3342:. Internal consistency requires that all values of the thermodynamic functions are correctly calculated by application of the appropriate thermodynamic equations. For example, values of the Gibbs energy obtained from high-temperature equilibrium emf methods must be identical to those calculated from calorimetric measurements of the enthalpy and entropy values. The database provider must use recognized data analysis procedures to resolve differences between data obtained by different types of experiments.
31:
1601:
3315:
to reproduce the tabular values. More recently, computerized databases are used which consist of the equation parameters and subroutines to calculate specific values at any temperature and prepare tables for printing. Computerized databases often include subroutines for calculating reaction properties and displaying the data as charts.
4099:
3345:
All thermodynamic data is a non-linear function of temperature (and pressure), but there is no universal equation format for expressing the various functions. Here we describe a commonly used polynomial equation to express the temperature dependence of the heat content. A common six-term equation for
3314:
consists of sets of critically evaluated values for the major thermodynamic functions. Originally, data was presented as printed tables at 1 atm and at certain temperatures, usually 100° intervals and at phase transition temperatures. Some compilations included polynomial equations that could be used
1850:
function of temperature. The heat content of an ideal gas is independent of pressure (or volume), but the heat content of real gases varies with pressure, hence the need to define the state for the gas (real or ideal) and the pressure. Note that for some thermodynamic databases such as for steam, the
1731:
standard state is one whose properties are obtained by extrapolation from a physical state (for example, a solid superheated above the normal melting point, or an ideal gas at a condition where the real gas is non-ideal). Metastable liquids and solids are important because some substances can persist
4642:
The table format is a common way to display thermodynamic data. The FREED table gives additional information in the top rows, such as the mass and amount composition and transition temperatures of the constituent elements. Transition temperatures for the constituent elements have dashes ------- in
1716:
standard state is one that exists for a time sufficient to allow measurements of its properties. The most common physical standard state is one that is stable thermodynamically (i.e., the normal one). It has no tendency to transform into any other physical state. If a substance can exist but is not
1689:
is a set of equation parameters from which the numerical data values can be calculated. Tables and datafiles are usually presented at a standard pressure of 1 bar or 1 atm, but in the case of steam and other industrially important gases, pressure may be included as a variable. Function values depend
3858:
4296:
Depending on the accuracy of the data and the length of the temperature span, the heat content equation may require more or fewer terms. Over a very long temperature span, two equations may be used instead of one. It is unwise to extrapolate the equations to obtain values outside the range of
4305:
The equation parameters and all other information required to calculate values of the important thermodynamic functions are stored in a thermodynamic datafile. The values are organized in a format that makes them readable by a thermodynamic calculation program or for use in a spreadsheet. For
1986:
2385:
at phase transitions between substances in their standard states. Hence, the main functional application of Gibbs energy from a thermodynamic database is its change in value during the formation of a compound from the standard-state elements, or for any standard chemical reaction
1836:
means the reference temperature (usually 298.15 K, but abbreviated in heat content symbols as 298). All of these terms mean the molar heat content for a substance in its normal standard state above a reference temperature of 298.15 K. Data for gases is for the hypothetical
4643:
the first column in a blank row, such as at 922 K, the melting point of Mg. Transition temperatures for the substance have two blank rows with dashes, and a center row with the defined transition and the enthalpy change, such as the melting point of MgCl
1732:
and be used in that state indefinitely. Thermodynamic functions that refer to conditions in the normal standard state are designated with a small superscript °. The relationship between certain physical and thermodynamic properties may be described by an
3899:
4196:
3657:
3033:
2817:
4208:
deviates only slightly from linearity with temperature, so over a short temperature span, the seven-term equation can be replaced by a three-term equation, whose parameter values are obtained by regression of tabular values.
3179:
2042:
takes place. The amount of substance that transforms is a function of the amount of heat added. After the transition is complete, adding more heat increases the temperature. In other words, the enthalpy of a substance changes
3301:
3673:
3499:
2276:
of a system is another thermodynamic quantity that is not easily measured. However, using a combination of theoretical and experimental techniques, entropy can in fact be accurately estimated. At low temperatures, the
4628:
2303:/T are plotted against T for the whole range of temperatures where the substance exists in the same physical state. The data are extrapolated from the lowest experimental temperature to 0 K using the Debye model. The
4292:
1865:
4317:
1662:. Numerical values of these thermodynamic properties are collected as tables or are calculated from thermodynamic datafiles. Data is expressed as temperature-dependent values for one mole of substance at the
2253:
2517:
1845:
unit for enthalpy is J/mol, and is a positive number above the reference temperature. The heat content has been measured and tabulated for virtually all known substances, and is commonly expressed as a
4647:
at 980 K. The datafile equations are at the bottom of the table, and the entire table is in an Excel worksheet. This is particularly useful when the data is intended for making specific calculations.
2406:
1752:), since the internal energy of a substance can take many forms, each of which has its own typical temperature at which it begins to become important in thermodynamic reactions. It is therefore the
2015:
1320:
2000:
2347:
2184:
2654:
3338:
measurements of reversible reactions. A proper database takes all available information about the elements and compounds in the database, and assures that the presented results are
2894:
2353:. The solid line refers to the entropy of strontium in its normal standard state at 1 atm pressure. The dashed line refers to the entropy of strontium vapor in a non-physical state.
1996:
is therefore the slope of a plot of temperature vs. isobaric heat content (or the derivative of a temperature/heat content equation). The SI units for heat capacity are J/(mol·K).
2006:
of four substances in their designated states above 298.15 K and at 1 atm pressure. CaO(c) and Rh(c) are in their normal standard state of crystalline solid at all temperatures. S
4094:{\displaystyle \Delta G_{form}^{\circ }=(\Delta A-\Delta F')T-\Delta A(T\ln T)-\Delta B(T^{2})+\textstyle {\frac {1}{2}}\Delta C(T^{-1})+2\Delta D(T^{\textstyle {\frac {1}{2}}})}
2373:. The entropy change is obtained by summing the absolute entropies of the products minus the sum of the absolute entropies of the reactants. Like enthalpy, the Gibbs energy
2241:
undergoes discontinuities at a phase transition temperatures of the constituent element(s) and the compound. The enthalpy change for any standard reaction is designated Δ
1155:
1100:
1045:
852:
805:
720:
673:
585:
538:
756:
624:
2078:
990:
4105:
489:
2343:°) at the normal phase transition temperature is equal to the heat of transition divided by the transition temperature. The SI units for entropy are J/(mol·K).
