6360:
2073:
6352:. 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.
6169:) 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 zero. By considering a thermal expansion linear with temperature (i.e. a constant coefficient of thermal expansion), the value of 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 0–100 °C, giving a remarkable consistency to the currently accepted value of −273.15 °C.
2081:
159:
6328:
1729:
6121:
36:
133:
3188:
1863:, rather than "thermal contraction". For example, the coefficient of thermal expansion of water drops to zero as it is cooled to 3.983 °C (39.169 °F) 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.
6100:
5892:
6242:
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.
6339:
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
6323:
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
4434:
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 a block of steel has a volume of 2 cubic meters,
3166:
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
1949:
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
6177:
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
5472:
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
5160:
3195:
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
1953:
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
6311:
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
6245:
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
6241:
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
2053:
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
6285:
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
4546:
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
6355:
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
6236:
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
6289:
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
3162:
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.
2257:
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
1819:
of a substance. As energy in particles increases, they start moving faster and faster, weakening the intermolecular forces between them and therefore expanding the substance. When a substance is heated, molecules begin to vibrate and move more, usually creating more distance between themselves.
6216:
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
3178:
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
1893:
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
6312:
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
3679:
6246:
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
4770:
2041:
6095:{\displaystyle \alpha _{V}\equiv {\frac {1}{V}}\left({\frac {\partial V}{\partial T}}\right)_{p}={\frac {1}{V_{m}}}\left({\frac {\partial V_{m}}{\partial T}}\right)_{p}={\frac {1}{V_{m}}}\left({\frac {R}{p}}\right)={\frac {R}{pV_{m}}}={\frac {1}{T}}}
4657:
1908:
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.
4963:
6207:
In general, liquids expand on heating, except cold water; below 4 °C it contracts, leading to a negative thermal expansion coefficient. At higher temperatures it shows more typical behavior, with a positive thermal expansion coefficient.
1950:
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.
5489:
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. There are some exceptions: for example,
2245:
7219:
5494:
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 coefficient that is dependent on temperature.
4371:
4128:
3259:
6716:
5247:
4064:
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, one may write:
3535:
3987:
3898:
2258:(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.
5648:
3828:
6598:
4487:
4236:
3371:
1448:
4923:
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
2160:
4661:
1964:
6147:) by about 1/273 parts per degree Celsius of temperature's change up or down, between 0° and 100 °C. This suggested that the volume of a gas cooled at about −273 °C would reach zero.
4550:
6297:
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
5887:
3530:
1958:. For isotropic materials, the area and volumetric thermal expansion coefficient are, respectively, approximately twice and three times larger than the linear thermal expansion coefficient.
5421:
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 m to 1.02 m and its volume expands from 1.00 m to 1.03 m.
6294:
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.
4429:
3471:
3317:
7223:
5364:
4915:
6374:
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.
3728:
1917:
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
1866:
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
3769:
6717:"Sheer and Thermal Expansion Tensors - Part 1 | Video Lectures | Symmetry, Structure, and Tensor Properties of Materials | Materials Science and Engineering | MIT OpenCourseWare"
4435:
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.
6274:
2172:
5838:
4298:
3433:
3175:
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.
4806:
1889:
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
7426:"Essay II. On the force of steam or vapour from water and various other liquids, both in vacuum and in air" and Essay IV. "On the expansion of elastic fluids by heat,"
5528:
5470:
4030:
1283:
1228:
1173:
4518:
980:
933:
848:
801:
713:
666:
5740:
5578:
4311:
4068:
3199:
1870:(−255 and −153 °C; −427 and −244 °F). ALLVAR Alloy 30, a titanium alloy, exhibits anisotropic negative thermal expansion across a wide range of temperatures.
6889:
6308:
5416:
5318:
5295:
5272:
4541:
4261:
3396:
2067:
884:
752:
6920:
4958:
5174:
1118:
5695:
5393:
4864:
4837:
4182:
6418:
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.
617:
5800:
5780:
5760:
5668:
4391:
4148:
3279:
956:
909:
824:
777:
689:
642:
5155:{\displaystyle 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+3V{\frac {\Delta L}{L}}.}
3903:
7741:
6734:
Bönisch, Matthias; Panigrahi, Ajit; Stoica, Mihai; Calin, Mariana; Ahrens, Eike; Zehetbauer, Michael; Skrotzki, Werner; Eckert, Jürgen (10 November 2017).
3837:
5583:
3777:
7521:
7496:"On an Absolute Thermometric Scale founded on Carnot's Theory of the Motive Power of Heat, and calculated from Regnault's Observations (1881 reprint)"
6794:
3481:
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
6976:
4308:
For a solid, one can ignore the effects of pressure on the material, and the volumetric (or cubical) thermal expansion coefficient can be written:
4032:
is the linear coefficient of thermal expansion in "per degree
Fahrenheit", "per degree Rankine", "per degree Celsius", or "per kelvin", denoted by
1758:
6945:
4441:
4190:
3325:
2871:
1459:
7714:
6407:
Precision engineering nearly always requires the engineer to pay attention to the thermal expansion of the product. For example, when using a
1347:
6178:
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
7788:
2125:
7070:
6474:
581:
4547:
does change appreciably with temperature, or the increase in volume is significant, then the above equation will have to be integrated:
7469:"On an Absolute Thermometric Scale founded on Carnot's Theory of the Motive Power of Heat, and calculated from Regnault's Observations"
7819:
7805:
7201:
6151:
5503:
Since gases fill the entirety of the container which they occupy, the volumetric thermal expansion coefficient at constant pressure,
1437:
5297:
are small), but it does not hold if trying to go back and forth between volumetric and linear coefficients using larger values of
5368:
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
3674:{\displaystyle \varepsilon _{\mathrm {thermal} }={\frac {(L_{\mathrm {final} }-L_{\mathrm {initial} })}{L_{\mathrm {initial} }}}}
1470:
6335:
The control of thermal expansion in brittle materials is a key concern for a wide range of reasons. For example, both glass and
2115:. For liquids usually the coefficient of volumetric expansion is listed and linear expansion is calculated here for comparison.
100:
6442:
5326:
4877:
72:
7278:
7046:
6874:
6836:
6659:
6626:
6575:
6521:
1040:
6896:
6924:
6480:
6229:. The ratio of apparent increase in volume of the liquid per unit rise of temperature to the original volume is called its
5477:
with up to six independent elements. A good way to determine the elements of the tensor is to study the expansion by x-ray
3375:
This estimation works well as long as the linear-expansion coefficient does not change much over the change in temperature
1751:
1338:
1007:
574:
452:
6340:
attached to the underlying porcelain (or other body type) their thermal expansion must be tuned to 'fit' the body so that
5481:. The thermal expansion coefficient tensor for the materials possessing cubic symmetry (for e.g. FCC, BCC) is isotropic.
3196:
the fractional change in length per degree of temperature change. Assuming negligible effect of pressure, one may write:
390:
79:
5320:. In this case, the third term (and sometimes even the fourth term) in the expression above must be taken into account.
2118:
For common materials like many metals and compounds, the thermal expansion coefficient is inversely proportional to the
6359:
5843:
5478:
4240:
This equation works well as long as the area expansion coefficient does not change much over the change in temperature
3488:
2909:
1522:
1496:
1017:
471:
53:
6331:
Drinking glass with fracture due to uneven thermal expansion after pouring of hot liquid into the otherwise cool glass
7004:
6124:
423:
119:
17:
6411:
small changes in temperature such as 1 degree can cause a sample to change its position relative to the focus point.
6599:"ALLVAR alloy athermalization: A novel and cost-effective alternative for small to moderate sized space telescopes"
1575:
1046:
445:
86:
6102:
which is a strong function of temperature; doubling the temperature will halve the thermal expansion coefficient.
2072:
7623:
6537:
6398:
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.
4396:
3438:
3284:
2372:
1843:
is available, it can be used to predict the values of the thermal expansion at all the required temperatures and
1744:
7766:
7738:
1675:
207:
57:
7108:
Becker, P.; Seyfried, P.; Siegert, H. (1982). "The lattice parameter of highly pure silicon single crystals".
1570:
68:
1650:
1423:
400:
7776:
7468:
6344:
or shivering do not occur. Good example of products whose thermal expansion is the key to their success are
4874:
For isotropic materials the volumetric thermal expansion coefficient is three times the linear coefficient:
4765:{\displaystyle {\frac {\Delta V}{V}}=\exp \left(\int _{T_{i}}^{T_{f}}\alpha _{V}(T)\,\mathrm {d} T\right)-1}
3686:
2036:{\displaystyle \alpha =\alpha _{\text{V}}={\frac {1}{V}}\,\left({\frac {\partial V}{\partial T}}\right)_{p}}
1961:
In the general case of a gas, liquid, or solid, the volumetric coefficient of thermal expansion is given by
7854:
7529:
6408:
6263:
4652:{\displaystyle \ln \left({\frac {V+\Delta V}{V}}\right)=\int _{T_{i}}^{T_{f}}\alpha _{V}(T)\,\mathrm {d} T}
1035:
238:
228:
7237:
Monroe, James A.; McAllister, Jeremy S.; Zgarba, Jay; Squires, David; Deegan, John P. (18 November 2019).
6798:
3733:
2049:" to the derivative indicates that the pressure is held constant during the expansion, and the subscript
1918:
243:
233:
6984:
6250:
expansion of the liquid is the apparent expansion corrected for the expansion of the containing vessel.
7013:
6436:
3831:
3482:
1860:
1804:
1527:
1491:
269:
203:
7294:
6367:
Heat-induced expansion has to be taken into account in most areas of engineering. A few examples are:
6324:
temperature. This enables calculation of the relative change in length per degree temperature change.
1565:
7859:
6812:
Ahmed, Ashraf; Tavakol, Behrouz; Das, Rony; Joven, Ronald; Roozbehjavan, Pooneh; Minaie, Bob (2012).
5812:
4266:
3401:
1878:
Unlike gases or liquids, solid materials tend to keep their shape when undergoing thermal expansion.
1320:
1068:
514:
327:
317:
7771:
7763:
Thermal expansion measurement, definitions, thermal expansion calculation from the glass composition
6952:
4775:
1859:
A number of materials contract on heating within certain temperature ranges; this is usually called
7824:
7313:
6291:
6267:
6233:. The absolute expansion can be measured by a variety of techniques, including ultrasonic methods.
7152:
7844:
7441:
6462:
6305:
10 K. These alloys are useful in aerospace applications where wide temperature swings may occur.
6140:
5506:
5448:
4008:
1732:
1560:
1357:
1238:
1183:
1128:
1060:
999:
535:
524:
190:
46:
7781:
7760:
4492:
962:
915:
830:
783:
695:
648:
7849:
7814:
7650:"Determining absolute thermal expansion of titania–silica glasses: a refined ultrasonic method"
7295:"Applied Mechanics of Solids (A.F. Bower) Chapter 3: Constitutive laws - 3.2 Linear Elasticity"
6513:
Physics for
Scientists and Engineers - Volume 1 Mechanics/Oscillations and Waves/Thermodynamics
5704:
5544:
1665:
1382:
466:
220:
195:
93:
7425:
7077:
6563:
6511:
6456:
6395:
uses an arrangement of different metals to maintain a more temperature stable pendulum length.
5398:
5300:
5277:
5254:
4523:
4243:
3378:
1585:
866:
731:
7829:
6187:
6155:
4930:
1600:
1177:
490:
336:
185:
6465: – Difference in properties of one mole of substance in a mixture vs. an ideal solution
1088:
7703:
Elementary treatise on physics experimental and applied for the use of colleges and schools
7661:
7575:
7335:
7184:
7117:
7094:
6862:
6747:
6688:
6606:
6471: – Physical property describing the energy required to change a material's temperature
5673:
5371:
5251:
The above approximation holds for small temperature and dimensional changes (that is, when
4842:
4815:
4153:
1680:
1605:
1595:
395:
257:
7802:
7027:
Kosinski, J.A.; Gualtieri, J.G.; Ballato, A. (1991). "Thermal expansion of alpha quartz".
5168:
is a small quantity which on squaring gets much smaller and on cubing gets smaller still.
