Thermal expansion - Knowledge (XXG)

6360: 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. 2073: 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: 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. 6121: 36: 6100: 133: 3188: 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.

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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

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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

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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,

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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.

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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

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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.

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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

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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

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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

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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

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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.

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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.

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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.

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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,

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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.

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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: 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: 2067: 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.

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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.

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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.

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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

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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.

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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.

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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: 5416: 5318: 5295: 5272: 4541: 4261: 3396: 1758: 884: 752: 6920: 4958: 5174: 1118: 5695: 5393: 4864: 4837: 4182: 1459: 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: 1347: 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).

6474: 3837: 581: 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)" 6151: 1437: 6794: 6359: 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

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For a solid, one can ignore the effects of pressure on the material, and the volumetric (or cubical) thermal expansion coefficient can be written:

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is the linear coefficient of thermal expansion in "per degree Fahrenheit", "per degree Rankine", "per degree Celsius", or "per kelvin", denoted by

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Precision engineering nearly always requires the engineer to pay attention to the thermal expansion of the product. For example, when using a

2072: 7278: 7046: 6874: 6836: 6659: 6626: 6575: 6521: 1040: 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

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does change appreciably with temperature, or the increase in volume is significant, then the above equation will have to be integrated:

390: 7469:"On an Absolute Thermometric Scale founded on Carnot's Theory of the Motive Power of Heat, and calculated from Regnault's Observations" 1522: 1496: 1017: 471: 53: 7819: 7805: 7201: 5503:

Since gases fill the entirety of the container which they occupy, the volumetric thermal expansion coefficient at constant pressure,

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are small), but it does not hold if trying to go back and forth between volumetric and linear coefficients using larger values of

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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} }}}} 1046: 445: 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: 2372: 1744: 5326: 4877: 72: 1675: 207: 57: 6896: 1570: 6924: 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

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This estimation works well as long as the linear-expansion coefficient does not change much over the change in temperature

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attached to the underlying porcelain (or other body type) their thermal expansion must be tuned to 'fit' the body so that

1650: 1423: 400: 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:

79: 7854: 6408: 6263: 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

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This equation works well as long as the area expansion coefficient does not change much over the change in temperature

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Drinking glass with fracture due to uneven thermal expansion after pouring of hot liquid into the otherwise cool glass

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small changes in temperature such as 1 degree can cause a sample to change its position relative to the focus point.

7013: 6599:"ALLVAR alloy athermalization: A novel and cost-effective alternative for small to moderate sized space telescopes" 6436: 3831: 3482: 1860: 1804: 1565: 1527: 1491: 203: 86: 6102:

which is a strong function of temperature; doubling the temperature will halve the thermal expansion coefficient.

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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.

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is available, it can be used to predict the values of the thermal expansion at all the required temperatures and

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Becker, P.; Seyfried, P.; Siegert, H. (1982). "The lattice parameter of highly pure silicon single crystals".

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or shivering do not occur. Good example of products whose thermal expansion is the key to their success are

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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: 2080: 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

1732: 1560: 1357: 1060: 999: 535: 524: 190: 7529: 4652:{\displaystyle \ln \left({\frac {V+\Delta V}{V}}\right)=\int _{T_{i}}^{T_{f}}\alpha _{V}(T)\,\mathrm {d} T} 7849: 7237:

Monroe, James A.; McAllister, Jeremy S.; Zgarba, Jay; Squires, David; Deegan, John P. (18 November 2019).

6798: 6456: 3733: 2909: 1665: 1585: 1382: 466: 220: 195: 2049:" to the derivative indicates that the pressure is held constant during the expansion, and the subscript 6984: 6250:

expansion of the liquid is the apparent expansion corrected for the expansion of the containing vessel.

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

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temperature. This enables calculation of the relative change in length per degree temperature change.

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Ahmed, Ashraf; Tavakol, Behrouz; Das, Rony; Joven, Ronald; Roozbehjavan, Pooneh; Minaie, Bob (2012).

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Unlike gases or liquids, solid materials tend to keep their shape when undergoing thermal expansion.

