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Thermal expansion is the tendency of matter to change its
shape A shape or figure is a graphical representation of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture, or material type. A plane shape or plane figure is constrained to lie ...
,
area Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while '' surface area'' refers to the area of an ope ...
,
volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). Th ...
, and
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
in response to a change in
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
, usually not including
phase transitions In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...
. Temperature is a
monotonic function In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order ...
of the average molecular
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acc ...
of a substance. When a substance is heated, molecules begin to vibrate and move more, usually creating more distance between themselves. Substances which contract with increasing temperature are unusual, and only occur within limited temperature ranges (see examples below). The relative expansion (also called
strain Strain may refer to: Science and technology * Strain (biology), variants of plants, viruses or bacteria; or an inbred animal used for experimental purposes * Strain (chemistry), a chemical stress of a molecule * Strain (injury), an injury to a mu ...
) divided by the change in temperature is called the material's coefficient of linear thermal expansion and generally varies with temperature. As energy in particles increases, they start moving faster and faster weakening the intermolecular forces between them, therefore expanding the substance.


Overview


Predicting expansion

If an equation of state is available, it can be used to predict the values of the thermal expansion at all the required temperatures and
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
s, along with many other state functions.


Contraction effects (negative thermal expansion)

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 3.983 °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. Other materials are also known to exhibit negative thermal expansion. Fairly pure silicon has a negative coefficient of thermal expansion for temperatures between about 18 and 120
kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phy ...
. ALLVAR Alloy 30, a titanium alloy, exhibits an anisotropic negative thermal expansion across a wide range of temperatures


Factors affecting thermal expansion

Unlike gases or liquids, solid materials tend to keep their shape when undergoing thermal expansion. Thermal expansion generally decreases with increasing bond energy, which also has an effect on the
melting point The melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depen ...
of solids, so, high melting point materials are more likely to have lower thermal expansion. In general, liquids expand slightly more than solids. The thermal expansion of
glass Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling ( quenching ...
es is slightly higher compared to that of crystals. At the glass transition temperature, rearrangements that occur in an amorphous material lead to characteristic discontinuities of coefficient of thermal expansion and specific heat. These discontinuities allow detection of the glass transition temperature where a supercooled liquid transforms to a glass. An interesting "cooling-by-heating" effect occurs when a glass-forming liquid is heated from the outside, resulting in a temperature drop deep inside the liquid. 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 due to thermal expansion. Common plastics exposed to water can, in the long term, expand by many percent.


Effect on density

Thermal expansion changes the space between particles of a substance, which changes the volume of the substance while negligibly changing its mass (the negligible amount comes from energy-mass equivalence), thus changing its density, which has an effect on any buoyant forces acting on it. This plays a crucial role in
convection Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the conve ...
of unevenly heated fluid masses, notably making thermal expansion partly responsible for
wind Wind is the natural movement of air or other gases relative to a planet's surface. Winds occur on a range of scales, from thunderstorm flows lasting tens of minutes, to local breezes generated by heating of land surfaces and lasting a few ho ...
and
ocean currents An ocean current is a continuous, directed movement of sea water generated by a number of forces acting upon the water, including wind, the Coriolis effect, breaking waves, cabbeling, and temperature and salinity differences. Depth contour ...
.


Coefficient of thermal expansion

The coefficient of thermal expansion describes how the size of an object changes with a change in temperature. Specifically, it measures the fractional change in size per degree change in temperature at a constant pressure, such that lower coefficients describe lower propensity for change in size. Several types of coefficients have been developed: volumetric, area, and linear. The choice of coefficient depends on the particular application and which dimensions are considered important. For solids, one might only be concerned with the change along a length, or over some area. The volumetric thermal expansion coefficient is the most basic thermal expansion coefficient, and the most relevant for fluids. In general, substances expand or contract when their temperature changes, with expansion or contraction occurring in all directions. Substances that expand at the same rate in every direction are called isotropic. For isotropic materials, the area and volumetric thermal expansion coefficient are, respectively, approximately twice and three times larger than the linear thermal expansion coefficient. Mathematical definitions of these coefficients are defined below for solids, liquids, and gases.