8:
6313:
5491:
4049:
2240:{\displaystyle \alpha \approx {\frac {0.038}{T_{m}}}-7.0\cdot 10^{-6}\,\mathrm {K} ^{-1}}
2080:
1929:
of unevenly heated fluid masses, notably making thermal expansion partly responsible for
1625:
1387:
409:
375:
370:
283:
7777:
Engineering
Toolbox – List of coefficients of Linear Expansion for some common materials
7665:
7339:
7121:
6866:
6751:
6692:
6610:
1620:
599:
7495:
7407:
7351:
7325:
7133:
7052:
6768:
6735:
6632:
5785:
5765:
5745:
5653:
5442:
5323:
Similarly, the area thermal expansion coefficient is two times the linear coefficient:
4376:
4133:
3990:
3264:
3168:
2501:
1824:
1812:
1714:
1377:
1372:
1325:
941:
894:
809:
762:
674:
627:
557:
541:
428:
380:
365:
355:
164:
158:
6281:. This phenomenon resulted in 190 train derailments during 1998–2002 in the US alone.
6277:
Thermal expansion of long continuous sections of rail tracks is the driving force for
6143:
that, at constant pressure, ideal gases expanded or contracted their volume linearly (
3435:. If either of these conditions does not hold, the exact differential equation (using
7772:
DoITPoMS Teaching and
Learning Package on Thermal Expansion and the Bi-material Strip
7677:
7411:
7399:
7355:
7274:
7137:
7042:
6870:
6832:
6773:
6655:
6636:
6622:
6571:
6517:
6392:
6341:
2687:
1840:
1709:
1670:
1660:
1232:
1030:
360:
350:
292:
7601:
7056:
7669:
7389:
7343:
7249:
7125:
7034:
6763:
6755:
6696:
6614:
6489:
6422:
6259:
6144:
6111:
3989:
is the difference of the temperature between the two recorded strains, measured in
1795:
1630:
1615:
1555:
1550:
1367:
1362:
1012:
480:
345:
6603:
Astronomical Optics: Design, Manufacture, and Test of Space and Ground
Systems III
4366:{\displaystyle \alpha _{V}={\frac {1}{V}}\,{\frac {\mathrm {d} V}{\mathrm {d} T}}}
4123:{\displaystyle \alpha _{A}={\frac {1}{A}}\,{\frac {\mathrm {d} A}{\mathrm {d} T}}}
3254:{\displaystyle \alpha _{L}={\frac {1}{L}}\,{\frac {\mathrm {d} L}{\mathrm {d} T}}}
7809:
7792:
7745:
7726:
7394:
7377:
6856:
6492: – Relationship between volume and temperature of a gas at constant pressure
6401:
6381:
6132:
3998:
3994:
3774:
For most solids, thermal expansion is proportional to the change in temperature:
3028:
2953:
1580:
1428:
1082:
723:
546:
307:
274:
136:
6677:"Configurons: thermodynamic parameters and symmetry changes at glass transition"
4300:. If either of these conditions does not hold, the equation must be integrated.
7347:
7166:
6759:
6278:
6247:
5395:. Also, the same considerations must be made when dealing with large values of
5242:{\displaystyle {\frac {\Delta V}{V}}=3{\Delta L \over L}=3\alpha _{L}\Delta T.}
3319:
is the rate of change of that linear dimension per unit change in temperature.
2619:
1882:
1848:
1816:
1635:
1405:
505:
385:
322:
312:
180:
150:
6538:"Details for IEV number 561-06-08: "coefficient of linear thermal expansion ""
4438:
If the expansion coefficient is known, the change in volume can be calculated
7838:
7455:
7403:
7314:"Equation of state of cubic boron nitride at high pressures and temperatures"
7038:
6468:
6166:
5538:
2816:
2119:
2076:
Volumetric thermal expansion coefficient for a semicrystalline polypropylene.
2055:
1934:
1922:
1886:
1704:
1022:
591:
552:
264:
7681:
6777:
6601:. In Hallibert, Pascal; Hull, Tony B.; Kim, Daewook; Keller, Fanny (eds.).
6115:
5803:
5698:
2853:
2354:
1655:
1640:
1590:
1073:
6377:
Metal hot water heating pipes should not be used in long straight lengths.
2253:
is from 10 K for hard solids to 10 K for organic liquids. The coefficient
27:
Tendency of matter to change volume in response to a change in temperature
7798:
MatWeb: Free database of engineering properties for over 79,000 materials
7673:
7330:
6415:
6345:
6317:
6179:
6136:
5438:
5430:
4053:
2779:
2760:
2741:
2383:
1895:
1791:
1610:
418:
140:
6814:
Study of
Thermal Expansion in Carbon Fiber Reinforced Polymer Composites
6327:
7649:
7254:
7238:
7129:
6618:
6349:
4920:
2520:
1926:
1905:
1699:
1645:
6701:
6676:
3982:{\displaystyle \Delta T=(T_{\mathrm {final} }-T_{\mathrm {initial} })}
7602:"Is sea level rising? Yes, sea level is rising at an increasing rate"
7376:
Mann, Arne; Germann, Thiemo; Ruiter, Mats; Groche, Peter (May 2020).
6183:
5534:
4808:
is the volumetric expansion coefficient as a function of temperature
3893:{\displaystyle \varepsilon _{\mathrm {thermal} }=\alpha _{L}\Delta T}
2532:
2318:
297:
7460:
7028:
6120:
5643:{\displaystyle p\mathrm {d} V_{m}+V_{m}\mathrm {d} p=R\mathrm {d} T}
2088:
This section summarizes the coefficients for some common materials.
35:
7803:
USA NIST Website – Temperature and
Dimensional Measurement workshop
7487:
6736:"Giant thermal expansion and α-precipitation pathways in Ti-alloys"
6605:. Vol. 11820. San Diego, United States: SPIE. pp. 52–59.
6447:
6425:
and bends due to the differing thermal expansion of the two metals.
6385:
4184:
is the rate of change of that area per unit change in temperature.
3151:
exhibits negative thermal expansion in broad range of temperatures
3083:
3065:
2935:
2917:
2798:
2516:
2465:
2393:
1955:
1901:
1844:
1413:
1330:
1122:
530:
302:
7550:
7030:
Proceedings of the 45th Annual
Symposium on Frequency Control 1991
6566:. In O'Mara, William C.; Herring, Robert B.; Hunt, Lee P. (eds.).
2091:
For isotropic materials the coefficients linear thermal expansion
6336:
5434:
3823:{\displaystyle \varepsilon _{\mathrm {thermal} }\propto \Delta T}
3120:
2971:
2567:
2447:
2429:
1787:
519:
1827:) divided by the change in temperature is called the material's
7444:(1802), "Recherches sur la dilatation des gaz et des vapeurs",
7429:
Memoirs of the
Literary and Philosophical Society of Manchester
7006:
The coefficients of thermal expansion of wood and wood products
6816:. Proceedings of SAMPE International Symposium. Charleston, SC.
5474:
4919:
This ratio arises because volume is composed of three mutually
4002:
3187:
3008:
2989:
2889:
2705:
2637:
2411:
2163:
1867:
1783:
1775:
132:
7239:"Negative thermal expansion ALLVAR alloys for athermalization"
6273:
5537:, a formula can be readily obtained by differentiation of the
5445:, will generally have different linear expansion coefficients
7311:
7236:
6597:
Monroe, James A.; East, Matthew; Hull, Tony B. (2021-08-24).
6298:
3172:
3101:
3046:
2673:
2602:
2524:
2483:
2336:
2167:
1890:
7312:
Datchi, F.; Dewaele, A.; Le Godec, Y.; Loubeyre, P. (2007).
1798:). Substances usually contract with decreasing temperature (
6570:. Park Ridge, New Jersey: Noyes Publications. p. 431.
6258:
For applications using the thermal expansion property, see
3322:
The change in the linear dimension can be estimated to be:
3167:
stress/strain relationship characterised by the elastic or
2655:
2549:
2084:
Linear thermal expansion coefficient for some steel grades.
1930:
1854:
1802:), with rare exceptions within limited temperature ranges (
1779:
495:
7727:
Cost or savings of thermal expansion in above ground tanks
4960:
and the new volume, after a temperature increase, will be
2068:
Thermal expansion coefficients of the elements (data page)
7729:. Artofbeingcheap.com (2013-09-06). Retrieved 2014-01-19.
6854:
4482:{\displaystyle {\frac {\Delta V}{V}}=\alpha _{V}\Delta T}
4231:{\displaystyle {\frac {\Delta A}{A}}=\alpha _{A}\Delta T}
3366:{\displaystyle {\frac {\Delta L}{L}}=\alpha _{L}\Delta T}
2835:
2723:
2585:
1921:), thus changing its density, which has an effect on any
7797:
7026:
7375:
6165:
In a footnote
Thomson calculated that "infinite cold" (
4431:
is the rate of change of that volume with temperature.
6290:
pushed over the shaft, thus achieving a 'shrink fit'.
1881:
Thermal expansion generally decreases with increasing
7107:
6977:"WDSC 340. Class Notes on Thermal Properties of Wood"
6221:, while the actual expansion of the liquid is called
5895:
5846:
5815:
5788:
5768:
5748:
5707:
5676:
5656:
5586:
5547:
5509:
5451:
5401:
5374:
5329:
5303:
5280:
5257:
5177:
4966:
4933:
4880:
4866:
are the initial and final temperatures respectively.
4845:
4818:
4778:
4664:
4553:
4526:
4520:
is the fractional change in volume (e.g., 0.002) and
4495:
4444:
4399:
4379:
4314:
4269:
4246:
4193:
4156:
4136:
4071:
4011:
3906:
3840:
3780:
3736:
3689:
3538:
3491:
3441:
3404:
3381:
3328:
3287:
3267:
3202:
2175:
2155:{\displaystyle \alpha \approx {\frac {0.020}{T_{m}}}}
2128:
1967:
1241:
1186:
1131:
1091:
965:
944:
918:
897:
869:
833:
812:
786:
765:
734:
698:
677:
651:
630:
602:
6811:
6516:. New York, NY: Worth Publishers. pp. 666–670.
6485:
Pages displaying wikidata descriptions as a fallback
6452:
Pages displaying wikidata descriptions as a fallback
7378:"The challenge of upscaling paraffin wax actuators"
6850:
6848:
6380:Large structures such as railways and bridges need
6197:is still calculated from the experimental value of
5889:and the isobaric thermal expansion coefficient is:
4052:, thermal expansion and its effects are treated as
3730:is the length before the change of temperature and
3191:
Change in length of a rod due to thermal expansion.
60:. Unsourced material may be challenged and removed.
7705:, William and Wood & Co, New York, pp. 272–73.
6094:
5881:
5832:
5794:
5774:
5754:
5734:
5689:
5662:
5642:
5572:
5522:
5464:
5410:
5387:
5358:
5312:
5289:
5266:
5241:
5154:
4952:
4909:
4858:
4831:
4800:
4764:
4651:
4535:
4512:
4481:
4423:
4385:
4365:
4292:
4255:
4230:
4176:
4142:
4122:
4024:
3981:
3892:
3822:
3763:
3722:
3673:
3524:
3465:
3427:
3390:
3365:
3311:
3273:
3253:
2239:
2154:
2035:
1277:
1222:
1167:
1112:
974:
950:
927:
903:
878:
842:
818:
795:
771:
746:
707:
683:
660:
636:
611:
7820:Understanding Thermal Expansion in Ceramic Glazes
7717:. Volpe Center, U.S. Department of Transportation
7440:
7003:Weatherwax, Richard C.; Stamm, Alfred J. (1956).
5882:{\displaystyle p\mathrm {d} V_{m}=R\mathrm {d} T}
3525:{\displaystyle \varepsilon _{\mathrm {thermal} }}
2884:Parallel to a-axis/c-axis T = –50 to 150 °C
7836:
7268:
6845:
6404:absorb the thermal expansion in a piping system.
6150:In October 1848, William Thomson, a 24 year old
7002:
6797:. Western Washington University. Archived from
3771:is the length after the change of temperature.
3398:, and the fractional change in length is small
7269:Turcotte, Donald L.; Schubert, Gerald (2002).