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

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A number of materials contract on heating within certain temperature ranges; this is usually called

7824: 7313: 6313: 6233:. The absolute expansion can be measured by a variety of techniques, including ultrasonic methods. 5491: 4049: 1625: 1620: 1387: 409: 375: 370: 283: 7152: 2871: 7407: 7351: 7325: 7133: 7052: 6632: 6305:

10 K. These alloys are useful in aerospace applications where wide temperature swings may occur.

5506: 5478: 5448: 5442: 4008: 3990: 2501: 1824: 1812: 1714: 1377: 1325: 1238: 1183: 1128: 557: 541: 428: 380: 365: 355: 164: 158: 7781: 7760: 4492: 3168: 1372: 962: 915: 830: 783: 695: 648: 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: 93: 7677: 7425: 7399: 7274: 7077: 7042: 6870: 6832: 6773: 6655: 6622: 6571: 6563: 6517: 6511: 6395:

uses an arrangement of different metals to maintain a more temperature stable pendulum length.

6392: 5398: 5300: 5277: 5254: 4523: 4243: 3378: 2687: 1840: 1709: 1670: 1660: 1232: 1030: 866: 731: 360: 350: 292: 7829: 4930: 7669: 7389: 7343: 7249: 7125: 7034: 6763: 6755: 6696: 6614: 6489: 6465: – Difference in properties of one mole of substance in a mixture vs. an ideal solution 6422: 6259: 6144: 6111: 1795: 1630: 1615: 1555: 1550: 1367: 1362: 1088: 1012: 480: 345: 7703:

Elementary treatise on physics experimental and applied for the use of colleges and schools

7575: 7184: 7094: 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

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Kosinski, J.A.; Gualtieri, J.G.; Ballato, A. (1991). "Thermal expansion of alpha quartz".

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is a small quantity which on squaring gets much smaller and on cubing gets smaller still.

3998: 3994: 3028: 2953: 1580: 1428: 1082: 723: 546: 307: 274: 136: 2240:{\displaystyle \alpha \approx {\frac {0.038}{T_{m}}}-7.0\cdot 10^{-6}\,\mathrm {K} ^{-1}} 1929:

of unevenly heated fluid masses, notably making thermal expansion partly responsible for

17: 7777:

Engineering Toolbox – List of coefficients of Linear Expansion for some common materials

7665: 7339: 7121: 6866: 6751: 6692: 6610: 599: 7495: 6768: 6735: 6278: 6247: 5785: 5765: 5745: 5653: 5323:

Similarly, the area thermal expansion coefficient is two times the linear coefficient:

4376: 4133: 3264: 2619: 1882: 1848: 1816: 1635: 1405: 941: 894: 809: 762: 674: 627: 505: 385: 322: 312: 180: 150: 6327: 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

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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 7838: 7772:

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

7411: 7355: 7137: 6636: 6468: 6341: 6166: 5538: 2816: 2119: 2055: 1934: 1922: 1886: 1704: 1022: 591: 552: 264: 7601: 7056: 5803: 5698: 3989:

is the difference of the temperature between the two recorded strains, measured in

2853: 2354: 1655: 1640: 1590: 1073: 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}}} 7726: 7394: 7377: 6856: 6492: – Relationship between volume and temperature of a gas at constant pressure 3774:

For most solids, thermal expansion is proportional to the change in temperature:

6677:"Configurons: thermodynamic parameters and symmetry changes at glass transition" 6415: 6345: 6317: 6179: 6136: 6120: 5438: 5430: 4300:. If either of these conditions does not hold, the equation must be integrated. 4053: 2779: 2760: 2741: 2383: 1895: 1791: 1610: 418: 140: 35: 7347: 7166: 6759: 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.

6538:"Details for IEV number 561-06-08: "coefficient of linear thermal expansion "" 6349: 4920: 4438:

If the expansion coefficient is known, the change in volume can be calculated

2520: 1926: 1905: 1699: 1645: 7455: 7403: 7314:"Equation of state of cubic boron nitride at high pressures and temperatures" 7038: 2076:

Volumetric thermal expansion coefficient for a semicrystalline polypropylene.

6183: 5534: 2532: 2318: 297: 7681: 6777: 6601:. In Hallibert, Pascal; Hull, Tony B.; Kim, Daewook; Keller, Fanny (eds.). 6377:

Metal hot water heating pipes should not be used in long straight lengths.

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is from 10 K for hard solids to 10 K for organic liquids. The coefficient

132: 27:

Tendency of matter to change volume in response to a change in temperature

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MatWeb: Free database of engineering properties for over 79,000 materials

7673: 7330: 6447: 6385: 3083: 3065: 2935: 2917: 2798: 2516: 2465: 2393: 1955: 1901: 1844: 1413: 1330: 1122: 530: 302: 6814:

Study of Thermal Expansion in Carbon Fiber Reinforced Polymer Composites

6273: 7649: 7254: 7238: 7129: 6618: 6336: 5434: 3120: 2971: 2567: 2447: 2429: 1787: 519: 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).