General thermal expansion coefficient

In the general case of a gas, liquid, or solid, the volumetric coefficient of thermal expansion is given by \alpha = \alpha_ = \frac\,\left(\frac\right)_ The subscript "''p''" to the derivative indicates that the pressure is held constant during the expansion, and the subscript ''V'' stresses that it is the volumetric (not linear) expansion that enters this general definition. In the case of a gas, the fact that the pressure is held constant is important, because the volume of a gas will vary appreciably with pressure as well as temperature. For a gas of low density this can be seen from the ideal gas law.


Expansion in solids

When calculating thermal expansion it is necessary to consider whether the body is free to expand or is constrained. If the body is free to expand, the expansion or strain resulting from an increase in temperature can be simply calculated by using the applicable coefficient of Thermal Expansion. If the body is constrained so that it cannot expand, then internal stress will be caused (or changed) by a change in temperature. This stress can be calculated by considering the strain that would occur if the body were free to expand and the stress required to reduce that strain to zero, through the stress/strain relationship characterised by the elastic or
Young's modulus Young's modulus E, the Young modulus, or the modulus of elasticity in tension or compression (i.e., negative tension), is a mechanical property that measures the tensile or compressive stiffness of a solid material when the force is applied le ...
. In the special case of
solid Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic energy. A solid is characterized by structural ...
materials, external ambient pressure does not usually appreciably affect the size of an object and so it is not usually necessary to consider the effect of pressure changes. 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, practical calculations can be based on a constant, average, value of the coefficient of expansion.


Linear expansion

Linear expansion means change in one dimension (length) as opposed to change in volume (volumetric expansion). To a first approximation, the change in length measurements of an object due to thermal expansion is related to temperature change by a coefficient of linear thermal expansion (CLTE). It is the fractional change in length per degree of temperature change. Assuming negligible effect of pressure, we may write: \alpha_L = \frac\,\frac where L is a particular length measurement and \mathrmL/\mathrmT is the rate of change of that linear dimension per unit change in temperature. The change in the linear dimension can be estimated to be: \frac = \alpha_L \Delta T This estimation works well as long as the linear-expansion coefficient does not change much over the change in temperature \Delta T, and the fractional change in length is small \Delta L/L \ll 1. If either of these conditions does not hold, the exact differential equation (using \mathrmL/\mathrmT) must be integrated.


Effects on strain

For solid materials with a significant length, like rods or cables, an estimate of the amount of thermal expansion can be described by the material
strain Strain may refer to: Science and technology * Strain (biology), variants of plants, viruses or bacteria; or an inbred animal used for experimental purposes * Strain (chemistry), a chemical stress of a molecule * Strain (injury), an injury to a mu ...
, given by \epsilon_\mathrm and defined as: \epsilon_\mathrm = \frac where L_\mathrm is the length before the change of temperature and L_\mathrm is the length after the change of temperature. For most solids, thermal expansion is proportional to the change in temperature: \epsilon_\mathrm \propto \Delta T Thus, the change in either the
strain Strain may refer to: Science and technology * Strain (biology), variants of plants, viruses or bacteria; or an inbred animal used for experimental purposes * Strain (chemistry), a chemical stress of a molecule * Strain (injury), an injury to a mu ...
or temperature can be estimated by: \epsilon_\mathrm = \alpha_L \Delta T where \Delta T = (T_\mathrm - T_\mathrm) is the difference of the temperature between the two recorded strains, measured in
degrees Fahrenheit The Fahrenheit scale () is a temperature scale based on one proposed in 1724 by the physicist Daniel Gabriel Fahrenheit (1686–1736). It uses the degree Fahrenheit (symbol: °F) as the unit. Several accounts of how he originally defined his ...
, degrees Rankine, degrees Celsius, or
kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phy ...
, and \alpha_L is the linear coefficient of thermal expansion in "per degree Fahrenheit", "per degree Rankine", “per degree Celsius”, or “per kelvin”, denoted by , , , or , respectively. In the field of continuum mechanics, the thermal expansion and its effects are treated as eigenstrain and eigenstress.