2021:
of four substances in their designated states at 1 atm pressure. CaO(c) and Rh(c) are in their normal standard state of crystalline solid at all temperatures. S
828:
781:
696:
649:
561:
514:
3523:
2903:
2687:
2038:
substance, its temperature increases until a phase change temperature is reached. With further addition of heat, the temperature remains constant while the
1712:
and a pressure of 1 bar or 1 atm. However, since any non-normal condition could be chosen as a standard state, it must be defined in the context of use. A
3062:
4877:
Gurvich, L.V., Veitz, I.V., et al. (1989) Thermodynamic
Properties of Individual Substances. Fourth edition, Hemisphere Pub Co. NY, L., Vol.1 in 2 parts.
3853:{\displaystyle S_{T}^{\circ }=A(\ln T)+2B(T)+\textstyle {\frac {1}{2}}C(T^{-2})-D(T^{\textstyle -{\frac {1}{2}}})+1\textstyle {\frac {1}{2}}E(T^{2})+F'}
3205:
3351:
2165:
are usually given for the transition at the normal standard state temperature for the two states, and if so, are designated with a superscript °. Δ
1630:
3183:
The Gibbs energy function has the same units as entropy, but unlike entropy, exhibits no discontinuity at normal phase transition temperatures.
1331:
2549:
Compilers of thermochemical databases may contain some additional thermodynamic functions. For example, the absolute enthalpy of a substance
1219:
4214:
3511:
at 298.15 K, plus the sum of the heat content parameters of the products minus the sum of the heat content parameters of the reactants. The
2540:
is not discontinuous at these phase transition temperatures, but does undergo a change in slope, which is almost imperceptible on the chart.
2314:
is zero, the area under the curve from 0 K to any temperature gives the entropy at that temperature. Even though the Debye model contains
1981:{\displaystyle C_{P}(T)=\left\{\lim _{\Delta T\to 0}{\frac {\Delta H}{\Delta T}}\right\}=\left({\frac {\partial H}{\partial T}}\right)_{p}}
4327:(c,l,g) from FREED. Some values have truncated significant figures for display purposes. The explanation for the values is shown below.
1694:
of the substance, which must be defined for the value to have any meaning. The state of aggregation for thermodynamic purposes is the
1309:
4893:
2416:
1342:
2060:. This applies to the transformations from one solid phase to another, such as the transformation from α-Fe (bcc ferrite) to
912:
2357:
The standard entropy change for the formation of a compound from the elements, or for any standard reaction is designated Δ
2331:
The absolute value of entropy for a substance in its standard state at the reference temperature of 298.15 K is designated
1623:
1210:
879:
446:
324:
262:
2562:
2296:. Experimentally, the heat capacity is measured at temperature intervals to as low a temperature as possible. Values of
1394:
1368:
889:
343:
4932:
A chemical database based on
Quantum Mechanics and QSPR, providing thermodynamic properties for millions of compounds.
4914:
Critically evaluated thermophysical property database useful for chemical process design and equilibrium calculations.
4945:
4871:
4792:
4773:
4754:
4735:
4714:
4682:
4620:
Most computerized databases will create a table of thermodynamic values using the values from the datafile. For MgCl
2339:. Entropy increases with temperature, and is discontinuous at phase transition temperatures. The change in entropy (Δ
1696:
1663:
295:
2169:
for a phase transition is a weak function of temperature. In some texts, the heats of phase transitions are called
1647:
1447:
918:
317:
2229:
are usually given where the elements and compound are in their normal standard states, and as such are designated
1616:
4493:
equations required. Here five; three for species phases and two because one of the elements has a phase change.
1681:
is usually presented as a table or chart of function values for one mole of a substance (or in the case of the
1547:
79:
1442:
2263:(c,l) from the elements, showing discontinuities at transition temperatures of the elements and the compound.
1522:
1295:
272:
2834:
907:
110:
100:
4861:
4841:
Pankratz, L. B. (1994). "Thermodynamic
Properties of Carbides, Nitrides, and Other Selected Substances".
2304:
115:
105:
2047:
as it undergoes a physical change. The enthalpy change resulting from a phase transition is designated Δ
1860:
C is the ratio of heat added to the temperature increase. For an incremental isobaric addition of heat:
1399:
1363:
141:
75:
4638:(c,l,g), from the FREED datafile. Some values have truncated significant figures for display purposes.
2190:
above 298.15 K and at 1 atm pressure, showing discontinuities at the melting and boiling points. The Δ
1708:
standard state is commonly defined as the most stable physical form of the substance at the specified
1437:
2025:(g) is a non-physical state below about 882 K and NiO(g) is a non-physical state at all temperatures.
2010:(g) is a non-physical state below about 882 K and NiO(g) is a non-physical state at all temperatures.
1192:
940:
386:
199:
189:
4627:
4657:
2124:
1604:
1432:
1229:
1110:
1055:
1000:
932:
871:
407:
396:
62:
1744:
It is very difficult to measure the absolute amount of any thermodynamic quantity involving the
834:
787:
702:
655:
567:
520:
4672:
2147:
is infinite at phase transition temperatures because the enthalpy changes isothermally. At the
1537:
1254:
338:
92:
67:
4191:{\displaystyle -\textstyle {\frac {1}{2}}\Delta E(T^{3})+\Delta F+\Delta H_{form298}^{\circ }}
3503:
Regardless of the equation format, the heat of formation of a compound at any temperature is Δ
1457:
738:
603:
2063:
1472:
1049:
362:
208:
57:
960:
4926:
Various on-line tools for obtaining thermodynamic data and making equilibrium calculations.
4905:
3331:
3191:
2405:
2328:, the difference between the two at temperatures near 0 K is so small as to be negligible.
2252:
1667:
1552:
1477:
1467:
267:
129:
4316:
8:
4828:
Pankratz, L. B.; A. D. Mah; S. W. Watson (1987). "Thermodynamic
Properties of Sulfides".
3335:
1497:
1259:
281:
247:
242:
155:
3652:{\displaystyle C_{P}=A+2B(T)-C(T^{-2})+\textstyle {\frac {1}{2}}D(T^{-0.5})+3E(T^{2})\,}
1492:
471:
4890:
A gateway to the data collection of the
National Institute of Standards and Technology.