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is the volumetric expansion coefficient as a function of temperature

4002: 3893:{\displaystyle \varepsilon _{\mathrm {thermal} }=\alpha _{L}\Delta T} 3008: 2989: 2889: 2705: 2637: 2411: 2163: 1867: 1783: 1775: 7028: 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.

7803:

USA NIST Website – Temperature and Dimensional Measurement workshop

6736:"Giant thermal expansion and α-precipitation pathways in Ti-alloys" 6605:. Vol. 11820. San Diego, United States: SPIE. pp. 52–59. 6425:

and bends due to the differing thermal expansion of the two metals.

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is the rate of change of that area per unit change in temperature.

3151:

exhibits negative thermal expansion in broad range of temperatures

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Proceedings of the 45th Annual Symposium on Frequency Control 1991

6566:. In O'Mara, William C.; Herring, Robert B.; Hunt, Lee P. (eds.). 6358: 6326: 6298: 3186: 3172: 3101: 3046: 2673: 2602: 2524: 2483: 2336: 2167: 2091:

For isotropic materials the coefficients linear thermal expansion

2079: 2071: 1890: 131: 3823:{\displaystyle \varepsilon _{\mathrm {thermal} }\propto \Delta T} 2655: 2549: 1930: 1827:) divided by the change in temperature is called the material's 1779: 495: 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. 4919:

This ratio arises because volume is composed of three mutually

7239:"Negative thermal expansion ALLVAR alloys for athermalization" 5537:, a formula can be readily obtained by differentiation of the 5445:, will generally have different linear expansion coefficients 2835: 2723: 2585: 29: 6597:

Monroe, James A.; East, Matthew; Hull, Tony B. (2021-08-24).

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

2084:

Linear thermal expansion coefficient for some steel grades.

1802:), with rare exceptions within limited temperature ranges ( 7727:

Cost or savings of thermal expansion in above ground tanks

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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. 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} 1921:), thus changing its density, which has an effect on any 7797: 6165:

In a footnote Thomson calculated that "infinite cold" (

4431:

is the rate of change of that volume with temperature.

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pushed over the shaft, thus achieving a 'shrink fit'.

1881:

Thermal expansion generally decreases with increasing

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: 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 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 6404:absorb the thermal expansion in a piping system. 6150:In October 1848, William Thomson, a 24 year old 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). 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: 8: 6858:Principles of Physics: A Calculus-Based Text 6568:Handbook of semiconductor silicon technology 6483: – thermodynamic property of a material 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. 7576:"Kinetic particle theory and state changes" 7095:"Basic Parameters of Silicon Carbide (SiC)" 6998: 6996: 6994: 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 6789: 6787: 6654:. Sheffield: Society of Glass Technology. 2276: 1759: 1745: 1308: 460: 279: 157: 146: 7393: 7329: 7253: 6767: 6700: 6542:International Electrotechnical Vocabulary 6421:A bi-metal mechanical thermometer uses a 6371:Metal-framed windows need rubber spacers. 6082: 6070: 6057: 6040: 6028: 6019: 6010: 5989: 5979: 5966: 5957: 5948: 5924: 5909: 5900: 5894: 5871: 5859: 5850: 5845: 5816: 5814: 5787: 5767: 5747: 5724: 5712: 5706: 5681: 5675: 5655: 5632: 5618: 5612: 5599: 5590: 5585: 5555: 5546: 5514: 5508: 5456: 5450: 5400: 5379: 5373: 5350: 5334: 5328: 5302: 5279: 5256: 5224: 5199: 5178: 5176: 5134: 5107: 5091: 5078: 5062: 5034: 5018: 5005: 4965: 4944: 4932: 4901: 4885: 4879: 4850: 4844: 4823: 4817: 4783: 4777: 4743: 4742: 4727: 4715: 4710: 4703: 4698: 4665: 4663: 4641: 4640: 4625: 4613: 4608: 4601: 4596: 4564: 4552: 4525: 4502: 4494: 4467: 4445: 4443: 4413: 4408: 4400: 4398: 4378: 4352: 4342: 4339: 4338: 4328: 4319: 4313: 4276: 4268: 4245: 4216: 4194: 4192: 4163: 4155: 4135: 4109: 4099: 4096: 4095: 4085: 4076: 4070: 4016: 4010: 3951: 3950: 3924: 3923: 3905: 3878: 3846: 3845: 3839: 3786: 3785: 3779: 3742: 3741: 3735: 3695: 3694: 3688: 3644: 3643: 3610: 3609: 3583: 3582: 3572: 3544: 3543: 3537: 3497: 3496: 3490: 3455: 3450: 3442: 3440: 3411: 3403: 3380: 3351: 3329: 3327: 3301: 3296: 3288: 3286: 3266: 3240: 3230: 3227: 3226: 3216: 3207: 3201: 2228: 2223: 2221: 2212: 2191: 2182: 2174: 2144: 2135: 2127: 2027: 2003: 1997: 1987: 1978: 1966: 1774:is the tendency of matter to increase in 1240: 1185: 1130: 1090: 964: 943: 917: 896: 868: 832: 811: 785: 764: 733: 697: 676: 650: 629: 601: 120:Learn how and when to remove this message 7830:Thermal expansion via density calculator 7153:"Thermal Expansion Coefficients at 20 C" 6272: 6131:From 1787 to 1802, it was determined by 6119: 5359:{\displaystyle \alpha _{A}=2\alpha _{L}} 4910:{\displaystyle \alpha _{V}=3\alpha _{L}} 1885:energy, which also has an effect on the 1855:Contraction effects (negative expansion) 1831:and generally varies with temperature. 7739:Lateral, Angular and Combined Movements 7202:"Properties of Common Liquid Materials" 6502: 3281:is a particular length measurement and 1829:coefficient of linear thermal expansion 1505: 1482: 1436: 1396: 1346: 1311: 504: 479: 408: 335: 282: 149: 7624:"Volumetric (Cubic) Thermal Expansion" 6921:"DuPont™ Kapton® 200EN Polyimide Film" 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). 6477: – Thermodynamic properties list 6439: – Process in physical chemistry 6127:, the namesake of the unit of measure 7: 6855:Raymond Serway; John Jewett (2005), 6481:Material properties (thermodynamics) 3834:or temperature can be estimated by: 3764:{\displaystyle L_{\mathrm {final} }} 1823:The relative expansion (also called 58:adding citations to reliable sources 7522:"On an Absolute Thermometric Scale" 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 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: 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). 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 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} 1523:Maxwell's thermodynamic surface 45:needs additional citations for 7456:English translation (extract). 7167:"Sitall CO-115M (Astrositall)" 6890:"Technical Glasses Data Sheet" 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: 1: 7825:Thermal Expansion Calculators 7076:. kyocera.com. Archived from 6951:. corning.com. Archived from 3134:from 0 °C to 50 °C 2274:is usually used for solids.) 