Area expansion

The area thermal expansion coefficient relates the change in a material's area dimensions to a change in temperature. It is the fractional change in area per degree of temperature change. Ignoring pressure, we may write: \alpha_A = \frac\,\frac where A is some area of interest on the object, and dA/dT is the rate of change of that area per unit change in temperature. The change in the area can be estimated as: \frac = \alpha_A\Delta T This equation works well as long as the area expansion coefficient does not change much over the change in temperature \Delta T, and the fractional change in area is small \Delta A/A \ll 1. If either of these conditions does not hold, the equation must be integrated.


Volume expansion

For a solid, we can ignore the effects of pressure on the material, and the volumetric (or cubical) thermal expansion coefficient can be written: \alpha_V = \frac\,\frac where V is the volume of the material, and \mathrmV/\mathrmT is the rate of change of that volume with temperature. This means that the volume of a material changes by some fixed fractional amount. For example, a steel block with a volume of 1 cubic meter might expand to 1.002 cubic meters when the temperature is raised by 50 K. This is an expansion of 0.2%. If we had a block of steel with a volume of 2 cubic meters, then under the same conditions, it would expand to 2.004 cubic meters, again an expansion of 0.2%. The volumetric expansion coefficient would be 0.2% for 50 K, or 0.004% K−1. If we already know the expansion coefficient, then we can calculate the change in volume \frac = \alpha_V \Delta T where \Delta V/V is the fractional change in volume (e.g., 0.002) and \Delta T is the change in temperature (50 °C). The above example assumes that the expansion coefficient did not change as the temperature changed and the increase in volume is small compared to the original volume. This is not always true, but for small changes in temperature, it is a good approximation. If the volumetric expansion coefficient does change appreciably with temperature, or the increase in volume is significant, then the above equation will have to be integrated: \ln\left(\frac\right) = \int_^\alpha_V(T)\,\mathrmT \frac = \exp\left(\int_^\alpha_V(T)\,\mathrmT\right) - 1 where \alpha_V(T) is the volumetric expansion coefficient as a function of temperature ''T'', and T_i,T_f are the initial and final temperatures respectively.


Isotropic materials

For isotropic materials the volumetric thermal expansion coefficient is three times the linear coefficient: \alpha_V = 3\alpha_L This ratio arises because volume is composed of three mutually orthogonal directions. Thus, in an isotropic material, for small differential changes, one-third of the volumetric expansion is in a single axis. As an example, take a cube of steel that has sides of length . The original volume will be V = L^3 and the new volume, after a temperature increase, will be V + \Delta V = \left(L + \Delta L\right)^3 = L^3 + 3L^2\Delta L + 3L\Delta L^2 + \Delta L^3 \approx L^3 + 3L^2\Delta L = V + 3 V \frac. We can easily ignore the terms as Δ''L'' is a small quantity which on squaring gets much smaller and on cubing gets smaller still. So \frac = 3 = 3\alpha_L\Delta T. The above approximation holds for small temperature and dimensional changes (that is, when \Delta T and \Delta L are small); but it does not hold if we are trying to go back and forth between volumetric and linear coefficients using larger values of \Delta T. In this case, the third term (and sometimes even the fourth term) in the expression above must be taken into account. Similarly, the area thermal expansion coefficient is two times the linear coefficient: \alpha_A = 2\alpha_L This ratio can be found in a way similar to that in the linear example above, noting that the area of a face on the cube is just L^2. Also, the same considerations must be made when dealing with large values of \Delta T. Put more simply, if the length of a cubic solid expands from 1.00 m to 1.01 m then the area of one of its sides expands from 1.00 m2 to 1.02 m2 and its volume expands from 1.00 m3 to 1.03 m3.


Anisotropic materials

Materials with anisotropic structures, such as
crystals A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...
(with less than cubic symmetry, for example
martensitic Martensite is a very hard form of steel crystalline structure. It is named after German metallurgist Adolf Martens. By analogy the term can also refer to any crystal structure that is formed by diffusionless transformation. Properties Marte ...
phases) and many composites, will generally have different linear expansion coefficients \alpha_L in different directions. As a result, the total volumetric expansion is distributed unequally among the three axes. If the crystal symmetry is monoclinic or triclinic, even the angles between these axes are subject to thermal changes. In such cases it is necessary to treat the coefficient of thermal expansion as a
tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensor ...
with up to six independent elements. A good way to determine the elements of the tensor is to study the expansion by x-ray
powder diffraction Powder diffraction is a scientific technique using X-ray, neutron, or electron diffraction on powder or microcrystalline samples for structural characterization of materials. An instrument dedicated to performing such powder measurements is call ...
. The thermal expansion coefficient tensor for the materials possessing cubic symmetry (for e.g. FCC, BCC) is isotropic.