6596:
6301:36, with expansion approximately equal to 0.6
4263:, and the fractional change in area is small
2122:. In particular, for metals the relation is:
1752:
6858:Principles of Physics: A Calculus-Based Text
6568:Handbook of semiconductor silicon technology
6483: – thermodynamic property of a material
6253:
6105:
5437:(with less than cubic symmetry, for example
4187:The change in the area can be estimated as:
4150:is some area of interest on the object, and
143:used to avoid damage from thermal expansion.
7647:
7576:"Kinetic particle theory and state changes"
7519:
7095:"Basic Parameters of Silicon Carbide (SiC)"
6998:
6996:
6994:
6509:
6475:Thermodynamic databases for pure substances
6459: – Thermodynamical parameter of solids
4543:is the change in temperature (50 °C).
4424:{\displaystyle \mathrm {d} V/\mathrm {d} T}
3466:{\displaystyle \mathrm {d} L/\mathrm {d} T}
3312:{\displaystyle \mathrm {d} L/\mathrm {d} T}
1925:acting on it. This plays a crucial role in
7513:
6789:
6787:
6654:. Sheffield: Society of Glass Technology.
1759:
1745:
157:
7393:
7329:
7253:
6767:
6700:
6649:
6542:International Electrotechnical Vocabulary
6421:A bi-metal mechanical thermometer uses a
6371:Metal-framed windows need rubber spacers.
5484:
4742:
4640:
4338:
4095:
3226:
2221:
1997:
1774:is the tendency of matter to increase in
120:Learn how and when to remove this message
7830:Thermal expansion via density calculator
7194:
7153:"Thermal Expansion Coefficients at 20 C"
6991:
6358:
6326:
6272:
6211:
6131:From 1787 to 1802, it was determined by
6119:
5424:
5359:{\displaystyle \alpha _{A}=2\alpha _{L}}
4910:{\displaystyle \alpha _{V}=3\alpha _{L}}
3186:
2079:
2071:
2061:
1885:energy, which also has an effect on the
1855:Contraction effects (negative expansion)
1831:and generally varies with temperature.
131:
7739:Lateral, Angular and Combined Movements
7202:"Properties of Common Liquid Materials"
6826:
6784:
3281:is a particular length measurement and
1829:coefficient of linear thermal expansion
14:
7837:
7624:"Volumetric (Cubic) Thermal Expansion"
6921:"DuPont™ Kapton® 200EN Polyimide Film"
6674:
6561:
4869:
3723:{\displaystyle L_{\mathrm {initial} }}
3023:average for −60 °C to 60 °C
7520:Lord Kelvin, William (October 1848).
7431:, vol. 8, pt. 2, pp. 550–74, 595–602.
7016:, United States Forest Service. 1487.
6510:Tipler, Paul A.; Mosca, Gene (2008).
6503:
6477: – Thermodynamic properties list
6439: – Process in physical chemistry
6127:, the namesake of the unit of measure
6855:Raymond Serway; John Jewett (2005),
6481:Material properties (thermodynamics)
3834:or temperature can be estimated by:
3764:{\displaystyle L_{\mathrm {final} }}
3476:
1912:
1823:The relative expansion (also called
58:adding citations to reliable sources
29:
7522:"On an Absolute Thermometric Scale"
7493:
7466:
6530:
5809:For an isobaric thermal expansion,
5762:the total number of moles of gas),
5164:We can easily ignore the terms as Δ
4393:is the volume of the material, and
24:
7767:Water thermal expansion calculator
7648:Hagy, H.E.; Shirkey, W.D. (1975).
6363:Expansion loop on heating pipeline
5997:
5982:
5935:
5927:
5872:
5851:
5817:
5633:
5619:
5591:
5402:
5304:
5281:
5258:
5230:
5202:
5181:
5137:
5113:
5071:
5055:
5040:
4994:
4973:
4744:
4668:
4642:
4573:
4527:
4496:
4473:
4448:
4414:
4401:
4353:
4343:
4270:
4247:
4222:
4197:
4110:
4100:
3970:
3967:
3964:
3961:
3958:
3955:
3952:
3937:
3934:
3931:
3928:
3925:
3907:
3884:
3865:
3862:
3859:
3856:
3853:
3850:
3847:
3814:
3805:
3802:
3799:
3796:
3793:
3790:
3787:
3755:
3752:
3749:
3746:
3743:
3714:
3711:
3708:
3705:
3702:
3699:
3696:
3663:
3660:
3657:
3654:
3651:
3648:
3645:
3629:
3626:
3623:
3620:
3617:
3614:
3611:
3596:
3593:
3590:
3587:
3584:
3563:
3560:
3557:
3554:
3551:
3548:
3545:
3516:
3513:
3510:
3507:
3504:
3501:
3498:
3456:
3443:
3405:
3382:
3357:
3332:
3302:
3289:
3241:
3231:
2249:In the table below, the range for
2224:
2014:
2006:
966:
919:
834:
787:
699:
652:
472:Intensive and extensive properties
25:
7871:
7754:
6861:, Cengage Learning, p. 506,
6652:Fundamentals of inorganic glasses
6231:coefficient of apparent expansion
6160:On an Absolute Thermometric Scale
2095:and volumetric thermal expansion
7701:Ganot, A., Atkinson, E. (1883).
7150:
6829:Young and Geller College Physics
5782:is the absolute temperature and
4048:, respectively. In the field of
1947:coefficient of thermal expansion
1790:, in response to an increase in
1728:
1727:
1047:Table of thermodynamic equations
34:
7815:Hyperphysics: Thermal expansion
7732:
7720:
7708:
7695:
7641:
7616:
7594:
7568:
7543:
7434:
7418:
7369:
7305:
7287:
7262:
7230:
7212:
7177:
7159:
7144:
7101:
7087:
7063:
7020:
6969:
6938:
6913:
6882:
6820:
6805:
6450: – greenhouse farming tool
6443:Mie–Grüneisen equation of state
6152:professor of Natural Philosophy
5833:{\displaystyle \mathrm {d} p=0}
5530:, is the only one of interest.
4293:{\displaystyle \Delta A/A\ll 1}
3830:Thus, the change in either the
3428:{\displaystyle \Delta L/L\ll 1}
1940:
1523:Maxwell's thermodynamic surface
45:needs additional citations for
7456:English translation (extract).
7167:"Sitall CO-115M (Astrositall)"
6890:"Technical Glasses Data Sheet"
6727:
6709:
6668:
6643:
6590:
6555:
4927:. The original volume will be
4801:{\displaystyle \alpha _{V}(T)}
4795:
4789:
4739:
4733:
4637:
4631:
3976:
3916:
3635:
3575:
1954:in every direction are called
1898:liquid transforms to a glass.
1257:
1245:
1202:
1190:
1147:
1135:
1107:
1095:
13:
1:
7825:Thermal Expansion Calculators
7076:. kyocera.com. Archived from
6951:. corning.com. Archived from
6497:
6172:
3134:from 0 °C to 50 °C
2274:is usually used for solids.)
1834:
1424:Mechanical equivalent of heat
7395:10.1016/j.matdes.2020.108580
6923:. matweb.com. Archived from
6895:. schott.com. Archived from
6409:scanning electron microscope
6264:mercury-in-glass thermometer
3157:
2515:matched sealing partner for
1036:Onsager reciprocal relations
7:
7273:(2nd ed.). Cambridge.
7155:. Georgia State University.
6429:
6384:in the structures to avoid
5523:{\displaystyle \alpha _{V}}
5498:
5465:{\displaystyle \alpha _{L}}
4025:{\displaystyle \alpha _{L}}
2736:Perpendicular to the grain
1528:Entropy as energy dispersal
1339:"Perpetual motion" machines
1278:{\displaystyle G(T,p)=H-TS}
1223:{\displaystyle A(T,V)=U-TS}
1168:{\displaystyle H(S,p)=U+pV}
10:
7876:
7348:10.1103/PhysRevB.75.214104
7014:Forest Products Laboratory
6760:10.1038/s41467-017-01578-1
6733:
6562:Bullis, W. Murray (1990).
6437:Negative thermal expansion
6257:
6109:
4513:{\displaystyle \Delta V/V}
3179:coefficient of expansion.
2065:
1873:
1861:negative thermal expansion
1805:negative thermal expansion
975:{\displaystyle \partial T}
928:{\displaystyle \partial V}
843:{\displaystyle \partial p}
796:{\displaystyle \partial V}
708:{\displaystyle \partial T}
661:{\displaystyle \partial S}
7555:The Physics Hypertextbook
7242:(Conference Presentation)
7185:"Thermal Expansion table"
6650:Varshneya, A. K. (2006).
6254:Examples and applications
6116:Kelvin § Lord Kelvin
6106:Absolute zero computation
5735:{\displaystyle V_{m}=V/n}
5573:{\displaystyle pV_{m}=RT}
4303:
3182:
3171:. In the special case of
1815:of the average molecular
1449:An Inquiry Concerning the
7501:. Philosophical Magazine
7475:. Philosophical Magazine
7110:Zeitschrift für Physik B
7039:10.1109/FREQ.1991.145883
6292:Induction shrink fitting
6237:simultaneously measures
6217:container is called its
5411:{\displaystyle \Delta T}
5313:{\displaystyle \Delta T}
5290:{\displaystyle \Delta L}
5267:{\displaystyle \Delta T}
4536:{\displaystyle \Delta T}
4256:{\displaystyle \Delta T}
3391:{\displaystyle \Delta T}
2948:Parallel to C axis, or
1847:, along with many other
1786:, changing its size and
1462:Heterogeneous Substances
879:{\displaystyle \alpha =}
747:{\displaystyle \beta =-}
7761:Glass Thermal Expansion
7715:Track Buckling Research
7628:The Engineering Toolbox
6463:Apparent molar property
6141:Joseph Louis Gay-Lussac
4953:{\displaystyle V=L^{3}}
4059:
3060:Depends on composition
1919:mass–energy equivalence
7526:Philosophical Magazine
7382:Materials & Design
6675:Ojovan, M. I. (2008).
6364:
6332:
6314:micrometer screw gauge
6282:
6158:, published the paper
6128:
6096:
5883:
5834:
5796:
5776:
5756:
5736:
5691:
5664:
5644:
5574:
5524:
5485:Temperature dependence
5466:
5412:
5389:
5360:
5314:
5291:
5268:
5243:
5156:
4954:
4911:
4860:
4833:
4802:
4766:
4653:
4537:
4514:
4483:
4425:
4387:
4367:
4294:
4257:
4232:
4178:
4144:
4124:
4026:
3983:
3894:
3824:
3765:
3724:
3675:
3526:
3473:) must be integrated.
3467:
3429:
3392:
3367:
3313:
3275:
3255:
3192:
2241:
2156:
2085:
2077:
2037:
1279:
1224:
1169:
1114:
1113:{\displaystyle U(S,V)}
976:
952:
929:
905:
880:
844:
820:
797:
773:
748:
709:
685:
662:
638:
613:
592:Specific heat capacity
196:Quantum thermodynamics
144:
6740:Nature Communications
6362:
6330:
6309:Pullinger's apparatus
6276:
6268:Tyndall's bar breaker
6212:Apparent and absolute
6188:global climate change
6156:University of Glasgow
6123:
6097:
5884:
5835:
5797:
5777:
5757:
5737:
5692:
5690:{\displaystyle V_{m}}
5665:
5645:
5575:
5525:
5467:
5425:Anisotropic materials
5413:
5390:
5388:{\displaystyle L^{2}}
5361:
5315:
5292:
5269:
5244:
5157:
4955:
4912:
4861:
4859:{\displaystyle T_{f}}
4834:
4832:{\displaystyle T_{i}}
4803:
4767:
4654:
4538:
4515:
4484:
4426:
4388:
4368:
4295:
4258:
4233:
4179:
4177:{\displaystyle dA/dT}
4145:
4125:
4027:
3984:
3895:
3825:
3766:
3725:
3676:
3527:
3468:
3430:
3393:
3368:
3314:
3276:
3256:
3190:
2242:
2157:
2083:
2075:
2062:For various materials
2038:
1460:On the Equilibrium of
1280:
1225:
1178:Helmholtz free energy
1170:
1115:
977:
953:
930:
906:
881:
845:
821:
798:
774:
749:
710:
686:
663:
639:
614:
135:
7674:10.1364/AO.14.002099
7012:(Technical report).