4687:
4662:
2014:
1586:
1249:
1244:
1197:
813:
766:
681:
634:
546:
499:
429:
413:
300:
252:
237:
227:
36:
30:
3870:. The Gibbs energy of formation of a compound is obtained from the defining equation Δ
3028:{\displaystyle \Delta G_{form}^{\circ }=G(T)compound-\sum \left\{G(T)elements\right\}}
2812:{\displaystyle \Delta H_{form}^{\circ }=H(T)compound-\sum \left\{H(T)elements\right\}}
2307:
states that the entropy of a perfect crystalline substance becomes zero at 0 K. When
2051:. There are four types of enthalpy changes resulting from a phase transition. To wit:
1999:
4867:
4788:
4769:
4750:
4731:
4710:
4667:
3323:
2208:
2148:
1733:
1659:
1581:
1542:
1532:
1104:
902:
730:
232:
222:
164:
3174:{\displaystyle (H_{298}^{\circ }-G_{T}^{\circ })/T=S_{T}^{\circ }-(H_{T}-H_{298})/T}
4692:
2212:
2039:
1502:
1487:
1427:
1422:
1239:
1234:
884:
352:
217:
3296:{\displaystyle \log _{10}\left(K_{eq}\right)=-\Delta G_{form}^{\circ }/(19.1448T)}
2557:) is defined in terms of its formation enthalpy and its heat content as follows:
4725:
4677:
4307:
1745:
1452:
1300:
954:
595:
418:
179:
146:
2346:
4313:
creates the following type of datafile, here for a standard pressure of 1 atm.
3200:
is often listed, which is calculated from the defining thermodynamic equation.
2035:
1719:
1691:
1507:
1277:
377:
257:
194:
184:
52:
22:
4764:
Hummel, Wolfgang; Urs Berner; Enzo Curti; F. J. Pearson; Tres
Thoenen (2002).
1666:
of 101.325 kPa (1 atm), or 100 kPa (1 bar). Both of these definitions for the
4939:
3494:{\displaystyle H_{T}-H_{298}=A(T)+B(T^{2})+C(T^{-1})+D(T^{0.5})+E(T^{3})+F\,}
2293:
1856:
1766:
1756:
in these functions that is of most interest. The isobaric change in enthalpy
1717:
thermodynamically stable (for example, a supercooled liquid), it is called a
1576:
894:
463:
424:
136:
3518:
equation is obtained by taking the derivative of the heat content equation.
2183:
4802:
Pankratz, L. B. (1982). "Thermodynamic
Properties of Elements and Oxides".
3327:
2112:. This applies to the transition of a liquid to a vapor and is designated Δ
2108:
2096:. This applies to the transition of a solid to a liquid and is designated Δ
1527:
1512:
1462:
945:
4923:
4863:
Yaws
Handbook of Thermodynamic Properties for Hydrocarbons & Chemicals
2128:. This applies to the transition of a solid to a vapor and is designated Δ
3319:
2278:
2170:
1778:. Different databases designate this term in different ways; for example
1760:
above the common reference temperature of 298.15 K (25 °C) is called the
1709:
1482:
290:
4763:
2402:). The SI units of Gibbs energy are the same as for enthalpy (J/mol).
1847:
1571:
1517:
4287:{\displaystyle \Delta G_{form}^{\circ }=\alpha T+\beta (T\ln T)+\chi }
2158:
shows a sharp discontinuity while the enthalpy has a change in slope.
2528:
shows discontinuities at the melting points of Pb (600.65 K) and PbCl
1842:
1838:
169:
4899:
4730:(Fourth ed.). Journal of Physical and Chemical Reference Data.
4917:
2292:, and that for perfect crystalline solids it should become zero at
1749:
1651:
1285:
1202:
994:
402:
174:
2829:) is defined by the absolute enthalpy and entropy of a substance:
4855:
Thermodynamic
Properties of Minerals . . . at Higher Temperatures
4360:
equations required. Here, three because of three species phases.
3318:
Thermodynamic data comes from many types of experiments, such as
2273:
2092:
1655:
391:
4815:
Pankratz, L. B. (1984). "Thermodynamic
Properties of Halides".
2211:. For the special case of the formation of a compound from the
4827:
1682:
2512:{\displaystyle Pb(c,l)+2HCl(g)\Rightarrow PbCl_{2}+H_{2}(g)}
4887:
3057:
which is defined in terms of the entropy and heat content.
1739:
367:
4745:
Cox, J. D.; Wagman, Donald D.; Medvedev, Vadim A. (1989).
4311:
4297:
experimental data used to derive the equation parameters.
2202:
4896:
A web interface to generate tabulated thermodynamic data.
2381:
that is of interest. Furthermore, there is no change in
4929:
3037:
Some tables may also contain the Gibbs energy function (
4911:
4595:
Row 20. Values of the seven parameters for the fourth Δ
4573:
Row 18. Values of the seven parameters for the second Δ
2080:-Fe (fcc austenite). The transformation is designated Δ
2029:
4785:
CRC Handbook of Thermophysical and Thermochemical Data
4606:
Row 21. Values of the seven parameters for the fifth Δ
4584:
Row 19. Values of the seven parameters for the third Δ
4562:
Row 17. Values of the seven parameters for the first Δ
4112:
4073:
4017:
3862:
F' is a constant of integration obtained by inserting
3807:
3781:
3734:
3589:
2233:
of formation, as designated by a superscript °. The Δ
4782:
4529:
Row 14. Values of the six parameters for the fourth Δ
4507:
Row 12. Values of the six parameters for the second Δ
4217:
4108:
3902:
3676:
3526:
3354:
3208:
3065:
2906:
2837:
2690:
2565:
2419:
2066:
1868:
1113:
1058:
1003:
963:
837:
816:
790:
769:
741:
705:
684:
658:
637:
606:
570:
549:
523:
502:
474:
4540:
Row 15. Values of the six parameters for the fifth Δ
4518:
Row 13. Values of the six parameters for the third Δ
4496:
Row 11. Values of the six parameters for the first Δ
4373:
Row 4. Values of the five parameters for the second
4334:
Row 1. Molar mass of species, density at 298.15 K, Δ
3661:
The entropy equation is obtained by integrating the
1704:, and defined by specifying certain conditions. The
4853:Robie, Richard A., and Bruce S. Hemingway (1995).
4787:(book & disk ed.). Boca Raton: CRC Press.