Temperature dependence

Thermal expansion coefficients of solids usually show little dependence on temperature (except at very low temperatures) whereas liquids can expand at different rates at different temperatures. However, there are some known exceptions: for example, cubic boron nitride exhibits significant variation of its thermal expansion coefficient over a broad range of temperatures. Another example is paraffin which in its solid form has a thermal expansion coefficent that is dependent on tempertaure.


Isobaric expansion in ideal gases

Since gases fill the entirety of the container which they occupy, the volumetric thermal expansion coefficient at constant pressure, \alpha_, is the only one of interest. For an
ideal gas An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is a ...
, a formula can be readily obtained by differentiation of the ideal gas law, p V_m = RT. This yields p \mathrmV_m + V_m \mathrmp = R\mathrmT where p is the pressure, V_m is the
molar volume In chemistry and related fields, the molar volume, symbol ''V''m, or \tilde V of a substance is the ratio of the volume occupied by a substance to the amount of substance, usually given at a given temperature and pressure. It is equal to the molar ...
( V_m = V / n, with n the total number of moles of gas), T is the absolute temperature and R is equal to the gas constant. For an isobaric thermal expansion we have \mathrmp=0, so that p \mathrmV_m=R \mathrmT and the isobaric thermal expansion coefficient is: \alpha_ \equiv \frac \left(\frac\right)_p = \frac \left(\frac\right)_p = \frac \left(\frac\right) = \frac = \frac which is a strong function of temperature; doubling the temperature will halve the thermal expansion coefficient.


Computation of the absolute zero

In October 1848, William Thomson, a 24 year old professor of Natural Philosophy at the
University of Glasgow , image = UofG Coat of Arms.png , image_size = 150px , caption = Coat of arms Flag , latin_name = Universitas Glasguensis , motto = la, Via, Veritas, Vita , ...
, published a paper ''On an Absolute Thermometric Scale''. In a footnote Thomson calculated that "infinite cold" ( absolute zero) was equivalent to −273 °C (he called the temperature in °C as the "temperature of the air thermometers" of the time). This value of "−273" was considered to be the temperature at which the ideal gas volume reaches the zero. By considering a thermal expansion linear with temperature (i.e. a constant coefficient of thermal expansion), the value of the absolute zero was linearly extrapolated as the negative reciprocal of 0.366/100 °C — the accepted average coefficient of thermal expansion of an ideal gas in the temperature interval 0 °C-100 °C, giving a remarkable consistency to the currently accepted value of -273.15 °C.


Expansion in liquids

The thermal expansion of liquids is usually higher than in solids because the intermolecular forces present in liquids are relatively weak and its constituent molecules are more mobile. Unlike solids, liquids have no definite shape and they take the shape of the container. Consequently, liquids have no definite length and area, so linear and areal expansions of liquids only have significance in that they may be applied to topics such as
thermometry Temperature measurement (also known as thermometry) describes the process of measuring a current local temperature for immediate or later evaluation. Datasets consisting of repeated standardized measurements can be used to assess temperature tren ...
and estimates of
sea level Mean sea level (MSL, often shortened to sea level) is an average surface level of one or more among Earth's coastal bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical datuma standardise ...
rising due to global climate change. However, ''αL'' is sometimes still calculated from the experimental value of ''αV''. In general, liquids expand on heating. However water is an exception to this general behavior: below 4 °C it contracts on heating, leading to a negative thermal expansion coefficient. At higher temperatures water shows more typical behavior, with a positive thermal expansion coefficient.