6981:forestry.caf.wvu.edu
5893:
5844:
5813:
5786:
5766:
5746:
5705:
5674:
5654:
5584:
5545:
5507:
5449:
5433:structures, such as
5399:
5372:
5327:
5301:
5278:
5255:
5175:
4964:
4931:
4878:
4843:
4816:
4776:
4662:
4551:
4524:
4493:
4442:
4397:
4377:
4312:
4267:
4244:
4191:
4154:
4134:
4069:
4009:
3904:
3838:
3778:
3734:
3687:
3536:
3489:
3439:
3402:
3379:
3326:
3285:
3265:
3200:
2650:DuPont Kapton 200EN
2173:
2126:
1965:
1894:temperature where a
1473:Motive Power of Fire
1239:
1184:
1129:
1089:
1041:Bridgman's equations
1018:Fundamental relation
963:
942:
916:
895:
867:
831:
810:
784:
763:
732:
696:
675:
649:
628:
600:
54:improve this article
7855:Physical properties
7666:1975ApOpt..14.2099H
7551:"Thermal Expansion"
7340:2007PhRvB..75u4104D
7122:1982ZPhyB..48...17B
6867:2006ppcb.book.....J
6795:"Thermal Expansion"
6752:2017NatCo...8.1429B
6693:2008Entrp..10..334O
6611:2021SPIE11820E..0BM
6457:Grüneisen parameter
5492:cubic boron nitride
4870:Isotropic materials
4722:
4620:
4050:continuum mechanics
1800:thermal contraction
1794:(usually excluding
1451:Source ... Friction
1383:Loschmidt's paradox
575:Material properties
453:Conjugate variables
69:"Thermal expansion"
7808:2011-06-28 at the
7791:2009-02-25 at the
7744:2020-05-09 at the
7532:on 1 February 2008
7494:Thomson, William.
7467:Thomson, William.
7424:J. Dalton (1802),
7299:solidmechanics.org
7255:10.1117/12.2536862
7130:10.1007/BF02026423
7097:. Ioffe Institute.
6946:"Macor data sheet"
6619:10.1117/12.2594816
6365:
6333:
6283:
6227:absolute expansion
6219:apparent expansion
6129:
6092:
5879:
5830:
5792:
5772:
5752:
5732:
5687:
5660:
5640:
5570:
5520:
5479:powder diffraction
5462:
5408:
5385:
5356:
5310:
5287:
5264:
5239:
5152:
4950:
4907:
4856:
4829:
4798:
4762:
4694:
4649:
4592:
4533:
4510:
4479:
4421:
4383:
4363:
4290:
4253:
4228:
4174:
4140:
4120:
4022:
3991:degrees Fahrenheit
3979:
3890:
3820:
3761:
3720:
3671:
3522:
3463:
3425:
3388:
3363:
3309:
3271:
3251:
3193:
2793:parallel to grain
2502:Borosilicate glass
2237:
2152:
2086:
2078:
2033:
1813:monotonic function
1715:Order and disorder
1471:Reflections on the
1378:Heat death paradox
1275:
1220:
1165:
1110:
972:
948:
925:
901:
876:
840:
816:
793:
769:
744:
705:
681:
658:
634:
612:{\displaystyle c=}
609:
582:Property databases
558:Reduced properties
542:Chemical potential
506:Functions of state
429:Thermal efficiency
165:Carnot heat engine
145:
7446:Annales de Chimie
7442:Gay-Lussac, J. L.
7280:978-0-521-66624-4
7048:978-0-87942-658-3
6876:978-0-534-49143-7
6838:978-0-8053-9218-0
6702:10.3390/e10030334
6661:978-0-12-714970-7
6628:978-1-5106-4478-6
6577:978-0-8155-1237-0
6523:978-1-4292-0132-2
6393:gridiron pendulum
6356:tanks in summer.
6182:and estimates of
6090:
6077:
6048:
6034:
6004:
5972:
5942:
5917:
5795:{\displaystyle R}
5775:{\displaystyle T}
5755:{\displaystyle n}
5670:is the pressure,
5663:{\displaystyle p}
5441:phases) and many
5212:
5191:
5147:
4678:
4583:
4458:
4386:{\displaystyle V}
4361:
4336:
4207:
4143:{\displaystyle A}
4118:
4093:
4056:and eigenstress.
3669:
3477:Effects on strain
3342:
3274:{\displaystyle L}
3249:
3224:
3155:
3154:
2288:coefficient CLTE
2197:
2150:
2021:
1995:
1981:
1913:Effect on density
1841:equation of state
1811:Temperature is a
1796:phase transitions
1772:Thermal expansion
1769:
1768:
1710:Self-organization
1535:
1534:
1233:Gibbs free energy
1031:Maxwell relations
989:
988:
985:
984:
951:{\displaystyle V}
904:{\displaystyle 1}
859:Thermal expansion
853:
852:
819:{\displaystyle V}
772:{\displaystyle 1}
718:
717:
684:{\displaystyle N}
637:{\displaystyle T}
565:
564:
481:Process functions
467:Property diagrams
446:System properties
436:
435:
401:Endoreversibility
293:Equation of state
130:
129:
122:
104:
18:Thermal Expansion
16:(Redirected from
7867:
7860:Building defects
7782:Article on how α
7749:
7736:
7730:
7724:
7718:
7712:
7706:
7699:
7693:
7692:
7690:
7688:
7660:(9): 2099–2103.
7645:
7639:
7638:
7636:
7634:
7620:
7614:
7613:
7611:
7609:
7598:
7592:
7591:
7589:
7587:
7572:
7566:
7565:
7563:
7561:
7547:
7541:
7540:
7538:
7537:
7528:. Archived from
7517:
7511:
7510:
7508:
7506:
7500:
7491:
7485:
7484:
7482:
7480:
7464:
7458:
7453:
7438:
7432:
7422:
7416:
7415:
7397:
7373:
7367:
7366:
7364:
7362:
7333:
7331:cond-mat/0702656
7309:
7303:
7302:
7291:
7285:
7284:
7266:
7260:
7259:
7257:
7243:
7234:
7228:
7227:
7222:. Archived from
7216:
7210:
7209:
7198:
7192:
7191:
7189:
7181:
7175:
7174:
7171:Star Instruments
7163:
7157:
7156:
7148:
7142:
7141:
7105:
7099:
7098:
7091:
7085:
7084:
7082:
7075:
7067:
7061:
7060:
7024:
7018:
7017:
7011:
7000:
6989:
6988:
6983:. Archived from
6973:
6967:
6966:
6964:
6963:
6957:
6950:
6942:
6936:
6935:
6933:
6932:
6917:
6911:
6910:
6908:
6907:
6901:
6894:
6886:
6880:
6879:
6852:
6843:
6842:
6831:(8th ed.).
6824:
6818:
6817:
6809:
6803:
6802:
6791:
6782:
6781:
6771:
6731:
6725:
6724:
6713:
6707:
6706:
6704:
6672:
6666:
6665:
6647:
6641:
6640:
6594:
6588:
6587:
6585:
6584:
6559:
6553:
6552:
6550:
6549:
6534:
6528:
6527:
6507:
6486:
6453:
6423:bimetallic strip
6402:Expansion joints
6382:expansion joints
6304:
6260:bimetallic strip
6101:
6099:
6098:
6093:
6091:
6083:
6078:
6076:
6075:
6074:
6058:
6053:
6049:
6041:
6035:
6033:
6032:
6020:
6015:
6014:
6009:
6005:
6003:
5995:
5994:
5993:
5980:
5973:
5971:
5970:
5958:
5953:
5952:
5947:
5943:
5941:
5933:
5925:
5918:
5910:
5905:
5904:
5888:
5886:
5885:
5880:
5875:
5864:
5863:
5854:
5839:
5837:
5836:
5831:
5820:
5802:is equal to the
5801:
5799:
5798:
5793:
5781:
5779:
5778:
5773:
5761:
5759:
5758:
5753:
5741:
5739:
5738:
5733:
5728:
5717:
5716:
5696:
5694:
5693:
5688:
5686:
5685:
5669:
5667:
5666:
5661:
5649:
5647:
5646:
5641:
5636:
5622:
5617:
5616:
5604:
5603:
5594:
5579:
5577:
5576:
5571:
5560:
5559:
5529:
5527:
5526:
5521:
5519:
5518:
5471:
5469:
5468:
5463:
5461:
5460:
5417:
5415:
5414:
5409:
5394:
5392:
5391:
5386:
5384:
5383:
5365:
5363:
5362:
5357:
5355:
5354:
5339:
5338:
5319:
5317:
5316:
5311:
5296:
5294:
5293:
5288:
5273:
5271:
5270:
5265:
5248:
5246:
5245:
5240:
5229:
5228:
5213:
5208:
5200:
5192:
5187:
5179:
5161:
5159:
5158:
5153:
5148:
5143:
5135:
5112:
5111:
5096:
5095:
5083:
5082:
5067:
5066:
5039:
5038:
5023:
5022:
5010:
5009:
5004:
5000:
4959:
4957:
4956:
4951:
4949:
4948:
4926:
4916:
4914:
4913:
4908:
4906:
4905:
4890:
4889:
4865:
4863:
4862:
4857:
4855:
4854:
4838:
4836:
4835:
4830:
4828:
4827:
4807:
4805:
4804:
4799:
4788:
4787:
4771:
4769:
4768:
4763:
4755:
4751:
4747:
4732:
4731:
4721:
4720:
4719:
4709:
4708:
4707:
4679:
4674:
4666:
4658:
4656:
4655:
4650:
4645:
4630:
4629:
4619:
4618:
4617:
4607:
4606:
4605:
4588:
4584:
4579:
4565:
4542:
4540:
4539:
4534:
4519:
4517:
4516:
4511:
4506:
4488:
4486:
4485:
4480:
4472:
4471:
4459:
4454:
4446:
4430:
4428:
4427:
4422:
4417:
4412:
4404:
4392:
4390:
4389:
4384:
4372:
4370:
4369:
4364:
4362:
4360:
4356:
4350:
4346:
4340:
4337:
4329:
4324:
4323:
4299:
4297:
4296:
4291:
4280:
4262:
4260:
4259:
4254:
4237:
4235:
4234:
4229:
4221:
4220:
4208:
4203:
4195:
4183:
4181:
4180:
4175:
4167:
4149:
4147:
4146:
4141:
4129:
4127:
4126:
4121:
4119:
4117:
4113:
4107:
4103:
4097:
4094:
4086:
4081:
4080:
4047:
4043:
4039:
4035:
4031:
4029:
4028:
4023:
4021:
4020:
3988:
3986:
3985:
3980:
3975:
3974:
3973:
3942:
3941:
3940:
3899:
3897:
3896:
3891:
3883:
3882:
3870:
3869:
3868:
3829:
3827:
3826:
3821:
3810:
3809:
3808:
3770:
3768:
3767:
3762:
3760:
3759:
3758:
3729:
3727:
3726:
3721:
3719:
3718:
3717:
3680:
3678:
3677:
3672:
3670:
3668:
3667:
3666:
3638:
3634:
3633:
3632:
3601:
3600:
3599:
3573:
3568:
3567:
3566:
3532:and defined as:
3531:
3529:
3528:
3523:
3521:
3520:
3519:
3472:
3470:
3469:
3464:
3459:
3454:
3446:
3434:
3432:
3431:
3426:
3415:
3397:
3395:
3394:
3389:
3372:
3370:
3369:
3364:
3356:
3355:
3343:
3338:
3330:
3318:
3316:
3315:
3310:
3305:
3300:
3292:
3280:
3278:
3277:
3272:
3260:
3258:
3257:
3252:
3250:
3248:
3244:
3238:
3234:
3228:
3225:
3217:
3212:
3211:
3139:ALLVAR Alloy 30
2388:Fiber direction
2277:
2276:
2273:
2246:
2244:
2243:
2238:
2236:
2235:
2227:
2220:
2219:
2198:
2196:
2195:
2183:
2161:
2159:
2158:
2153:
2151:
2149:
2148:
2136:
2114:
2042:
2040:
2039:
2034:
2032:
2031:
2026:
2022:
2020:
2012:
2004:
1996:
1988:
1983:
1982:
1979:
1761:
1754:
1747:
1731:
1730:
1438:Key publications
1419:
1418:("living force")
1368:Brownian ratchet
1363:Entropy and life
1358:Entropy and time
1309:
1308:
1284:
1282:
1281:
1276:
1229:
1227:
1226:
1221:
1174:
1172:
1171:
1166:
1119:
1117:
1116:
1111:
1013:Clausius theorem
1008:Carnot's theorem
981:
979:
978:
973:
957:
955:
954:
949:
934:
932:
931:
926:
910:
908:
907:
902:
889:
888:
885:
883:
882:
877:
849:
847:
846:
841:
825:
823:
822:
817:
802:
800:
799:
794:
778:
776:
775:
770:
757:
756:
753:
751:
750:
745:
714:
712:
711:
706:
690:
688:
687:
682:
667:
665:
664:
659:
643:
641:
640:
635:
622:
621:
618:
616:
615:
610:
588:
587:
461:
460:
280:
279:
161:
147:
146:
125:
118:
114:
111:
105:
103:
62:
38:
30:
21:
7875:
7874:
7870:
7869:
7868:
7866:
7865:
7864:
7835:
7834:
7810:Wayback Machine
7793:Wayback Machine
7785:
7757:
7752:
7746:Wayback Machine
7737:
7733:
7725:
7721:
7713:
7709:
7700:
7696:
7686:
7684:
7646:
7642:
7632:
7630:
7622:
7621:
7617:
7607:
7605:
7600:
7599:
7595:
7585:
7583:
7574:
7573:
7569:
7559:
7557:
7549:
7548:
7544:
7535:
7533:
7518:
7514:
7504:
7502:
7498:
7492:
7488:
7478:
7476:
7465:
7461:
7439:
7435:
7423:
7419:
7374:
7370:
7360:
7358:
7310:
7306:
7293:
7292:
7288:
7281:
7267:
7263:
7241:
7235:
7231:
7218:
7217:
7213:
7200:
7199:
7195:
7187:
7183:
7182:
7178:
7165:
7164:
7160:
7149:
7145:
7106:
7102:
7093:
7092:
7088:
7080:
7073:
7069:
7068:
7064:
7049:
7025:
7021:
7009:
7001:
6992:
6975:
6974:
6970:
6961:
6959:
6955:
6948:
6944:
6943:
6939:
6930:
6928:
6919:
6918:
6914:
6905:
6903:
6899:
6892:
6888:
6887:
6883:
6877:
6853:
6846:
6839:
6827:Young; Geller.