4474:
equation; temperature limit for the equation, and Δ
4449:
equation; temperature limit for the equation, and Δ
4435:Row 8. Values of the six parameters for the second
4424:
equation; temperature limit for the equation, and Δ
4383:Row 5. Values of the five parameters for the third
4363:Row 3. Values of the five parameters for the first
4460:Row 9. Values of the six parameters for the third
4410:Row 7. Values of the six parameters for the first
4286:
4190:
4093:
3852:
3651:
3493:
3295:
3173:
3027:
2888:
2811:
2666:) and are identical at all temperatures because Δ
2649:{\displaystyle H(T)=\Delta H_{form,298}^{\circ }+}
2648:
2511:
2281:leads to the result that the atomic heat capacity
2222:and is a weak function of temperature. Values of Δ
2072:
1980:
1149:
1094:
1039:
984:
846:
822:
799:
775:
750:
714:
690:
667:
643:
618:
579:
555:
532:
508:
483:
4744:
4937:
1897:
4350:. and the upper temperature limit for the file.
2377:has no intrinsic value, so it is the change in
4902:Database for more than 3,000 chemical species.
4614:equation; temperature limit for the equation.
4603:equation; temperature limit for the equation.
4592:equation; temperature limit for the equation.
4581:equation; temperature limit for the equation.
4570:equation; temperature limit for the equation.
4548:equation; temperature limit for the equation.
4537:equation; temperature limit for the equation.
4526:equation; temperature limit for the equation.
4515:equation; temperature limit for the equation.
4504:equation; temperature limit for the equation.
4390:equation; temperature limit for the equation.
4380:equation; temperature limit for the equation.
4370:equation; temperature limit for the equation.
1624:
4908:The Design Institute for Physical Properties
2267:
4783:Lide, David R.; Henry V. Kehiaian (1994).
4766:Nagra/Psi Chemical Thermodynamic Data Base
4300:
3305:
1851:reference temperature is 273.15 K (0 °C).
1631:
1617:
29:
3647:
3490:
1841:at the designated standard pressure. The
1650:for substances, the most important being
4857:, U. S. Geological Survey Bulletin 2131.
4840:
4814:
4801:
4626:
4315:
2404:
2345:
2251:
2182:
2013:
1998:
1740:Enthalpy, heat content and heat capacity
2544:
2203:Enthalpy change for a chemical reaction
4938:
4707:Thermochemical Data of Pure Substances
2889:{\displaystyle G(T)=H(T)-T\times S(T)}
4723:
4704:
2821:Similarly, the absolute Gibbs energy
2410:Standard heat and Gibbs energy change
2288:for solids should be proportional to
1673:
4747:CODATA Key Values for Thermodynamics
4310:-based thermodynamic database FREED
2674:is zero, and of course at 298.15 K,
2030:Enthalpy change of phase transitions
2207:An enthalpy change occurs during a
2194:°m of zinc is 7323 J/mol, and the Δ
13:
4727:NIST - JANAF Thermochemical Tables
4218:
4157:
4148:
4123:
4059:
4028:
3992:
3965:
3945:
3936:
3903:
3249:
2907:
2691:
2581:
1959:
1951:
1926:
1918:
1901:
1772:relative high-temperature enthalpy
838:
791:
706:
659:
571:
524:
344:Intensive and extensive properties
14:
4957:
4881:
4683:Standard temperature and pressure
4749:. John Benjamins Publishing Co.
2257:Standard molar heat of formation
1600:
1599:
919:Table of thermodynamic equations
4900:Burcat's Thermodynamic Database
1668:standard condition for pressure
1395:Maxwell's thermodynamic surface
4920:calculator based on IAPWS-IF97
4843:U. S. Bureau of Mines Bulletin
4830:U. S. Bureau of Mines Bulletin
4817:U. S. Bureau of Mines Bulletin
4804:U. S. Bureau of Mines Bulletin
4632:Thermodynamic properties table
4275:
4260:
4142:
4129:
4087:
4065:
4050:
4034:
4011:
3998:
3986:
3971:
3956:
3933:
3834:
3821:
3798:
3773:
3764:
3748:
3728:
3722:
3710:
3698:
3644:
3631:
3619:
3603:
3583:
3567:
3558:
3552:
3481:
3468:
3459:
3446:
3437:
3421:
3412:
3399:
3390:
3384:
3346:the isobaric heat content is:
3330:, composition measurements of
3290:
3281:
3160:
3134:
3102:
3066:
2993:
2987:
2946:
2940:
2883:
2877:
2862:
2856:
2847:
2841:
2777:
2771:
2730:
2724:
2643:
2617:
2575:
2569:
2506:
2500:
2465:
2462:
2456:
2438:
2426:
1907:
1885:
1879:
1129:
1117:
1074:
1062:
1019:
1007:
979:
967:
1:
4698:
4624:(c,l,g) at 1 atm pressure:
4211:
4102:
3896:
3670:
3520:
3348:
3202:
3059:
2900:
2831:
2684:
2559:
2413:
2351:Absolute entropy of strontium
1862:
1762:high temperature heat content
1296:Mechanical equivalent of heat
16:Thermodynamic properties list
4866:, Gulf Publishing Company.
4457:for the second phase change.
2215:, the change is designated Δ
1774:, and called henceforth the
908:Onsager reciprocal relations
7:
4651:
4482:for the third phase change.
4432:for the first phase change.
2305:third law of thermodynamics
1400:Entropy as energy dispersal
1211:"Perpetual motion" machines
1150:{\displaystyle G(T,p)=H-TS}
1095:{\displaystyle A(T,V)=U-TS}
1040:{\displaystyle H(S,p)=U+pV}
10:
4962:
2058:Enthalpy of transformation
1646:contain information about
847:{\displaystyle \partial T}
800:{\displaystyle \partial V}
715:{\displaystyle \partial p}
668:{\displaystyle \partial V}
580:{\displaystyle \partial T}
533:{\displaystyle \partial S}
1321:An Inquiry Concerning the
4946:Thermodynamics databases
4918:Free Steam Tables Online
4768:. Universal Publishers.
2682:) = 0. For a compound:
2268:Entropy and Gibbs energy
2034:When heat is added to a
1648:thermodynamic properties
1334:Heterogeneous Substances
751:{\displaystyle \alpha =}
619:{\displaystyle \beta =-}
4860:Yaws, Carl L. (2007).
4658:Chemical thermodynamics
4301:Thermodynamic datafiles
3894:), and is expressed as
3306:Thermodynamic databases
2073:{\displaystyle \gamma }
1700:, sometimes called the
1644:Thermodynamic databases
4894:NASA Glenn ThermoBuild
4673:Laws of thermodynamics
4639:
4328:
4321:Thermodynamic datafile
4288:
4200:For most substances, Δ
4192:
4095:
3854:
3653:
3495:
3312:thermodynamic database
3297:
3175:
3029:
2890:
2813:
2650:
2541:
2513:
2354:
2264:
2199:
2188:Molar enthalpy of zinc
2091:Enthalpy of fusion or
2074:
2026:
2011:
1982:
1687:thermodynamic datafile
1151:
1096:
1041:
986:
985:{\displaystyle U(S,V)}
848:
824:
801:
777:
752:
716:
692:
669:
645:
620:
581:
557:
534:
510:
485:
464:Specific heat capacity
68:Quantum thermodynamics
4724:Chase, M. W. (1998).