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 2515:matched sealing partner for 1036:Onsager reciprocal relations 7273:(2nd ed.). Cambridge. 7155:. Georgia State University. 6384:in the structures to avoid 5523:{\displaystyle \alpha _{V}} 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} 7876: 7348:10.1103/PhysRevB.75.214104 7014:Forest Products Laboratory 6760:10.1038/s41467-017-01578-1 6562:Bullis, W. Murray (1990). 6437:Negative thermal expansion 6257: 6109: 4513:{\displaystyle \Delta V/V} 3179:coefficient of expansion. 2065: 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} 3171:. In the special case of 1815:of the average molecular 1449:An Inquiry Concerning the 18:Coefficient of dilatation 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}} 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: 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:. 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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: 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: 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: 280: 161: 147: 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: 7647: 7646: 7642: 7632: 7630: 7622: 7621: 7617: 7607: 7605: 7600: 7599: 7595: 7585: 7583: 7574: 7573: 7569: 7559: 7557: 7549: 7548: 7544: 7535: 7533: 7519: 7518: 7514: 7504: 7502: 7498: 7493: 7492: 7488: 7478: 7476: 7466: 7465: 7461: 7440: 7439: 7435: 7423: 7419: 7375: 7374: 7370: 7360: 7358: 7311: 7310: 7306: 7293: 7292: 7288: 7281: 7268: 7267: 7263: 7241: 7236: 7235: 7231: 7218: 7217: 7213: 7200: 7199: 7195: 7187: 7183: 7182: 7178: 7165: 7164: 7160: 7150: 7149: 7145: 7107: 7106: 7102: 7093: 7092: 7088: 7080: 7073: 7069: 7068: 7064: 7049: 7026: 7025: 7021: 7009: 7002: 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: 6854: 6853: 6846: 6839: 6827:Young; Geller. 6826: 6825: 6821: 6811: 6810: 6806: 6793: 6792: 6785: 6733: 6732: 6728: 6715: 6714: 6710: 6674: 6673: 6669: 6662: 6649: 6648: 6644: 6629: 6596: 6595: 6591: 6582: 6580: 6578: 6561: 6560: 6556: 6547: 6545: 6536: 6535: 6531: 6524: 6509: 6508: 6504: 6500: 6495: 6484: 6451: 6432: 6302: 6271: 6256: 6214: 6202: 6195: 6175: 6135:(unpublished), 6133:Jacques Charles 6118: 6108: 6066: 6062: 6036: 6024: 5996: 5985: 5981: 5975: 5974: 5962: 5934: 5926: 5920: 5919: 5896: 5891: 5890: 5855: 5842: 5841: 5811: 5810: 5784: 5783: 5764: 5763: 5744: 5743: 5708: 5703: 5702: 5677: 5672: 5671: 5652: 5651: 5608: 5595: 5582: 5581: 5551: 5543: 5542: 5510: 5505: 5504: 5501: 5487: 5473:expansion as a 5452: 5447: 5446: 5429:Materials with 5427: 5397: 5396: 5375: 5370: 5369: 5346: 5330: 5325: 5324: 5299: 5298: 5276: 5275: 5253: 5252: 5220: 5201: 5180: 5173: 5172: 5136: 5103: 5087: 5074: 5058: 5030: 5014: 4987: 4983: 4982: 4962: 4961: 4940: 4929: 4928: 4924: 4897: 4881: 4876: 4875: 4872: 4846: 4841: 4840: 4819: 4814: 4813: 4779: 4774: 4773: 4723: 4711: 4699: 4693: 4689: 4667: 4660: 4659: 4621: 4609: 4597: 4566: 4560: 4549: 4548: 4522: 4521: 4491: 4490: 4463: 4447: 4440: 4439: 4395: 4394: 4375: 4374: 4351: 4341: 4315: 4310: 4309: 4306: 4265: 4264: 4242: 4241: 4212: 4196: 4189: 4188: 4152: 4151: 4132: 4131: 4108: 4098: 4072: 4067: 4066: 4062: 4045: 4041: 4037: 4033: 4012: 4007: 4006: 3999:degrees Celsius 3995:degrees Rankine 3946: 3919: 3902: 3901: 3874: 3841: 3836: 3835: 3781: 3776: 3775: 3737: 3732: 3731: 3690: 3685: 3684: 3639: 3605: 3578: 3574: 3539: 3534: 3533: 3492: 3487: 3486: 3479: 3437: 3436: 3400: 3399: 3377: 3376: 3347: 3331: 3324: 3323: 3283: 3282: 3263: 3262: 3239: 3229: 3203: 3198: 3197: 3185: 3169:Young's modulus 3160: 3029:Stainless steel 2954:Silicon Carbide 2309: 2307: 2305: 2299: 2294: 2292: 2287: 2267: 2262: 2222: 2208: 2187: 2171: 2170: 2140: 2124: 2123: 2108: 2103: 2102:are related by 2100: 2070: 2064: 2045:The subscript " 2013: 2005: 1999: 1998: 1974: 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: 1237: 1236: 1235: 1182: 1181: 1180: 1127: 1126: 1125: 1087: 1086: 1085: 1083:Internal energy 1078: 1063: 1053: 1052: 1027: 1002: 992: 991: 990: 961: 960: 940: 939: 914: 913: 893: 892: 865: 864: 829: 828: 808: 807: 782: 781: 761: 760: 730: 729: 724:Compressibility 694: 693: 673: 672: 647: 646: 626: 625: 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: 7871: 7863: 7862: 7857: 7852: 7847: 7845:Thermodynamics 7837: 7836: 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: 24: 14: 13: 10: 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: 7754: 7748:U.S. Bellows. 