including thermal expansion.
Pressure: Pressure is the force exerted per unit area on a surface, commonly measured in pascals (Pa). It plays a critical role in understanding how gases behave, how thermal expansion affects materials, and how energy transfers occur in systems. Pressure influences how gases expand or compress, impacts thermodynamic processes, and governs the interactions between molecules at the microscopic level.
Temperature: Temperature is a measure of the average kinetic energy of the particles (atoms or molecules) in a substance. It quantifies the degree of hotness or coldness of an object and is a fundamental concept in thermodynamics that is closely related to the transfer of heat energy.
Thermal expansion: Thermal expansion is the increase in volume of a substance due to an increase in temperature. This occurs because particles move more and spread apart as they gain thermal energy.
Thermal Expansion: Thermal expansion is the phenomenon where the size or volume of an object increases as its temperature rises. This occurs because the atoms or molecules within the object vibrate more and occupy a larger space as they gain kinetic energy from the increased temperature.
Thermal Fatigue: Thermal fatigue is the weakening or failure of a material due to repeated thermal cycling, where the material is subjected to alternating heating and cooling. This can lead to the development of cracks, deformation, and ultimately, the breakdown of the material over time.
Thermal stress: Thermal stress is the stress induced in a material due to changes in temperature. It occurs when thermal expansion or contraction is constrained, leading to internal forces within the material.
Thermal Stress: Thermal stress refers to the internal forces and deformations that arise within a material or structure due to changes in temperature. It is a crucial concept in the study of thermal expansion, as temperature variations can induce stresses that can lead to deformation, damage, or failure of the material or structure.
Thermostat: A thermostat is a device that regulates temperature by monitoring the environment and controlling the operation of heating or cooling equipment. It is a critical component in maintaining a desired temperature within a given space or system.
Volume: Volume is a fundamental physical quantity that describes the three-dimensional space occupied by an object or a substance. It is a measure of the amount of space enclosed within a defined boundary or container.
Volumetric Expansion: Volumetric expansion is the increase in the volume of a substance, typically a liquid or gas, due to the application of heat. It is a fundamental concept in the study of thermal expansion, which describes how materials change in size and shape in response to changes in temperature.
ΔL = αL₀ΔT: The formula ΔL = αL₀ΔT describes the relationship between the change in length (ΔL) of an object, the object's initial length (L₀), the coefficient of thermal expansion (α), and the change in temperature (ΔT). This formula is used to quantify the thermal expansion of materials.
ΔV = βV₀ΔT: The equation ΔV = βV₀ΔT describes the relationship between the change in volume (ΔV) of an object, the coefficient of volumetric thermal expansion (β), the initial volume (V₀), and the change in temperature (ΔT). This equation is used to quantify the thermal expansion of materials.
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