6825:
6821:
6810:
6806:
6793:
6792:
6785:
6732:
6728:
6715:
6714:
6710:
6673:
6669:
6662:
6648:
6644:
6629:
6595:
6591:
6582:
6580:
6578:
6560:
6556:
6547:
6545:
6536:
6535:
6531:
6524:
6508:
6504:
6500:
6495:
6484:
6451:
6432:
6302:
6271:
6256:
6214:
6202:
6195:
6175:
6135:(unpublished),
6133:Jacques Charles
6118:
6108:
6082:
6070:
6066:
6062:
6057:
6040:
6036:
6028:
6024:
6019:
6010:
5996:
5989:
5985:
5981:
5979:
5975:
5974:
5966:
5962:
5957:
5948:
5934:
5926:
5924:
5920:
5919:
5909:
5900:
5896:
5894:
5891:
5890:
5871:
5859:
5855:
5850:
5845:
5842:
5841:
5816:
5814:
5811:
5810:
5787:
5784:
5783:
5767:
5764:
5763:
5747:
5744:
5743:
5724:
5712:
5708:
5706:
5703:
5702:
5681:
5677:
5675:
5672:
5671:
5655:
5652:
5651:
5632:
5618:
5612:
5608:
5599:
5595:
5590:
5585:
5582:
5581:
5555:
5551:
5546:
5543:
5542:
5514:
5510:
5508:
5505:
5504:
5501:
5487:
5473:expansion as a
5456:
5452:
5450:
5447:
5446:
5429:Materials with
5427:
5400:
5397:
5396:
5379:
5375:
5373:
5370:
5369:
5350:
5346:
5334:
5330:
5328:
5325:
5324:
5302:
5299:
5298:
5279:
5276:
5275:
5256:
5253:
5252:
5224:
5220:
5201:
5199:
5180:
5178:
5176:
5173:
5172:
5136:
5134:
5107:
5103:
5091:
5087:
5078:
5074:
5062:
5058:
5034:
5030:
5018:
5014:
5005:
4987:
4983:
4982:
4965:
4962:
4961:
4944:
4940:
4932:
4929:
4928:
4924:
4901:
4897:
4885:
4881:
4879:
4876:
4875:
4872:
4850:
4846:
4844:
4841:
4840:
4823:
4819:
4817:
4814:
4813:
4783:
4779:
4777:
4774:
4773:
4743:
4727:
4723:
4715:
4711:
4710:
4703:
4699:
4698:
4693:
4689:
4667:
4665:
4663:
4660:
4659:
4641:
4625:
4621:
4613:
4609:
4608:
4601:
4597:
4596:
4566:
4564:
4560:
4552:
4549:
4548:
4525:
4522:
4521:
4502:
4494:
4491:
4490:
4467:
4463:
4447:
4445:
4443:
4440:
4439:
4413:
4408:
4400:
4398:
4395:
4394:
4378:
4375:
4374:
4352:
4351:
4342:
4341:
4339:
4328:
4319:
4315:
4313:
4310:
4309:
4306:
4276:
4268:
4265:
4264:
4245:
4242:
4241:
4216:
4212:
4196:
4194:
4192:
4189:
4188:
4163:
4155:
4152:
4151:
4135:
4132:
4131:
4109:
4108:
4099:
4098:
4096:
4085:
4076:
4072:
4070:
4067:
4066:
4062:
4045:
4041:
4037:
4033:
4016:
4012:
4010:
4007:
4006:
3999:degrees Celsius
3995:degrees Rankine
3951:
3950:
3946:
3924:
3923:
3919:
3905:
3902:
3901:
3878:
3874:
3846:
3845:
3841:
3839:
3836:
3835:
3786:
3785:
3781:
3779:
3776:
3775:
3742:
3741:
3737:
3735:
3732:
3731:
3695:
3694:
3690:
3688:
3685:
3684:
3644:
3643:
3639:
3610:
3609:
3605:
3583:
3582:
3578:
3574:
3572:
3544:
3543:
3539:
3537:
3534:
3533:
3497:
3496:
3492:
3490:
3487:
3486:
3479:
3455:
3450:
3442:
3440:
3437:
3436:
3411:
3403:
3400:
3399:
3380:
3377:
3376:
3351:
3347:
3331:
3329:
3327:
3324:
3323:
3301:
3296:
3288:
3286:
3283:
3282:
3266:
3263:
3262:
3240:
3239:
3230:
3229:
3227:
3216:
3207:
3203:
3201:
3198:
3197:
3185:
3169:Young's modulus
3160:
3029:Stainless steel
2954:Silicon Carbide
2309:
2307:
2305:
2299:
2294:
2292:
2287:
2267:
2262:
2228:
2223:
2222:
2212:
2208:
2191:
2187:
2182:
2174:
2171:
2170:
2144:
2140:
2135:
2127:
2124:
2123:
2108:
2103:
2102:are related by
2100:
2070:
2064:
2045:The subscript "
2027:
2013:
2005:
2003:
1999:
1998:
1987:
1978:
1974:
1966:
1963:
1962:
1943:
1915:
1876:
1857:
1849:state functions
1837:
1765:
1720:
1719:
1695:
1687:
1686:
1685:
1545:
1537:
1536:
1515:
1501:
1476:
1472:
1465:
1461:
1454:
1450:
1417:
1410:
1392:
1373:Maxwell's demon
1335:
1306:
1305:
1289:
1288:
1287:
1240:
1237:
1236:
1235:
1185:
1182:
1181:
1180:
1130:
1127:
1126:
1125:
1090:
1087:
1086:
1085:
1083:Internal energy
1078:
1063:
1053:
1052:
1027:
1002:
992:
991:
990:
964:
961:
960:
943:
940:
939:
917:
914:
913:
896:
893:
892:
868:
865:
864:
832:
829:
828:
811:
808:
807:
785:
782:
781:
764:
761:
760:
733:
730:
729:
724:Compressibility
697:
694:
693:
676:
673:
672:
650:
647:
646:
629:
626:
625:
601:
598:
597:
577:
567:
566:
547:Particle number
500:
459:
448:
438:
437:
396:Irreversibility
308:State of matter
275:Isolated system
260:
250:
249:
248:
223:
213:
212:
208:Non-equilibrium
200:
175:
167:
137:Expansion joint
126:
115:
109:
106:
63:
61:
51:
39:
28:
23:
22:
15:
12:
11:
5:
7873:
7863:
7862:
7857:
7852:
7847:
7845:Thermodynamics
7833:
7832:
7827:
7822:
7817:
7812:
7800:
7795:
7783:
7779:
7774:
7769:
7764:
7756:
7755:External links
7753:
7751:
7750:
7731:
7719:
7707:
7694:
7654:Applied Optics
7640:
7615:
7593:
7580:Bitesize: GCSE
7567:
7542:
7512:
7486:
7459:
7433:
7417:
7368:
7324:(21): 214104.
7304:
7286:
7279:
7261:
7229:
7226:on 2013-10-04.
7211:
7206:www.efunda.com
7193:
7176:
7158:
7143:
7100:
7086:
7083:on 2005-10-18.
7062:
7047:
7033:. p. 22.
7019:
6990:
6987:on 2009-03-30.
6968:
6937:
6912:
6881:
6875:
6844:
6837:
6819:
6804:
6801:on 2009-04-17.
6783:
6726:
6708:
6687:(3): 334–364.
6667:
6660:
6642:
6627:
6589:
6576:
6554:
6529:
6522:
6501:
6499:
6496:
6494:
6493:
6487:
6478:
6472:
6466:
6460:
6454:
6445:
6440:
6433:
6431:
6428:
6427:
6426:
6419:
6412:
6405:
6399:
6396:
6389:
6378:
6375:
6372:
6286:are expected.