Apparent and absolute expansion of a liquid

The expansion of liquids is usually measured in a container. When a liquid expands in a vessel, the vessel expands along with the liquid. Hence the observed increase in volume (as measured by the liquid level) is not the actual increase in its volume. The expansion of the liquid relative to the container is called its ''apparent expansion'', while the actual expansion of the liquid is called ''real expansion'' or ''absolute expansion''. The ratio of apparent increase in volume of the liquid per unit rise of temperature to the original volume is called its ''coefficient of apparent expansion''. The absolute expansion can be measured by a variety of techniques, including ultrasonic methods. Historically, this phenomenon complicated the experimental determination of thermal expansion coefficients of liquids, since a direct measurement of the change in height of a liquid column generated by thermal expansion is a measurement of the apparent expansion of the liquid. Thus the experiment simultaneously measures ''two'' coefficients of expansion and measurement of the expansion of a liquid must account for the expansion of the container as well. For example, when a flask with a long narrow stem, containing enough liquid to partially fill the stem itself, is placed in a heat bath, the height of the liquid column in the stem will initially drop, followed immediately by a rise of that height until the whole system of flask, liquid and heat bath has warmed through. The initial drop in the height of the liquid column is not due to an initial contraction of the liquid, but rather to the expansion of the flask as it contacts the heat bath first. Soon after, the liquid in the flask is heated by the flask itself and begins to expand. Since liquids typically have a greater percent expansion than solids for the same temperature change, the expansion of the liquid in the flask eventually exceeds that of the flask, causing the level of liquid in the flask to rise. For small and equal rises in temperature, the increase in volume (real expansion) of a liquid is equal to the sum of the apparent increase in volume (apparent expansion) of the liquid and the increase in volume of the containing vessel. The absolute expansion of the liquid is the apparent expansion corrected for the expansion of the containing vessel.