4705:Barin, Ihsan (2004).
4630:
4319:
4289:
4193:
4096:
3866:° at any temperature
3855:
3654:
3496:
3340:internally consistent
3298:
3176:
3030:
2891:
2814:
2651:
2514:
2408:
2349:
2255:
2186:
2178:latent heat of fusion
2075:
2017:
2002:
1983:
1332:On the Equilibrium of
1152:
1097:
1050:Helmholtz free energy
1042:
987:
849:
825:
802:
778:
753:
717:
693:
670:
646:
621:
582:
558:
535:
511:
486:
4215:
4106:
3900:
3674:
3524:
3352:
3332:chemical equilibrium
3206:
3192:equilibrium constant
3063:
2904:
2835:
2688:
2563:
2545:Additional functions
2417:
2198:°v is 115 330 J/mol.
2064:
1866:
1692:state of aggregation
1345:Motive Power of Fire
1111:
1056:
1001:
961:
913:Bridgman's equations
890:Fundamental relation
835:
814:
788:
767:
739:
703:
682:
656:
635:
604:
568:
547:
521:
500:
472:
4559:equations required.
4551:Row 16. Number of Δ
4485:Row 10. Number of Δ
4407:equations required.
4244:
4186:
3929:
3691:
3275:
3130:
3101:
3083:
2933:
2717:
2613:
2019:Molar heat capacity
1685:tables, one kg). A
1323:Source ... Friction
1255:Loschmidt's paradox
447:Material properties
325:Conjugate variables
4688:Dortmund Data Bank
4663:Physical chemistry
4640:
4329:
4284:
4221:
4188:
4187:
4160:
4091:
4090:
4084:
3906:
3850:
3849:
3848:
3795:
3677:
3649:
3648:
3491:
3293:
3252:
3171:
3116:
3087:
3069:
3025:
2910:
2886:
2809:
2694:
2646:
2584:
2542:
2509:
2412:for the reaction:
2355:
2265:
2200:
2070:
2027:
2012:
2004:Molar heat content
1978:
1914:
1679:Thermodynamic data
1674:Thermodynamic data
1587:Order and disorder
1343:Reflections on the
1250:Heat death paradox
1147:
1092:
1037:
982:
844:
820:
797:
773:
748:
712:
688:
665:
641:
616:
577:
553:
530:
506:
484:{\displaystyle c=}
481:
454:Property databases
430:Reduced properties
414:Chemical potential
378:Functions of state
301:Thermal efficiency
37:Carnot heat engine
4924:FACT-Web programs
4668:Materials science
4393:Row 6. Number of
4353:Row 2. Number of
4121:
4082:
4026:
3816:
3793:
3743:
3598:
2209:chemical reaction
2149:Curie temperature
1966:
1933:
1896:
1734:equation of state
1664:standard pressure
1660:Gibbs free energy
1641:
1640:
1582:Self-organization
1407:
1406:
1105:Gibbs free energy
903:Maxwell relations
861:
860:
857:
856:
823:{\displaystyle V}
776:{\displaystyle 1}
731:Thermal expansion
725:
724:
691:{\displaystyle V}
644:{\displaystyle 1}
590:
589:
556:{\displaystyle N}
509:{\displaystyle T}
437:
436:
353:Process functions
339:Property diagrams
318:System properties
308:
307:
273:Endoreversibility
165:Equation of state
4953:
4850:
4837:
4824:
4811:
4798:
4779:
4760:
4741:
4720:
4693:CALPHAD (method)
4293:
4291:
4290:
4285:
4243:
4238:
4197:
4195:
4194:
4189:
4185:
4180:
4141:
4140:
4122:
4114:
4100:
4098:
4097:
4092:
4086:
4085:
4083:
4075:
4049:
4048:
4027:
4019:
4010:
4009:
3955:
3928:
3923:
3859:
3857:
3856:
3851:
3847:
3833:
3832:
3817:
3809:
3797:
3796:
3794:
3786:
3763:
3762:
3744:
3736:
3690:
3685:
3658:
3656:
3655:
3650:
3643:
3642:
3618:
3617:
3599:
3591:
3582:
3581:
3536:
3535:
3500:
3498:
3497:
3492:
3480:
3479:
3458:
3457:
3436:
3435:
3411:
3410:
3377:
3376:
3364:
3363:
3324:phase equilibria
3302:
3300:
3299:
3294:
3280:
3274:
3269:
3242:
3238:
3237:
3218:
3217:
3180:
3178:
3177:
3172:
3167:
3159:
3158:
3146:
3145:
3129:
3124:
3109:
3100:
3095:
3082:
3077:
3034:
3032:
3031:
3026:
3024:
3020:
2932:
2927:
2898:For a compound:
2895:
2893:
2892:
2887:
2818:
2816:
2815:
2810:
2808:
2804:
2716:
2711:
2658:For an element,
2655:
2653:
2652:
2647:
2642:
2641:
2629:
2628:
2612:
2607:
2518:
2516:
2515:
2510:
2499:
2498:
2486:
2485:
2079:
2077:
2076:
2071:
2040:phase transition
1987:
1985:
1984:
1979:
1977:
1976:
1971:
1967:
1965:
1957:
1949:
1939:
1935:
1934:
1932:
1924:
1916:
1913:
1878:
1877:
1633:
1626:
1619:
1603:
1602:
1310:Key publications
1291:
1290:("living force")
1240:Brownian ratchet
1235:Entropy and life
1230:Entropy and time
1181:
1180:
1156:
1154:
1153:
1148:
1101:
1099:
1098:
1093:
1046:
1044:
1043:
1038:
991:
989:
988:
983:
885:Clausius theorem
880:Carnot's theorem
853:
851:
850:
845:
829:
827:
826:
821:
806:
804:
803:
798:
782:
780:
779:
774:
761:
760:
757:
755:
754:
749:
721:
719:
718:
713:
697:
695:
694:
689:
674:
672:
671:
666:
650:
648:
647:
642:
629:
628:
625:
623:
622:
617:
586:
584:
583:
578:
562:
560:
559:
554:
539:
537:
536:
531:
515:
513:
512:
507:
494:
493:
490:
488:
487:
482:
460:
459:
333:
332:
152:
151:
33:
19:
18:
4961:
4960:
4956:
4955:
4954:
4952:
4951:
4950:
4936:
4935:
4884:
4795:
4776:
4757:
4738:
4717:
4701:
4678:Thermochemistry
4654:
4646:
4637:
4623:
4613:
4602:
4591:
4580:
4569:
4558:
4547:
4536:
4525:
4514:
4503:
4492:
4481:
4473:
4466:
4456:
4448:
4441:
4431:
4423:
4416:
4406:
4399:
4389:
4379:
4369:
4359:
4349:
4341:
4326:
4303:
4294:
4239:
4225:
4216:
4213:
4212:
4207:
4198:
4181:
4164:
4136:
4132:
4113:
4107:
4104:
4103:
4101:
4074:
4072:
4068:
4041:
4037:
4018:
4005:
4001:
3948:
3924:
3910:
3901:
3898:
3897:
3893:
3885:
3877:
3860:
3840:
3828:
3824:
3808:
3785:
3780:
3776:
3755:
3751:
3735:
3686:
3681:
3675:
3672:
3671:
3667:
3659:
3638:
3634:
3610:
3606:
3590:
3574:
3570:
3531:
3527:
3525:
3522:
3521:
3517:
3510:
3501:
3475:
3471:
3453:
3449:
3428:
3424:
3406:
3402:
3372:
3368:
3359:
3355:
3353:
3350:
3349:
3308:
3303:
3276:
3270:
3256:
3230:
3226:
3222:
3213:
3209:
3207:
3204:
3203:
3199:
3189:
3181:
3163:
3154:
3150:
3141:
3137:
3125:
3120:
3105:
3096:
3091:
3078:
3073:
3064:
3061:
3060:
3052:
3044:
3035:
2983:
2979:
2928:
2914:
2905:
2902:
2901:
2896:
2836:
2833:
2832:
2819:
2767:
2763:
2712:
2698:
2689:
2686:
2685:
2673:
2656:
2637:
2633:
2624:
2620:
2608:
2588:
2564:
2561:
2560:
2547:
2539:
2531:
2527:
2519:
2494:
2490:
2481:
2477:
2418:
2415:
2414:
2401:
2393:
2372:
2364:
2338:
2327:
2320:
2313:
2302:
2287:
2270:
2262:
2248:
2240:
2228:
2221:
2205:
2156:
2145:
2134:
2118:
2102:
2086:
2065:
2062:
2061:
2036:condensed-phase
2032:
2024:
2009:
1994:
1988:
1972:
1958:
1950:
1948:
1944:
1943:
1925:
1917:
1915:
1900:
1895:
1891:
1873:
1869:
1867:
1864:
1863:
1835:
1831:
1819:
1811:
1803:
1791:
1784:
1746:internal energy
1742:
1702:reference state
1676:
1637:
1592:
1591:
1567:
1559:
1558:
1557:
1417:
1409:
1408:
1387:
1373:
1348:
1344:
1337:
1333:
1326:
1322:
1289:
1282:
1264:
1245:Maxwell's demon
1207:
1178:
1177:
1161:
1160:
1159:
1112:
1109:
1108:
1107:
1057:
1054:
1053:
1052:
1002:
999:
998:
997:
962:
959:
958:
957:
955:Internal energy
950:
935:
925:
924:
899:
874:
864:
863:
862:
836:
833:
832:
815:
812:
811:
789:
786:
785:
768:
765:
764:
740:
737:
736:
704:
701:
700:
683:
680:
679:
657:
654:
653:
636:
633:
632:
605:
602:
601:
596:Compressibility
569:
566:
565:
548:
545:
544:
522:
519:
518:
501:
498:
497:
473:
470:
469:
449:
439:
438:
419:Particle number
372:
331:
320:
310:
309:
268:Irreversibility
180:State of matter
147:Isolated system
132:
122:
121:
120:
95:
85:
84:
80:Non-equilibrium
72:
47:
39:
17:
12:
11:
5:
4959:
4949:
4948:
4934:
4933:
4927:
4921:
4915:
4909:
4903:
4897:
4891:
4883:
4882:External links
4880:
4879:
4878:
4875:
4858:
4851:
4838:
4825:
4812:
4799:
4793:
4780:
4774:
4761:
4755:
4742:
4736:
4721:
4715:
4700:
4697:
4696:
4695:
4690:
4685:
4680:
4675:
4670:
4665:
4660:
4653:
4650:
4644:
4635:
4621:
4618:
4617:
4616:
4615:
4611:
4604:
4600:
4593:
4589:
4582:
4578:
4571:
4567:
4560:
4556:
4549:
4545:
4538:
4534:
4527:
4523:
4516:
4512:
4505:
4501:
4494:
4490:
4483:
4479:
4471:
4464:
4458:
4454:
4446:
4439:
4433:
4429:
4421:
4414:
4408:
4404:
4397:
4391:
4387:
4381:
4377:
4371:
4367:
4361:
4357:
4351:
4347:
4339:
4324:
4302:
4299:
4283:
4280:
4277:
4274:
4271:
4268:
4265:
4262:
4259:
4256:
4253:
4250:
4247:
4242:
4237:
4234:
4231:
4228:
4224:
4220:
4205:
4184:
4179:
4176:
4173:
4170:
4167:
4163:
4159:
4156:
4153:
4150:
4147:
4144:
4139:
4135:
4131:
4128:
4125:
4120:
4117:
4111:
4089:
4081:
4078:
4071:
4067:
4064:
4061:
4058:
4055:
4052:
4047:
4044:
4040:
4036:
4033:
4030:
4025:
4022:
4016:
4013:
4008:
4004:
4000:
3997:
3994:
3991:
3988:
3985:
3982:
3979:
3976:
3973:
3970:
3967:
3964:
3961:
3958:
3954:
3951:
3947:
3944:
3941:
3938:
3935:
3932:
3927:
3922:
3919:
3916:
3913:
3909:
3905:
3891:
3883:
3875:
3846:
3843:
3839:
3836:
3831:
3827:
3823:
3820:
3815:
3812:
3806:
3803:
3800:
3792:
3789:
3784:
3779:
3775:
3772:
3769:
3766:
3761:
3758:
3754:
3750:
3747:
3742:
3739:
3733:
3730:
3727:
3724:
3721:
3718:
3715:
3712:
3709:
3706:
3703:
3700:
3697:
3694:
3689:
3684:
3680:
3665:
3646:
3641:
3637:
3633:
3630:
3627:
3624:
3621:
3616:
3613:
3609:
3605:
3602:
3597:
3594:
3588:
3585:
3580:
3577:
3573:
3569:
3566:
3563:
3560:
3557:
3554:
3551:
3548:
3545:
3542:
3539:
3534:
3530:
3515:
3508:
3489:
3486:
3483:
3478:
3474:
3470:
3467:
3464:
3461:
3456:
3452:
3448:
3445:
3442:
3439:
3434:
3431:
3427:
3423:
3420:
3417:
3414:
3409:
3405:
3401:
3398:
3395:
3392:
3389:
3386:
3383:
3380:
3375:
3371:
3367:
3362:
3358:
3334:mixtures, and
3307:
3304:
3292:
3289:
3286:
3283:
3279:
3273:
3268:
3265:
3262:
3259:
3255:
3251:
3248:
3245:
3241:
3236:
3233:
3229:
3225:
3221:
3216:
3212:
3197:
3187:
3170:
3166:
3162:
3157:
3153:
3149:
3144:
3140:
3136:
3133:
3128:
3123:
3119:
3115:
3112:
3108:
3104:
3099:
3094:
3090:
3086:
3081:
3076:
3072:
3068:
3050:
3042:
3023:
3019:
3016:
3013:
3010:
3007:
3004:
3001:
2998:
2995:
2992:
2989:
2986:
2982:
2978:
2975:
2972:
2969:
2966:
2963:
2960:
2957:
2954:
2951:
2948:
2945:
2942:
2939:
2936:
2931:
2926:
2923:
2920:
2917:
2913:
2909:
2885:
2882:
2879:
2876:
2873:
2870:
2867:
2864:
2861:
2858:
2855:
2852:
2849:
2846:
2843:
2840:
2807:
2803:
2800:
2797:
2794:
2791:
2788:
2785:
2782:
2779:
2776:
2773:
2770:
2766:
2762:
2759:
2756:
2753:
2750:
2747:
2744:
2741:
2738:
2735:
2732:
2729:
2726:
2723:
2720:
2715:
2710:
2707:
2704:
2701:
2697:
2693:
2671:
2645:
2640:
2636:
2632:
2627:
2623:
2619:
2616:
2611:
2606:
2603:
2600:
2597:
2594:
2591:
2587:
2583:
2580:
2577:
2574:
2571:
2568:
2546:
2543:
2537:
2529:
2525:
2508:
2505:
2502:
2497:
2493:
2489:
2484:
2480:
2476:
2473:
2470:
2467:
2464:
2461:
2458:
2455:
2452:
2449:
2446:
2443:
2440:
2437:
2434:
2431:
2428:
2425:
2422:
2399:
2391:
2370:
2362:
2336:
2325:
2318:
2311:
2300:
2285:
2269:
2266:
2260:
2246:
2238:
2231:standard heats
2226:
2219:
2204:
2201:
2176:(for example,
2154:
2143:
2139:
2138:
2137:
2136:
2132:
2120:
2116:
2104:
2100:
2088:
2084:
2069:
2031:
2028:
2022:
2007:
1992:
1975:
1970:
1964:
1961:
1956:
1953:
1947:
1942:
1938:
1931:
1928:
1923:
1920:
1912:
1909:
1906:
1903:
1899:
1894:
1890:
1887:
1884:
1881:
1876:
1872:
1833:
1829:
1817:
1809:
1801:
1789:
1782:
1741:
1738:
1697:standard state
1675:
1672:
1639:
1638:
1636:
1635:
1628:
1621:
1613:
1610:
1609:
1608:
1607:
1594:
1593:
1590:
1589:
1584:
1579:
1574:
1568:
1565:
1564:
1561:
1560:
1556:
1555:
1550:
1545:
1540:
1535:
1530:
1525:
1520:
1515:
1510:
1505:
1500:
1495:
1490:
1485:
1480:
1475:
1470:
1465:
1460:
1455:
1450:
1445:
1440:
1435:
1430:
1425:
1419:
1418:
1415:
1414:
1411:
1410:
1405:
1404:
1403:
1402:
1397:
1389:
1388:
1386:
1385:
1382:
1378:
1375:
1374:
1372:
1371:
1366:
1364:Thermodynamics
1360:
1357:
1356:
1352:
1351:
1350:
1349:
1340:
1338:
1329:
1327:
1318:
1313:
1312:
1306:
1305:
1304:
1303:
1298:
1293:
1281:
1280:
1278:Caloric theory
1274:
1271:
1270:
1266:
1265:
1263:
1262:
1257:
1252:
1247:
1242:
1237:
1232:
1226:
1223:
1222:
1216:
1215:
1214:
1213:
1206:
1205:
1200:
1195:
1189:
1186:
1185:
1179:
1176:
1175:
1172:
1168:
1167:
1166:
1163:
1162:
1158:
1157:
1146:
1143:
1140:
1137:
1134:
1131:
1128:
1125:
1122:
1119:
1116:
1102:
1091:
1088:
1085:
1082:
1079:
1076:
1073:
1070:
1067:
1064:
1061:
1047:
1036:
1033:
1030:
1027:
1024:
1021:
1018:
1015:
1012:
1009:
1006:
992:
981:
978:
975:
972:
969:
966:
951:
949:
948:
943:
937:
936:
931:
930:
927:
926:
923:
922:
915:
910:
905:
898:
897:
892:
887:
882:
876:
875:
870:
869:
866:
865:
859:
858:
855:
854:
843:
840:
830:
819:
808:
807:
796:
793:
783:
772:
758:
747:
744:
734:
727:
726:
723:
722:
711:
708:
698:
687:
676:
675:
664:
661:
651:
640:
626:
615:
612:
609:
599:
592:
591:
588:
587:
576:
573:
563:
552:
541:
540:
529:
526:
516:
505:
491:
480:
477:
467:
458:
457:
456:
450:
445:
444:
441:
440:
435:
434:
433:
432:
427:
422:
411:
400:
381:
380:
374:
373:
371:
370:
365:
359:
356:
355:
349:
348:
347:
346:
341:
322:
321:
316:
315:
312:
311:
306:
305:
304:
303:
298:
293:
285:
284:
278:
277:
276:
275:
270:
265:
260:
258:Free expansion
255:
250:
245:
240:
235:
230:
225:
220:
212:
211:
205:
204:
203:
202:
197:
195:Control volume
192:
187:
185:Phase (matter)
182:
177:
172:
167:
159:
158:
150:
149:
144:
139:
133:
128:
127:
124:
123:
119:
118:
113:
108:
103:
97:
96:
91:
90:
87:
86:
83:
82:
71:
70:
65:
60:
55:
49:
48:
45:
44:
41:
40:
35:The classical
34:
26:
25:
23:Thermodynamics
15:
9:
6:
4:
3:
2:
4958:
4947:
4944:
4943:
4941:
4931:
4930:Mol-Instincts
4928:
4925:
4922:
4919:
4916:
4913:
4910:
4907:
4904:
4901:
4898:
4895:
4892:
4889:
4886:
4885:
4876:
4873:
4872:1-933762-07-1
4869:
4865:
4864:
4859:
4856:
4852:
4848:
4844:
4839:
4835:
4831:
4826:
4822:
4818:
4813:
4809:
4805:
4800:
4796:
4794:0-8493-0197-1
4790:
4786:
4781:
4777:
4775:1-58112-620-4
4771:
4767:
4762:
4758:
4756:0-89116-758-7
4752:
4748:
4743:
4739:
4737:1-56396-831-2
4733:
4729:
4728:
4722:
4718:
4716:3-527-30993-4
4712:
4709:. Wiley-VCH.