6255:
6252:
6223:real expansion
6213:
6210:
6200:
6193:
6186:rising due to
6174:
6171:
6107:
6104:
6089:
6086:
6081:
6073:
6069:
6065:
6061:
6056:
6052:
6047:
6044:
6039:
6031:
6027:
6023:
6018:
6013:
6008:
6002:
5999:
5992:
5988:
5984:
5978:
5969:
5965:
5961:
5956:
5951:
5946:
5940:
5937:
5932:
5929:
5923:
5916:
5913:
5908:
5903:
5899:
5878:
5874:
5870:
5867:
5862:
5858:
5853:
5849:
5829:
5826:
5823:
5819:
5791:
5771:
5751:
5731:
5727:
5723:
5720:
5715:
5711:
5684:
5680:
5659:
5639:
5635:
5631:
5628:
5625:
5621:
5615:
5611:
5607:
5602:
5598:
5593:
5589:
5580:. This yields
5569:
5566:
5563:
5558:
5554:
5550:
5517:
5513:
5500:
5497:
5486:
5483:
5459:
5455:
5426:
5423:
5407:
5404:
5382:
5378:
5353:
5349:
5345:
5342:
5337:
5333:
5309:
5306:
5286:
5283:
5263:
5260:
5238:
5235:
5232:
5227:
5223:
5219:
5216:
5211:
5207:
5204:
5198:
5195:
5190:
5186:
5183:
5151:
5146:
5142:
5139:
5133:
5130:
5127:
5124:
5121:
5118:
5115:
5110:
5106:
5102:
5099:
5094:
5090:
5086:
5081:
5077:
5073:
5070:
5065:
5061:
5057:
5054:
5051:
5048:
5045:
5042:
5037:
5033:
5029:
5026:
5021:
5017:
5013:
5008:
5003:
4999:
4996:
4993:
4990:
4986:
4981:
4978:
4975:
4972:
4969:
4947:
4943:
4939:
4936:
4904:
4900:
4896:
4893:
4888:
4884:
4871:
4868:
4853:
4849:
4826:
4822:
4797:
4794:
4791:
4786:
4782:
4761:
4758:
4754:
4750:
4746:
4741:
4738:
4735:
4730:
4726:
4718:
4714:
4706:
4702:
4697:
4692:
4688:
4685:
4682:
4677:
4673:
4670:
4648:
4644:
4639:
4636:
4633:
4628:
4624:
4616:
4612:
4604:
4600:
4595:
4591:
4587:
4582:
4578:
4575:
4572:
4569:
4563:
4559:
4556:
4532:
4529:
4509:
4505:
4501:
4498:
4478:
4475:
4470:
4466:
4462:
4457:
4453:
4450:
4420:
4416:
4411:
4407:
4403:
4382:
4359:
4355:
4349:
4345:
4335:
4332:
4327:
4322:
4318:
4305:
4302:
4289:
4286:
4283:
4279:
4275:
4272:
4252:
4249:
4227:
4224:
4219:
4215:
4211:
4206:
4202:
4199:
4173:
4170:
4166:
4162:
4159:
4139:
4116:
4112:
4106:
4102:
4092:
4089:
4084:
4079:
4075:
4061:
4058:
4019:
4015:
3978:
3972:
3969:
3966:
3963:
3960:
3957:
3954:
3949:
3945:
3939:
3936:
3933:
3930:
3927:
3922:
3918:
3915:
3912:
3909:
3889:
3886:
3881:
3877:
3873:
3867:
3864:
3861:
3858:
3855:
3852:
3849:
3844:
3819:
3816:
3813:
3807:
3804:
3801:
3798:
3795:
3792:
3789:
3784:
3757:
3754:
3751:
3748:
3745:
3740:
3716:
3713:
3710:
3707:
3704:
3701:
3698:
3693:
3665:
3662:
3659:
3656:
3653:
3650:
3647:
3642:
3637:
3631:
3628:
3625:
3622:
3619:
3616:
3613:
3608:
3604:
3598:
3595:
3592:
3589:
3586:
3581:
3577:
3571:
3565:
3562:
3559:
3556:
3553:
3550:
3547:
3542:
3518:
3515:
3512:
3509:
3506:
3503:
3500:
3495:
3478:
3475:
3462:
3458:
3453:
3449:
3445:
3424:
3421:
3418:
3414:
3410:
3407:
3387:
3384:
3362:
3359:
3354:
3350:
3346:
3341:
3337:
3334:
3308:
3304:
3299:
3295:
3291:
3270:
3247:
3243:
3237:
3233:
3223:
3220:
3215:
3210:
3206:
3184:
3181:
3159:
3156:
3153:
3152:
3149:
3146:
3143:
3140:
3136:
3135:
3132:
3130:
3127:
3126:Glass-ceramic
3124:
3116:
3115:
3113:
3110:
3107:
3104:
3098:
3097:
3095:
3092:
3089:
3086:
3080:
3079:
3077:
3074:
3071:
3068:
3062:
3061:
3058:
3055:
3052:
3049:
3043:
3042:
3040:
3037:
3034:
3031:
3025:
3024:
3021:
3018:
3015:
3014:Glass-ceramic
3012:
3004:
3003:
3001:
2998:
2995:
2992:
2986:
2985:
2983:
2980:
2977:
2974:
2968:
2967:
2965:
2962:
2959:
2956:
2950:
2949:
2946:
2944:
2941:
2938:
2932:
2931:
2929:
2926:
2923:
2920:
2914:
2913:
2905:
2900:
2895:
2892:
2886:
2885:
2882:
2880:
2877:
2874:
2868:
2867:
2865:
2862:
2859:
2856:
2850:
2849:
2847:
2844:
2841:
2838:
2832:
2831:
2829:
2826:
2823:
2820:
2813:
2812:
2810:
2807:
2804:
2801:
2795:
2794:
2791:
2788:
2785:
2782:
2776:
2775:
2772:
2769:
2766:
2763:
2757:
2756:
2753:
2750:
2747:
2744:
2738:
2737:
2734:
2732:
2729:
2726:
2720:
2719:
2717:
2714:
2711:
2708:
2702:
2701:
2699:
2696:
2693:
2690:
2684:
2683:
2681:
2678:
2676:
2670:
2669:
2667:
2664:
2661:
2658:
2652:
2651:
2648:
2645:
2642:
2640:
2634:
2633:
2631:
2628:
2625:
2622:
2616:
2615:
2613:
2610:
2607:
2605:
2599:
2598:
2596:
2594:
2591:
2588:
2582:
2581:
2579:
2576:
2573:
2570:
2564:
2563:
2561:
2558:
2555:
2552:
2546:
2545:
2543:
2540:
2538:
2535:
2529:
2528:
2513:
2510:
2507:
2504:
2498:
2497:
2495:
2492:
2489:
2486:
2480:
2479:
2477:
2474:
2471:
2468:
2462:
2461:
2459:
2456:
2453:
2450:
2444:
2443:
2441:
2438:
2435:
2432:
2426:
2425:
2423:
2420:
2417:
2414:
2408:
2407:
2405:
2402:
2399:
2396:
2390:
2389:
2386:
2381:
2378:
2375:
2369:
2368:
2366:
2363:
2360:
2357:
2351:
2350:
2348:
2345:
2342:
2339:
2333:
2332:
2330:
2327:
2324:
2321:
2315:
2314:
2311:
2303:
2296:
2284:
2283:Material type
2281:
2265:
2234:
2231:
2226:
2218:
2215:
2211:
2207:
2204:
2201:
2194:
2190:
2186:
2181:
2178:
2147:
2143:
2139:
2134:
2131:
2106:
2098:
2066:Main article:
2063:
2060:
2054:seen from the
2030:
2025:
2019:
2016:
2011:
2008:
2002:
1994:
1991:
1986:
1977:
1973:
1970:
1942:
1939:
1935:ocean currents
1923:buoyant forces
1914:
1911:
1875:
1872:
1856:
1853:
1836:
1833:
1817:kinetic energy
1767:
1766:
1764:
1763:
1756:
1749:
1741:
1738:
1737:
1736:
1735:
1722:
1721:
1718:
1717:
1712:
1707:
1702:
1696:
1693:
1692:
1689:
1688:
1684:
1683:
1678:
1673:
1668:
1663:
1658:
1653:
1648:
1643:
1638:
1633:
1628:
1623:
1618:
1613:
1608:
1603:
1598:
1593:
1588:
1583:
1578:
1573:
1568:
1563:
1558:
1553:
1547:
1546:
1543:
1542:
1539:
1538:
1533:
1532:
1531:
1530:
1525:
1517:
1516:
1514:
1513:
1510:
1506:
1503:
1502:
1500:
1499:
1494:
1492:Thermodynamics
1488:
1485:
1484:
1480:
1479:
1478:
1477:
1468:
1466:
1457:
1455:
1446:
1441:
1440:
1434:
1433:
1432:
1431:
1426:
1421:
1409:
1408:
1406:Caloric theory
1402:
1399:
1398:
1394:
1393:
1391:
1390:
1385:
1380:
1375:
1370:
1365:
1360:
1354:
1351:
1350:
1344:
1343:
1342:
1341:
1334:
1333:
1328:
1323:
1317:
1314:
1313:
1307:
1304:
1303:
1300:
1296:
1295:
1294:
1291:
1290:
1286:
1285:
1274:
1271:
1268:
1265:
1262:
1259:
1256:
1253:
1250:
1247:
1244:
1230:
1219:
1216:
1213:
1210:
1207:
1204:
1201:
1198:
1195:
1192:
1189:
1175:
1164:
1161:
1158:
1155:
1152:
1149:
1146:
1143:
1140:
1137:
1134:
1120:
1109:
1106:
1103:
1100:
1097:
1094:
1079:
1077:
1076:
1071:
1065:
1064:
1059:
1058:
1055:
1054:
1051:
1050:
1043:
1038:
1033:
1026:
1025:
1020:
1015:
1010:
1004:
1003:
998:
997:
994:
993:
987:
986:
983:
982:
971:
968:
958:
947:
936:
935:
924:
921:
911:
900:
886:
875:
872:
862:
855:
854:
851:
850:
839:
836:
826:
815:
804:
803:
792:
789:
779:
768:
754:
743:
740:
737:
727:
720:
719:
716:
715:
704:
701:
691:
680:
669:
668:
657:
654:
644:
633:
619:
608:
605:
595:
586:
585:
584:
578:
573:
572:
569:
568:
563:
562:
561:
560:
555:
550:
539:
528:
509:
508:
502:
501:
499:
498:
493:
487:
484:
483:
477:
476:
475:
474:
469:
450:
449:
444:
443:
440:
439:
434:
433:
432:
431:
426:
421:
413:
412:
406:
405:
404:
403:
398:
393:
388:
386:Free expansion
383:
378:
373:
368:
363:
358:
353:
348:
340:
339:
333:
332:
331:
330:
325:
323:Control volume
320:
315:
313:Phase (matter)
310:
305:
300:
295:
287:
286:
278:
277:
272:
267:
261:
256:
255:
252:
251:
247:
246:
241:
236:
231:
225:
224:
219:
218:
215:
214:
211:
210:
199:
198:
193:
188:
183:
177:
176:
173:
172:
169:
168:
163:The classical
162:
154:
153:
151:Thermodynamics
128:
127:
110:September 2017
42:
40:
33:
26:
9:
6:
4:
3:
2:
7872:
7861:
7858:
7856:
7853:
7851:
7850:Heat transfer
7848:
7846:
7843:
7842:
7840:
7831:
7828:
7826:
7823:
7821:
7818:
7816:
7813:
7811:
7807:
7804:
7801:
7799:
7796:
7794:
7790:
7787:
7786:is determined
7780:
7778:
7775:
7773:
7770:
7768:
7765:
7762:
7759:
7758:
7748:U.S. Bellows.