Examples and applications

The expansion and contraction of the materials must be considered when designing large structures, when using tape or chain to measure distances for land surveys, when designing molds for casting hot material, and in other engineering applications when large changes in dimension due to temperature are expected. Thermal expansion is also used in mechanical applications to fit parts over one another, e.g. a bushing can be fitted over a shaft by making its inner diameter slightly smaller than the diameter of the shaft, then heating it until it fits over the shaft, and allowing it to cool after it has been pushed over the shaft, thus achieving a 'shrink fit'. Induction shrink fitting is a common industrial method to pre-heat metal components between 150 °C and 300 °C thereby causing them to expand and allow for the insertion or removal of another component. There exist some alloys with a very small linear expansion coefficient, used in applications that demand very small changes in physical dimension over a range of temperatures. One of these is
Invar Invar, also known generically as FeNi36 (64FeNi in the US), is a nickel–iron alloy notable for its uniquely low coefficient of thermal expansion (CTE or α). The name ''Invar'' comes from the word ''invariable'', referring to its relative lac ...
36, with expansion approximately equal to 0.6 K−1. These alloys are useful in aerospace applications where wide temperature swings may occur. Pullinger's apparatus is used to determine the linear expansion of a metallic rod in the laboratory. The apparatus consists of a metal cylinder closed at both ends (called a steam jacket). It is provided with an inlet and outlet for the steam. The steam for heating the rod is supplied by a boiler which is connected by a rubber tube to the inlet. The center of the cylinder contains a hole to insert a thermometer. The rod under investigation is enclosed in a steam jacket. One of its ends is free, but the other end is pressed against a fixed screw. The position of the rod is determined by a micrometer screw gauge or
spherometer A spherometer is an instrument used for the precise measurement of the radius of curvature of a sphere or a curved surface. Originally, these instruments were primarily used by opticians to measure the curvature of the surface of a lens. Backgr ...
. To determine the coefficient of linear thermal expansion of a metal, a pipe made of that metal is heated by passing steam through it. One end of the pipe is fixed securely and the other rests on a rotating shaft, the motion of which is indicated by a pointer. A suitable thermometer records the pipe's temperature. This enables calculation of the relative change in length per degree temperature change. The control of thermal expansion in brittle materials is a key concern for a wide range of reasons. For example, both glass and
ceramics A ceramic is any of the various hard, brittle, heat-resistant and corrosion-resistant materials made by shaping and then firing an inorganic, nonmetallic material, such as clay, at a high temperature. Common examples are earthenware, porcelain ...
are brittle and uneven temperature causes uneven expansion which again causes thermal stress and this might lead to fracture. Ceramics need to be joined or work in concert with a wide range of materials and therefore their expansion must be matched to the application. Because glazes need to be firmly attached to the underlying porcelain (or other body type) their thermal expansion must be tuned to 'fit' the body so that crazing or shivering do not occur. Good example of products whose thermal expansion is the key to their success are
CorningWare Corning Ware, also written CorningWare, was originally a brand name for a unique glass-ceramic ( Pyroceram) cookware resistant to thermal shock. It was first introduced in 1958 by Corning Glass Works (later Corning Inc.) in the United States. The ...
and the spark plug. The thermal expansion of ceramic bodies can be controlled by firing to create crystalline species that will influence the overall expansion of the material in the desired direction. In addition or instead the formulation of the body can employ materials delivering particles of the desired expansion to the matrix. The thermal expansion of glazes is controlled by their chemical composition and the firing schedule to which they were subjected. In most cases there are complex issues involved in controlling body and glaze expansion, so that adjusting for thermal expansion must be done with an eye to other properties that will be affected, and generally trade-offs are necessary. Thermal expansion can have a noticeable effect on gasoline stored in above-ground storage tanks, which can cause gasoline pumps to dispense gasoline which may be more compressed than gasoline held in underground storage tanks in winter, or less compressed than gasoline held in underground storage tanks in summer. 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 need to perform well over a range of temperatures, being passively heated or cooled by road surfaces and weather, and actively heated by mechanical flexing and friction. *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. *A gridiron pendulum uses an arrangement of different metals to maintain a more temperature stable pendulum length. *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. * Expansion joints absorb the thermal expansion in a piping system. *Precision engineering nearly always requires the engineer to pay attention to the thermal expansion of the product. For example, when using a scanning electron microscope small changes in temperature such as 1 degree can cause a sample to change its position relative to the focus point. *Liquid
thermometer A thermometer is a device that measures temperature or a temperature gradient (the degree of hotness or coldness of an object). A thermometer has two important elements: (1) a temperature sensor (e.g. the bulb of a mercury-in-glass thermometer ...
s contain a liquid (usually mercury or alcohol) in a tube, which constrains it to flow in only one direction when its volume expands due to changes in temperature. *A bi-metal mechanical thermometer uses a
bimetallic strip A bimetallic strip is used to convert a temperature change into mechanical displacement. The strip consists of two strips of different metals which expand at different rates as they are heated. The different expansions force the flat strip to be ...
and bends due to the differing thermal expansion of the two metals.


Thermal expansion coefficients for various materials

This section summarizes the coefficients for some common materials. For isotropic materials the coefficients linear thermal expansion ''α'' and volumetric thermal expansion ''αV'' are related by . For liquids usually the coefficient of volumetric expansion is listed and linear expansion is calculated here for comparison. For common materials like many metals and compounds, the thermal expansion coefficient is inversely proportional to the
melting point The melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depen ...
. In particular, for metals the relation is: \alpha \approx \frac for halides and oxides \alpha \approx \frac - 7.0 \cdot 10^ \, \mathrm^ In the table below, the range for ''α'' is from 10−7 K−1 for hard solids to 10−3 K−1 for organic liquids. The coefficient ''α'' varies with the temperature and some materials have a very high variation; see for example the variation vs. temperature of the volumetric coefficient for a semicrystalline polypropylene (PP) at different pressure, and the variation of the linear coefficient vs. temperature for some steel grades (from bottom to top: ferritic stainless steel, martensitic stainless steel, carbon steel, duplex stainless steel, austenitic steel). The highest linear coefficient in a solid has been reported for a Ti-Nb alloy. (The formula is usually used for solids.)


See also

* * * * * * * * *


References


External links


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


DoITPoMS Teaching and Learning Package on Thermal Expansion and the Bi-material Strip


* ttp://www.leybold-didactic.com/literatur/hb/e/p2/p2121_e.pdf Article on how αV is determined
MatWeb: Free database of engineering properties for over 79,000 materials

USA NIST Website – Temperature and Dimensional Measurement workshop







Thermal expansion via density calculator
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