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  • Define and describe thermal expansion.
  • Calculate the linear expansion of an object given its initial length, change in temperature, and coefficient of linear expansion.
  • Calculate the volume expansion of an object given its initial volume, change in temperature, and coefficient of volume expansion.
  • Calculate thermal stress on an object given its original volume, temperature change, volume change, and bulk modulus.
Thermal expansion joints like these in the Auckland Harbour Bridge in New Zealand allow bridges to change length without buckling. (credit: Ingolfson, Wikimedia Commons)

The expansion of alcohol in a thermometer is one of many commonly encountered examples of thermal expansion    , the change in size or volume of a given mass with temperature. Hot air rises because its volume increases, which causes the hot air’s density to be smaller than the density of surrounding air, causing a buoyant (upward) force on the hot air. The same happens in all liquids and gases, driving natural heat transfer upwards in homes, oceans, and weather systems. Solids also undergo thermal expansion. Railroad tracks and bridges, for example, have expansion joints to allow them to freely expand and contract with temperature changes.

What are the basic properties of thermal expansion? First, thermal expansion is clearly related to temperature change. The greater the temperature change, the more a bimetallic strip will bend. Second, it depends on the material. In a thermometer, for example, the expansion of alcohol is much greater than the expansion of the glass containing it.

What is the underlying cause of thermal expansion? As is discussed in Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature , an increase in temperature implies an increase in the kinetic energy of the individual atoms. In a solid, unlike in a gas, the atoms or molecules are closely packed together, but their kinetic energy (in the form of small, rapid vibrations) pushes neighboring atoms or molecules apart from each other. This neighbor-to-neighbor pushing results in a slightly greater distance, on average, between neighbors, and adds up to a larger size for the whole body. For most substances under ordinary conditions, there is no preferred direction, and an increase in temperature will increase the solid’s size by a certain fraction in each dimension.

Linear thermal expansion—thermal expansion in one dimension

The change in length Δ L size 12{ΔL} {} is proportional to length L size 12{L} {} . The dependence of thermal expansion on temperature, substance, and length is summarized in the equation

Δ L = αL Δ T , size 12{ΔL=αLΔT} {}

where Δ L size 12{ΔL} {} is the change in length L size 12{L} {} , Δ T size 12{ΔT} {} is the change in temperature, and α size 12{α} {} is the coefficient of linear expansion    , which varies slightly with temperature.

[link] lists representative values of the coefficient of linear expansion, which may have units of 1 / º C size 12{1/°C} {} or 1/K. Because the size of a kelvin and a degree Celsius are the same, both α size 12{α} {} and Δ T size 12{ΔT} {} can be expressed in units of kelvins or degrees Celsius. The equation Δ L = αL Δ T size 12{ΔL=αLΔT} {} is accurate for small changes in temperature and can be used for large changes in temperature if an average value of α size 12{α} {} is used.

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Source:  OpenStax, Physics 101. OpenStax CNX. Jan 07, 2013 Download for free at http://legacy.cnx.org/content/col11479/1.1
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