7747:
7743:
7740:
7735:
7728:
7723:
7716:
7711:
7704:
7698:
7683:
7679:
7675:
7671:
7667:
7663:
7659:
7655:
7651:
7644:
7629:
7625:
7619:
7603:
7597:
7581:
7577:
7571:
7556:
7552:
7546:
7531:
7527:
7523:
7516:
7497:
7490:
7474:
7470:
7463:
7457:
7451:
7447:
7443:
7437:
7430:
7427:
7421:
7413:
7409:
7405:
7401:
7396:
7391:
7387:
7383:
7379:
7372:
7357:
7353:
7349:
7345:
7341:
7337:
7332:
7327:
7323:
7319:
7315:
7308:
7300:
7296:
7290:
7282:
7276:
7272:
7265:
7256:
7251:
7247:
7240:
7233:
7225:
7221:
7215:
7207:
7203:
7197:
7186:
7180:
7172:
7168:
7162:
7154:
7147:
7139:
7135:
7131:
7127:
7123:
7119:
7115:
7111:
7104:
7096:
7090:
7079:
7072:
7066:
7058:
7054:
7050:
7044:
7040:
7036:
7032:
7031:
7023:
7015:
7008:
7007:
6999:
6997:
6995:
6986:
6982:
6978:
6972:
6958:on 2011-06-12
6954:
6947:
6941:
6927:on 2018-11-26
6926:
6922:
6916:
6902:on 2015-12-11
6898:
6891:
6885:
6878:
6872:
6868:
6864:
6860:
6859:
6851:
6849:
6840:
6834:
6830:
6823:
6815:
6808:
6800:
6796:
6790:
6788:
6779:
6775:
6770:
6765:
6761:
6757:
6753:
6749:
6745:
6741:
6737:
6730:
6722:
6718:
6712:
6703:
6698:
6694:
6690:
6686:
6682:
6678:
6671:
6663:
6657:
6653:
6646:
6638:
6634:
6630:
6624:
6620:
6616:
6612:
6608:
6604:
6600:
6593:
6579:
6573:
6569:
6565:
6558:
6544:(in Japanese)
6543:
6539:
6533:
6525:
6519:
6515:
6514:
6506:
6502:
6491:
6490:Charles's law
6488:
6482:
6479:
6476:
6473:
6470:
6469:Heat capacity
6467:
6464:
6461:
6458:
6455:
6449:
6446:
6444:
6441:
6438:
6435:
6434:
6424:
6420:
6417:
6413:
6410:
6406:
6403:
6400:
6397:
6394:
6390:
6387:
6383:
6379:
6376:
6373:
6370:
6369:
6368:
6361:
6357:
6353:
6351:
6347:
6343:
6338:
6329:
6325:
6321:
6319:
6315:
6310:
6306:
6300:
6295:
6293:
6287:
6280:
6279:rail buckling
6275:
6269:
6265:
6261:
6251:
6249:
6243:
6240:
6234:
6232:
6228:
6224:
6220:
6209:
6205:
6203:
6196:
6190:. Sometimes,
6189:
6185:
6181:
6170:
6168:
6167:absolute zero
6163:
6161:
6157:
6153:
6148:
6146:
6145:Charles's law
6142:
6138:
6134:
6126:
6122:
6117:
6113:
6112:Charles's law
6103:
6087:
6084:
6079:
6071:
6067:
6063:
6059:
6054:
6050:
6045:
6042:
6037:
6029:
6025:
6021:
6016:
6011:
6006:
6000:
5990:
5986:
5976:
5967:
5963:
5959:
5954:
5949:
5944:
5938:
5930:
5921:
5914:
5911:
5906:
5901:
5897:
5876:
5868:
5865:
5860:
5856:
5847:
5827:
5824:
5821:
5807:
5805:
5789:
5769:
5749:
5729:
5725:
5721:
5718:
5713:
5709:
5700:
5682:
5678:
5657:
5637:
5629:
5626:
5623:
5613:
5609:
5605:
5600:
5596:
5587:
5567:
5564:
5561:
5556:
5552:
5548:
5540:
5539:ideal gas law
5536:
5531:
5515:
5511:
5496:
5493:
5482:
5480:
5476:
5457:
5453:
5444:
5440:
5436:
5432:
5422:
5419:
5405:
5380:
5376:
5366:
5351:
5347:
5343:
5340:
5335:
5331:
5321:
5307:
5284:
5261:
5249:
5236:
5233:
5225:
5221:
5217:
5214:
5209:
5205:
5196:
5193:
5188:
5184:
5169:
5167:
5162:
5149:
5144:
5140:
5131:
5128:
5125:
5122:
5119:
5116:
5108:
5104:
5100:
5097:
5092:
5088:
5084:
5079:
5075:
5068:
5063:
5059:
5052:
5049:
5046:
5043:
5035:
5031:
5027:
5024:
5019:
5015:
5011:
5006:
5001:
4997:
4991:
4988:
4984:
4979:
4976:
4970:
4967:
4945:
4941:
4937:
4934:
4922:
4917:
4902:
4898:
4894:
4891:
4886:
4882:
4867:
4851:
4847:
4824:
4820:
4811:
4792:
4784:
4780:
4759:
4756:
4752:
4748:
4736:
4728:
4724:
4716:
4712:
4704:
4700:
4695:
4690:
4686:
4683:
4680:
4675:
4671:
4646:
4634:
4626:
4622:
4614:
4610:
4602:
4598:
4593:
4589:
4585:
4580:
4576:
4570:
4567:
4561:
4557:
4554:
4544:
4530:
4507:
4503:
4499:
4476:
4468:
4464:
4460:
4455:
4451:
4436:
4432:
4418:
4409:
4405:
4380:
4357:
4347:
4333:
4330:
4325:
4320:
4316:
4301:
4287:
4284:
4281:
4277:
4273:
4250:
4238:
4225:
4217:
4213:
4209:
4204:
4200:
4185:
4171:
4168:
4164:
4160:
4157:
4137:
4114:
4104:
4090:
4087:
4082:
4077:
4073:
4057:
4055:
4051:
4017:
4013:
4004:
4000:
3996:
3992:
3947:
3943:
3920:
3913:
3910:
3887:
3879:
3875:
3871:
3842:
3833:
3817:
3811:
3782:
3772:
3738:
3691:
3681:
3640:
3606:
3602:
3579:
3569:
3540:
3493:
3484:
3474:
3460:
3451:
3447:
3422:
3419:
3416:
3412:
3408:
3385:
3373:
3360:
3352:
3348:
3344:
3339:
3335:
3320:
3306:
3297:
3293:
3268:
3245:
3235:
3221:
3218:
3213:
3208:
3204:
3189:
3180:
3176:
3174:
3170:
3164:
3150:
3147:
3144:
3141:
3138:
3137:
3133:
3131:
3128:
3125:
3122:
3118:
3117:
3114:
3111:
3108:
3105:
3103:
3100:
3099:
3096:
3093:
3090:
3087:
3085:
3082:
3081:
3078:
3075:
3072:
3069:
3067:
3064:
3063:
3059:
3056:
3053:
3050:
3048:
3045:
3044:
3041:
3038:
3035:
3032:
3030:
3027:
3026:
3022:
3019:
3016:
3013:
3010:
3006:
3005:
3002:
2999:
2996:
2993:
2991:
2988:
2987:
2984:
2981:
2978:
2975:
2973:
2970:
2969:
2966:
2963:
2960:
2957:
2955:
2952:
2951:
2947:
2945:
2942:
2939:
2937:
2934:
2933:
2930:
2927:
2924:
2921:
2919:
2916:
2915:
2912:
2911:
2906:
2904:
2901:
2899:
2896:
2893:
2891:
2888:
2887:
2883:
2881:
2878:
2875:
2873:
2870:
2869:
2866:
2863:
2860:
2857:
2855:
2852:
2851:
2848:
2845:
2842:
2839:
2837:
2834:
2833:
2830:
2827:
2824:
2821:
2818:
2817:Polypropylene
2815:
2814:
2811:
2808:
2805:
2802:
2800:
2797:
2796:
2792:
2789:
2786:
2783:
2781:
2778:
2777:
2773:
2770:
2767:
2764:
2762:
2759:
2758:
2754:
2751:
2748:
2745:
2743:
2740:
2739:
2735:
2733:
2730:
2727:
2725:
2722:
2721:
2718:
2715:
2712:
2709:
2707:
2704:
2703:
2700:
2697:
2694:
2691:
2689:
2686:
2685:
2682:
2679:
2677:
2675:
2672:
2671:
2668:
2665:
2662:
2659:
2657:
2654:
2653:
2649:
2646:
2643:
2641:
2639:
2636:
2635:
2632:
2629:
2626:
2623:
2621:
2618:
2617:
2614:
2611:
2608:
2606:
2604:
2601:
2600:
2597:
2595:
2592:
2589:
2587:
2584:
2583:
2580:
2577:
2574:
2571:
2569:
2566:
2565:
2562:
2559:
2556:
2553:
2551:
2548:
2547:
2544:
2541:
2539:
2536:
2534:
2531:
2530:
2526:
2522:
2518:
2514:
2511:
2508:
2505:
2503:
2500:
2499:
2496:
2493:
2490:
2487:
2485:
2482:
2481:
2478:
2475:
2472:
2469:
2467:
2464:
2463:
2460:
2457:
2454:
2451:
2449:
2446:
2445:
2442:
2439:
2436:
2433:
2431:
2428:
2427:
2424:
2421:
2418:
2415:
2413:
2410:
2409:
2406:
2403:
2400:
2397:
2395:
2392:
2391:
2387:
2385:
2382:
2379:
2376:
2374:
2371:
2370:
2367:
2364:
2361:
2358:
2356:
2353:
2352:
2349:
2346:
2343:
2340:
2338:
2335:
2334:
2331:
2328:
2325:
2322:
2320:
2317:
2316:
2312:
2308:at 20 °C
2306:
2297:
2293:at 20 °C
2291:
2285:
2282:
2279:
2278:
2275:
2272:
2268:
2261:(The formula
2259:
2256:
2252:
2247:
2232:
2229:
2216:
2213:
2209:
2205:
2202:
2199:
2192:
2188:
2184:
2179:
2176:
2169:
2165:
2145:
2141:
2137:
2132:
2129:
2121:
2120:melting point
2116:
2113:
2109:
2101:
2094:
2089:
2082:
2074:
2069:
2059:
2057:
2056:ideal gas law
2052:
2048:
2043:
2028:
2023:
2017:
2009:
2000:
1992:
1989:
1984:
1975:
1971:
1968:
1959:
1957:
1951:
1948:
1938:
1936:
1932:
1928:
1924:
1920:
1910:
1907:
1903:
1899:
1897:
1892:
1888:
1887:melting point
1884:
1879:
1871:
1869:
1864:
1862:
1852:
1850:
1846:
1842:
1832:
1830:
1826:
1821:
1818:
1814:
1809:
1807:
1806:
1801:
1797:
1793:
1789:
1785:
1781:
1777:
1773:
1762:
1757:
1755:
1750:
1748:
1743:
1742:
1740:
1739:
1734:
1726:
1725:
1724:
1723:
1716:
1713:
1711:
1708:
1706:
1705:Self-assembly
1703:
1701:
1698:
1697:
1691:
1690:
1682:
1679:
1677:
1676:van der Waals
1674:
1672:
1669:
1667:
1664:
1662:
1659:
1657:
1654:
1652:
1649:
1647:
1644:
1642:
1639:
1637:
1634:
1632:
1629:
1627:
1624:
1622:
1619:
1617:
1614:
1612:
1609:
1607:
1604:
1602:
1601:von Helmholtz
1599:
1597:
1594:
1592:
1589:
1587:
1584:
1582:
1579:
1577:
1574:
1572:
1569:
1567:
1564:
1562:
1559:
1557:
1554:
1552:
1549:
1548:
1541:
1540:
1529:
1526:
1524:
1521:
1520:
1519:
1518:
1511:
1508:
1507:
1505:
1504:
1498:
1495:
1493:
1490:
1489:
1487:
1486:
1482:
1481:
1475:
1474:
1467:
1464:
1463:
1456:
1453:
1452:
1445:
1444:
1443:
1442:
1439:
1436:
1435:
1430:
1427:
1425:
1422:
1420:
1416:
1412:
1411:
1407:
1404:
1403:
1401:
1400:
1396:
1395:
1389:
1386:
1384:
1381:
1379:
1376:
1374:
1371:
1369:
1366:
1364:
1361:
1359:
1356:
1355:
1353:
1352:
1349:
1346:
1345:
1340:
1337:
1336:
1332:
1329:
1327:
1324:
1322:
1319:
1318:
1316:
1315:
1311:
1310:
1301:
1298:
1297:
1293:
1292:
1272:
1269:
1266:
1263:
1260:
1254:
1251:
1248:
1242:
1234:
1231:
1217:
1214:
1211:
1208:
1205:
1199:
1196:
1193:
1187:
1179:
1176:
1162:
1159:
1156:
1153:
1150:
1144:
1141:
1138:
1132:
1124:
1121:
1104:
1101:
1098:
1092:
1084:
1081:
1080:
1075:
1072:
1070:
1067:
1066:
1062:
1057:
1056:
1049:
1048:
1044:
1042:
1039:
1037:
1034:
1032:
1029:
1028:
1024:
1023:Ideal gas law
1021:
1019:
1016:
1014:
1011:
1009:
1006:
1005:
1001:
996:
995:
969:
959:
945:
938:
937:
922:
912:
898:
891:
890:
887:
873:
870:
863:
860:
857:
856:
837:
827:
813:
806:
805:
790:
780:
766:
759:
758:
755:
741:
738:
735:
728:
725:
722:
721:
702:
692:
678:
671:
670:
655:
645:
631:
624:
623:
620:
606:
603:
596:
593:
590:
589:
583:
580:
579:
576:
571:
570:
559:
556:
554:
553:Vapor quality
551:
549:
548:
543:
540:
538:
537:
532:
529:
526:
522:
521:
516:
513:
512:
511:
510:
507:
504:
503:
497:
494:
492:
489:
488:
486:
485:
482:
479:
478:
473:
470:
468:
465:
464:
463:
462:
458:
454:
447:
442:
441:
430:
427:
425:
422:
420:
417:
416:
415:
414:
411:
408:
407:
402:
399:
397:
394:
392:
391:Reversibility
389:
387:
384:
382:
379:
377:
374:
372:
369:
367:
364:
362:
359:
357:
354:
352:
349:
347:
344:
343:
342:
341:
338:
335:
334:
329:
326:
324:
321:
319:
316:
314:
311:
309:
306:
304:
301:
299:
296:
294:
291:
290:
289:
288:
285:
282:
281:
276:
273:
271:
268:
266:
265:Closed system
263:
262:
259:
254:
253:
245:
242:
240:
237:
235:
232:
230:
227:
226:
222:
217:
216:
209:
205:
202:
201:
197:
194:
192:
189:
187:
184:
182:
179:
178:
171:
170:
166:
160:
156:
155:
152:
149:
148:
142:
138:
134:
124:
121:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
7734:
7722:
7710:
7702:
7697:
7685:. Retrieved
7657:
7653:
7643:
7631:. Retrieved
7627:
7618:
7606:. Retrieved
7596:
7584:. Retrieved
7579:
7570:
7558:. Retrieved
7554:
7545:
7534:. Retrieved
7530:the original
7525:
7515:
7503:. Retrieved
7489:
7477:. Retrieved
7473:zapatopi.net
7472:
7462:
7449:
7445:
7436:
7428:
7420:
7385:
7381:
7371:
7359:. Retrieved
7321:
7318:Phys. Rev. B
7317:
7307:
7298:
7289:
7270:
7264:
7246:Optifab 2019
7245:
7232:
7224:the original
7214:
7205:
7196:
7179:
7170:
7161:
7146:
7113:
7109:
7103:
7089:
7078:the original
7065:
7029:
7022:
7005:
6985:the original
6980:
6971:
6960:. Retrieved
6953:the original
6940:
6929:. Retrieved
6925:the original
6915:
6904:. Retrieved
6897:the original
6884:
6857:
6828:
6822:
6813:
6807:
6799:the original
6743:
6739:
6729:
6720:
6711:
6684:
6680:
6670:
6651:
6645:
6602:
6592:
6581:. Retrieved
6567:
6557:
6546:. Retrieved
6541:
6532:
6512:
6505:
6416:thermometers
6366:
6354:
6334:
6322:
6307:
6296:
6288:
6284:
6244:
6238:
6235:
6230:
6226:
6222:
6218:
6215:
6206:
6198:
6191:
6176:
6164:
6159:
6149:
6130:
5808:
5804:gas constant
5699:molar volume
5532:
5502:
5488:
5428:
5420:
5367:
5322:
5250:
5170:
5165:
5163:
4918:
4873:
4809:
4545:
4437:
4433:
4307:
4239:
4186:
4063:
3773:
3682:
3480:
3374:
3321:
3194:
3177:
3165:
3161:
3148:anisotropic
3142:Metal alloy
3057:33.0 ~ 39.0
3054:11.0 ~ 13.0
3051:Metal alloy
3039:30.3 ~ 51.9
3036:10.1 ~ 17.3
3033:Metal alloy
2907:
2902:
2897:
2872:alpha-Quartz
2854:Fused quartz
2359:Metal alloy
2355:Carbon steel
2341:Metal alloy
2301:
2300:coefficient
2289:
2270:
2263:
2260:
2254:
2250:
2248:
2117:
2111:
2104:
2096:
2092:
2090:
2087:
2050:
2046:
2044:
1960:
1952:
1946:
1944:
1941:Coefficients
1916:
1900:
1880:
1877:
1865:
1858:
1838:
1828:
1822:
1810:
1803:
1799:
1771:
1770:
1566:Carathéodory
1497:Heat engines
1469:
1458:
1447:
1429:Motive power
1414:
1074:Free entropy
1045:
858:
545:
544: /
534:
533: /
525:introduction
518:
517: /
456:
419:Heat engines
206: /
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
7687:21 February
7633:21 February
7608:21 February
7586:21 February
7560:21 February
7505:21 February
7479:21 February
7361:21 February
7271:Geodynamics
7220:"Schott AG"
7151:Nave, Rod.
6746:(1): 1429.
6721:ocw.mit.edu
6564:"Chapter 6"
6346:CorningWare
6318:spherometer
6180:thermometry
6137:John Dalton
6125:Lord Kelvin
5439:martensitic
5431:anisotropic
4054:eigenstrain
3485:, given by
3129:≈0.007–0.1
2894:Biological
2784:Biological
2780:Douglas-fir
2774:tangential
2765:Biological
2761:Douglas-fir
2746:Biological
2742:Douglas-fir
2728:Biological
2384:Anisotropic
1896:supercooled
1792:temperature
1388:Synergetics
1069:Free energy
515:Temperature
376:Quasistatic
371:Isenthalpic
328:Instruments
318:Equilibrium
270:Open system
204:Equilibrium
186:Statistical
141:road bridge
7839:Categories
7536:2008-02-06
7388:: 108580.
7071:"Sapphire"
6962:2010-08-24
6931:2011-03-15
6906:2016-02-23
6583:2010-07-11
6548:2024-07-26
6498:References
6350:spark plug
6173:In liquids
6110:See also:
5840:, so that
5443:composites
4921:orthogonal
2879:12–16/6–9
2521:molybdenum
2398:Aggregate
2377:Composite
2298:Volumetric
1927:convection
1906:desorption
1902:Absorption
1835:Prediction
1700:Nucleation
1544:Scientists
1348:Philosophy
1061:Potentials
424:Heat pumps
381:Polytropic
366:Isentropic
356:Isothermal
80:newspapers
7412:214089757
7404:0264-1275
7356:115145222
7138:120132261
7116:(1): 17.
6637:238477713
6184:sea level
5998:∂
5983:∂
5936:∂
5928:∂
5907:≡
5898:α
5535:ideal gas
5512:α
5454:α
5403:Δ
5348:α
5332:α
5305:Δ
5282:Δ
5259:Δ
5231:Δ
5222:α
5203:Δ
5182:Δ
5138:Δ
5114:Δ
5085:≈
5072:Δ
5056:Δ
5041:Δ
4995:Δ
4974:Δ
4899:α
4883:α
4781:α
4757:−
4725:α
4696:∫
4687:
4669:Δ
4623:α
4594:∫
4574:Δ
4558:
4528:Δ
4497:Δ
4474:Δ
4465:α
4449:Δ
4317:α
4285:≪
4271:Δ
4248:Δ
4223:Δ
4214:α
4198:Δ
4074:α
4014:α
3944:−
3908:Δ
3885:Δ
3876:α
3843:ε
3815:Δ
3812:∝
3783:ε
3603:−
3541:ε
3494:ε
3420:≪
3406:Δ
3383:Δ
3358:Δ
3349:α
3333:Δ
3205:α
3158:In solids
3106:Nonmetal
2976:Nonmetal
2958:Nonmetal
2940:Nonmetal
2876:Nonmetal
2858:Nonmetal
2590:Nonmetal
2533:Glycerine
2434:Nonmetal
2319:Aluminium
2280:Material
2230:−
2214:−
2206:⋅
2200:−
2180:≈
2177:α
2133:≈
2130:α
2015:∂
2007:∂
1976:α
1969:α
1956:isotropic
1845:pressures
1681:Waterston
1631:von Mayer
1586:de Donder
1576:Clapeyron
1556:Boltzmann
1551:Bernoulli
1512:Education
1483:Timelines
1267:−
1212:−
1000:Equations
967:∂
920:∂
871:α
835:∂
788:∂
742:−
736:β
700:∂
653:∂
361:Adiabatic
351:Isochoric
337:Processes
298:Ideal gas
181:Classical
7806:Archived
7789:Archived
7742:Archived
7682:20154969
7057:96564753
6778:29127330
6448:Autovent
6430:See also
6386:sun kink
6348:and the
6337:ceramics
6248:absolute
5499:In gases
5435:crystals
3084:Tungsten
3066:Titanium
2936:Sapphire
2918:Rocksalt
2903:disputed
2898:disputed
2840:Polymer
2822:Polymer
2799:Platinum
2578:105–129
2517:tungsten
2466:Gasoline
2394:Concrete
2310:(x10 K)
2295:(x10 K)
1733:Category
1671:Thompson
1581:Clausius
1561:Bridgman
1415:Vis viva
1397:Theories
1331:Gas laws
1123:Enthalpy
531:Pressure
346:Isobaric
303:Real gas
191:Chemical
174:Branches
7662:Bibcode
7336:Bibcode
7118:Bibcode
6863:Bibcode
6769:5681671
6748:Bibcode
6689:Bibcode
6681:Entropy
6607:Bibcode
6414:Liquid
6342:crazing
6154:at the
5742:, with
5697:is the
5533:For an
3121:Zerodur
3020:0±0.45
3017:0±0.15
2972:Silicon
2755:radial
2692:Liquid
2688:Mercury
2568:Granite
2537:Liquid
2470:Liquid
2452:Liquid
2448:Ethanol
2430:Diamond
2164:halides
1891:glasses
1874:Factors
1868:kelvins
1788:density
1656:Smeaton
1651:Rankine
1641:Onsager
1626:Maxwell
1621:Massieu
1326:Entropy
1321:General
1312:History
1302:Culture
1299:History
523: (
520:Entropy
457:italics
258:Systems
94:scholar
7680:
7604:. NOAA
7410:
7402:
7354:
7277:
7248:: 18.
7136:
7055:
7045:
6873:
6835:
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6766:
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6625:
6574:
6520:
6266:, and
6139:, and
5650:where
5475:tensor
4812:, and
4772:where
4489:where
4373:where
4304:Volume
4130:where
4005:, and
4003:kelvin
3900:where
3832:strain
3683:where
3483:strain
3261:where
3183:Length
3088:Metal
3070:Metal
3009:Sitall
2994:Metal
2990:Silver
2890:Rubber
2803:Metal
2710:Metal
2706:Nickel
2660:Metal
2638:Kapton
2624:Metal
2575:35–43
2554:Metal
2506:Glass
2488:Glass
2416:Metal
2412:Copper
2323:Metal
2313:Notes
2286:Linear
2168:oxides
1839:If an
1825:strain
1784:volume
1776:length
1646:Planck
1636:Nernst
1611:Kelvin
1571:Carnot
861:
726:
594:
536:Volume
451:Note:
410:Cycles
239:Second
229:Zeroth
96:
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82:
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7582:. BBC
7499:(PDF)
7452:: 137
7450:XLIII
7408:S2CID
7352:S2CID
7326:arXiv
7188:(PDF)
7134:S2CID
7081:(PDF)
7074:(PDF)
7053:S2CID
7010:(PDF)
6956:(PDF)
6949:(PDF)
6900:(PDF)
6893:(PDF)
6633:S2CID
6299:Invar
4044:, or
4001:, or
3173:solid
3102:Water
3094:13.5
3047:Steel
2979:2.56
2964:8.31
2961:2.77
2922:Rock
2864:1.77
2861:0.59
2819:(PP)
2695:60.4
2674:Macor
2630:35.4
2627:11.8
2603:Invar
2572:Rock
2525:kovar
2494:25.5
2484:Glass
2380:–0.8
2365:32.4
2362:10.8
2337:Brass
2326:23.1
2185:0.038
2138:0.020
1782:, or
1694:Other
1661:Stahl
1616:Lewis
1606:Joule
1596:Gibbs
1591:Duhem
284:State
244:Third
234:First
139:in a
101:JSTOR
87:books
7689:2022
7678:PMID
7635:2022
7610:2022
7588:2022
7562:2022
7507:2022
7481:2022
7400:ISSN
7363:2022
7275:ISBN
7043:ISBN
6871:ISBN
6833:ISBN
6774:PMID
6656:ISBN
6623:ISBN
6572:ISBN
6518:ISBN
6114:and
5274:and
4839:and
4060:Area
3145:−30
3112:207
3091:4.5
3073:8.6
2943:5.3
2928:120
2910:Talk
2908:see
2846:156
2828:450
2825:150
2787:3.5
2698:181
2680:9.3
2656:Lead
2620:Iron
2612:3.6
2609:1.2
2550:Gold
2542:485
2523:and
2512:9.9
2509:3.3
2491:8.5
2476:950
2473:317
2458:750
2455:250
2373:CFRP
2166:and
2162:for
1945:The
1933:and
1931:wind
1883:bond
1780:area
1666:Tait
496:Heat
491:Work
221:Laws
73:news
7670:doi
7390:doi
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7344:doi
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7035:doi
6764:PMC
6756:doi
6697:doi
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6316:or
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3000:54
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