7747: 7743: 7740: 7735: 7732: 7728: 7723: 7720: 7716: 7711: 7708: 7704: 7698: 7695: 7683: 7679: 7675: 7671: 7667: 7663: 7659: 7655: 7651: 7644: 7641: 7629: 7625: 7619: 7616: 7603: 7597: 7594: 7581: 7577: 7571: 7568: 7556: 7552: 7546: 7543: 7531: 7527: 7523: 7516: 7513: 7497: 7490: 7487: 7474: 7470: 7463: 7460: 7457: 7451: 7447: 7443: 7437: 7434: 7430: 7427: 7421: 7418: 7413: 7409: 7405: 7401: 7396: 7391: 7387: 7383: 7379: 7372: 7369: 7357: 7353: 7349: 7345: 7341: 7337: 7332: 7327: 7323: 7319: 7315: 7308: 7305: 7300: 7296: 7290: 7287: 7282: 7276: 7272: 7265: 7262: 7256: 7251: 7247: 7240: 7233: 7230: 7225: 7221: 7215: 7212: 7207: 7203: 7197: 7194: 7186: 7180: 7177: 7172: 7168: 7162: 7159: 7154: 7147: 7144: 7139: 7135: 7131: 7127: 7123: 7119: 7115: 7111: 7104: 7101: 7096: 7090: 7087: 7079: 7072: 7066: 7063: 7058: 7054: 7050: 7044: 7040: 7036: 7032: 7031: 7023: 7020: 7015: 7008: 7007: 6999: 6997: 6995: 6991: 6986: 6982: 6978: 6972: 6969: 6958:on 2011-06-12 6954: 6947: 6941: 6938: 6927:on 2018-11-26 6926: 6922: 6916: 6913: 6902:on 2015-12-11 6898: 6891: 6885: 6882: 6878: 6872: 6868: 6864: 6860: 6859: 6851: 6849: 6845: 6840: 6834: 6830: 6823: 6820: 6815: 6808: 6805: 6800: 6796: 6790: 6788: 6784: 6779: 6775: 6770: 6765: 6761: 6757: 6753: 6749: 6745: 6741: 6737: 6730: 6727: 6722: 6718: 6712: 6709: 6703: 6698: 6694: 6690: 6686: 6682: 6678: 6671: 6668: 6663: 6657: 6653: 6646: 6643: 6638: 6634: 6630: 6624: 6620: 6616: 6612: 6608: 6604: 6600: 6593: 6590: 6579: 6573: 6569: 6565: 6558: 6555: 6544:(in Japanese) 6543: 6539: 6533: 6530: 6525: 6519: 6515: 6514: 6506: 6503: 6497: 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: 6429: 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: 6253: 6251: 6249: 6243: 6240: 6234: 6232: 6228: 6224: 6220: 6211: 6209: 6205: 6203: 6196: 6190:. Sometimes, 6189: 6185: 6181: 6172: 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 6105: 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: 5498: 5496: 5493: 5484: 5482: 5480: 5476: 5457: 5453: 5444: 5440: 5436: 5432: 5424: 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: 4869: 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: 4303: 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: 4059: 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: 3476: 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: 3182: 3180: 3176: 3174: 3170: 3164: 3157: 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: 2061: 2059: 2057: 2056:ideal gas law 2052: 2048: 2043: 2028: 2023: 2017: 2009: 2000: 1992: 1989: 1984: 1975: 1971: 1968: 1959: 1957: 1951: 1948: 1940: 1938: 1936: 1932: 1928: 1924: 1920: 1912: 1910: 1907: 1903: 1899: 1897: 1892: 1888: 1887:melting point 1884: 1879: 1873: 1871: 1869: 1864: 1862: 1854: 1852: 1850: 1846: 1842: 1834: 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: 1504: 1498: 1495: 1493: 1490: 1489: 1487: 1486: 1481: 1475: 1474: 1467: 1464: 1463: 1456: 1453: 1452: 1445: 1444: 1443: 1442: 1439: 1435: 1430: 1427: 1425: 1422: 1420: 1416: 1412: 1411: 1407: 1404: 1403: 1401: 1400: 1395: 1389: 1386: 1384: 1381: 1379: 1376: 1374: 1371: 1369: 1366: 1364: 1361: 1359: 1356: 1355: 1353: 1352: 1349: 1345: 1340: 1337: 1336: 1332: 1329: 1327: 1324: 1322: 1319: 1318: 1316: 1315: 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: 503: 497: 494: 492: 489: 488: 486: 485: 482: 478: 473: 470: 468: 465: 464: 463: 462: 458: 454: 447: 442: 441: 430: 427: 425: 422: 420: 417: 416: 415: 414: 411: 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: 334: 329: 326: 324: 321: 319: 316: 314: 311: 309: 306: 304: 301: 299: 296: 294: 291: 290: 289: 288: 285: 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: 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: 6776: 6766: 6658: 6635: 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: 89: 82: 75: 67: 7582:. 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