Thermal expansion: Wikis

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Material Properties
Specific heat	$c=\frac{T}{N}\left(\frac{\partial S}{\partial T}\right)$
Compressibility	$\beta=-\frac{1}{V}\left(\frac{\partial V}{\partial p}\right)$
Thermal expansion	$\alpha=\frac{1}{V}\left(\frac{\partial V}{\partial T}\right)$

Thermal expansion is the tendency of matter to change in volume in response to a change in temperature.^[1] When a substance is heated, its particles begin moving and become active thus maintaining a greater average separation. Materials which contract with increasing temperature are rare; this effect is limited in size, and only occurs within limited temperature ranges. The degree of expansion divided by the change in temperature is called the material's coefficient of thermal expansion and generally varies with temperature.

Common engineering solids usually have coefficients of thermal expansion that do not vary significantly over the range of temperatures where they are designed to be used, so where extremely high accuracy is not required, calculations can be based on a constant, average, value of the coefficient of expansion.

To more accurately calculate thermal expansion of a substance an equation of state must be used, which will then predict the values of the thermal expansion at all the required temperatures and pressures, along with many other state functions.

For solid materials with a significant length, like rods or cables, an estimate of the amount of thermal expansion can be described by the $\frac{}{}\epsilon_{thermal}$ ratio of strain:

$\epsilon_{thermal} = \frac{(L_{final} - L_{initial})} {L_{initial}}$

$\frac{}{}L_{initial}$ is the length before the change of temperature and

$\frac{}{}L_{final}$ is the length after the change of temperature.

For most solids, thermal expansion relates directly with temperature:

$\epsilon_{thermal} \propto {\Delta T }$

Thus, the change in either the strain or temperature can be estimated by:

$\frac{}{} \epsilon_{thermal} = \alpha_L \Delta T$

where

$\frac{}{}\Delta T = (T_{final} - T_{initial})$

is the difference of the temperature between the two recorded strains, measured in degrees Celsius or kelvins, and $\frac{}{}\alpha_L$ is the linear coefficient of thermal expansion in inverse kelvins.

Materials with anisotropic structures, such as crystals and many composites, will generally have different linear expansion coefficients $\frac{}{}\alpha_L$ in different directions. Isotropic materials, will by definition have the same $\frac{}{}\alpha_L$ in every direction. For an isotropic material,

$\frac{}{}\alpha = 3 \alpha_L$ .^[1]

A number of materials contract on heating within certain temperature ranges; this is usually called negative thermal expansion, rather than "thermal contraction". For example, the coefficient of thermal expansion of water drops to zero as it is cooled to roughly 4 °C and then becomes negative below this temperature, this means that water has a maximum density at this temperature, and this leads to bodies of water maintaining this temperature at their lower depths during extended periods of sub-zero weather.

Thermal expansion generally decreases with increasing bond energy, which also has an effect on the hardness of solids, so, harder materials are more likely to have lower thermal expansion. In general, liquids expand slightly more than solids.

Absorption or desorption of water (or other solvents) can change the size of many common materials; many organic materials change size much more due to this effect than they do to thermal expansion. Common plastics exposed to water can, in the long term, expand many percent.

Examples and applications

Heat-induced expansion has to be taken into account in most areas of engineering. A few examples are:

Metal framed windows need rubber spacers
Rubber tires
Metal hot water heating pipes should not be used in long straight lengths
Large structures such as railways and bridges need expansion joints in the structures to avoid sun kink
One of the reasons for the poor performance of cold car engines is that parts have inefficiently large spacings until the normal operating temperature is achieved.
A gridiron pendulum uses an arrangement of different metals to maintain a more temperature stable pendulum length.

This phenomenon can also be put to good use, for example in the process of thermal shrink-fitting parts are assembled with each at a different temperature, and sized such that when they reach the same temperature, the thermal expansion of the parts forces them together to form a stable joint.

Thermometers are another application of thermal expansion — most contain a liquid which is constrained to flow in only one direction (along the tube) due to changes in volume brought about by changes in temperature. A bi-metal mechanical thermometer uses a bimetallic strip and registers changes due to the differing coefficient of thermal expansion between the two materials.

A power line on a hot day is droopy, but on a cold day it is tight. This is because the metals expand under heat.

Notes

^ ^a ^b Paul A., Tipler; Gene Mosca (2008). Physics for Scientists and Engineers, Sixth Edition, Volume 1. New York, NY: Worth Publishers. pp. 666-670. ISBN 1-4292-0132-0. http://books.google.com/books?id=BMVR37-8Jh0C&pg=PA668&dq=%22Physics+for+Scientists+and+Engineers%22+tipler+%22thermal+expansion%22&as_brr=3&cd=1#.

External links

Glass Thermal Expansion Thermal expansion measurement, definitions, thermal expansion calculation from the glass composition
Water Expansion Calculator Water thermal expansion calculator

Categories: Thermodynamics | Building defects

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In physics, thermal expansion is the tendency of matter to change in volume in response to a change in temperature. When a substance is heated, its constituent particles move around more quickly and by doing so generally maintain a greater average separation. Materials that contract with an increase in temperature are very uncommon; this effect is limited in size, and only occurs within limited temperature ranges. The degree of expansion divided by the change in temperature is called the material's coefficient of thermal expansion and generally varies with temperature.

Common engineering solids usually have thermal expansion coefficients that do not vary significantly over the range of temperatures where they are designed to be used, so where extremely high accuracy is not required, calculations can be based on a constant, average, value of the coefficient of expansion.

Thermometers are an example of an application of thermal expansion – they contain a liquid which is constrained to flow in only one direction (along the tube) due to changes in volume brought about by changes in temperature.

Other websites

Glass Thermal Expansion Thermal expansion measurement, definitions, thermal expansion calculation from the glass composition

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