4708:
4703:
4702:
4694:
4691:
4689:
4686:
4684:
4681:
4679:
4676:
4674:
4671:
4669:
4666:
4664:
4661:
4659:
4656:
4655:
4649:
4633:
4629:
4625:
4609:
4605:
4598:
4594:
4587:
4583:
4576:
4572:
4565:
4561:
4554:
4550:
4543:
4539:
4532:
4528:
4521:
4517:
4510:
4506:
4499:
4495:
4488:
4484:
4477:
4470:
4463:
4459:
4452:
4445:
4438:
4434:
4427:
4420:
4413:
4409:
4403:
4396:
4392:
4386:
4382:
4376:
4372:
4366:
4362:
4356:
4352:
4345:
4337:
4333:
4332:
4331:
4330:
4322:
4318:
4314:
4312:
4309:
4306:example, the
4298:
4281:
4278:
4272:
4269:
4266:
4263:
4257:
4254:
4251:
4248:
4245:
4240:
4235:
4232:
4229:
4226:
4222:
4210:
4203:
4182:
4177:
4174:
4171:
4168:
4165:
4161:
4154:
4151:
4145:
4137:
4133:
4126:
4118:
4115:
4109:
4079:
4076:
4069:
4062:
4056:
4053:
4045:
4042:
4038:
4031:
4023:
4020:
4014:
4006:
4002:
3995:
3989:
3983:
3980:
3977:
3974:
3968:
3962:
3959:
3952:
3949:
3942:
3939:
3930:
3925:
3920:
3917:
3914:
3911:
3907:
3895:
3889:
3881:
3873:
3869:
3865:
3844:
3841:
3837:
3829:
3825:
3818:
3813:
3810:
3804:
3801:
3790:
3787:
3782:
3777:
3770:
3767:
3759:
3756:
3752:
3745:
3740:
3737:
3731:
3725:
3719:
3716:
3713:
3707:
3704:
3701:
3695:
3692:
3687:
3682:
3678:
3669:
3668:/T equation:
3664:
3639:
3635:
3628:
3625:
3622:
3614:
3611:
3607:
3600:
3595:
3592:
3586:
3578:
3575:
3571:
3564:
3561:
3555:
3549:
3546:
3543:
3540:
3537:
3532:
3528:
3519:
3514:
3506:
3487:
3484:
3476:
3472:
3465:
3462:
3454:
3450:
3443:
3440:
3432:
3429:
3425:
3418:
3415:
3407:
3403:
3396:
3393:
3387:
3381:
3378:
3373:
3369:
3365:
3360:
3356:
3347:
3343:
3341:
3337:
3333:
3329:
3325:
3321:
3316:
3313:
3287:
3284:
3277:
3271:
3266:
3263:
3260:
3257:
3253:
3246:
3243:
3239:
3234:
3231:
3227:
3223:
3219:
3214:
3210:
3201:
3196:
3193:
3184:
3168:
3164:
3155:
3151:
3147:
3142:
3138:
3131:
3126:
3121:
3117:
3113:
3110:
3106:
3097:
3092:
3088:
3084:
3079:
3074:
3070:
3058:
3056:
3048:
3040:
3021:
3017:
3014:
3011:
3008:
3005:
3002:
2999:
2996:
2990:
2984:
2980:
2976:
2973:
2970:
2967:
2964:
2961:
2958:
2955:
2952:
2949:
2943:
2937:
2934:
2929:
2924:
2921:
2918:
2915:
2911:
2899:
2880:
2874:
2871:
2868:
2865:
2859:
2853:
2850:
2844:
2838:
2830:
2828:
2824:
2805:
2801:
2798:
2795:
2792:
2789:
2786:
2783:
2780:
2774:
2768:
2764:
2760:
2757:
2754:
2751:
2748:
2745:
2742:
2739:
2736:
2733:
2727:
2721:
2718:
2713:
2708:
2705:
2702:
2699:
2695:
2683:
2681:
2677:
2669:
2665:
2661:
2638:
2634:
2630:
2625:
2621:
2614:
2609:
2604:
2601:
2598:
2595:
2592:
2589:
2585:
2578:
2572:
2566:
2558:
2556:
2552:
2535:
2523:
2503:
2495:
2491:
2487:
2482:
2478:
2474:
2471:
2468:
2459:
2453:
2450:
2447:
2444:
2441:
2435:
2432:
2429:
2423:
2420:
2411:
2407:
2403:
2397:
2389:
2384:
2380:
2376:
2368:
2360:
2352:
2348:
2344:
2342:
2334:
2329:
2324:
2317:
2310:
2306:
2299:
2295:
2294:absolute zero
2291:
2284:
2280:
2275:
2258:
2254:
2250:
2244:
2236:
2232:
2225:
2218:
2214:
2210:
2197:
2193:
2189:
2185:
2181:
2179:
2175:
2173:
2168:
2164:
2159:
2157:
2150:
2146:
2131:
2127:
2126:
2121:
2115:
2111:
2110:
2105:
2099:
2095:
2094:
2089:
2083:
2067:
2059:
2056:
2055:
2054:
2053:
2052:
2050:
2046:
2041:
2037:
2020:
2016:
2005:
2001:
1997:
1995:
1973:
1968:
1962:
1954:
1945:
1940:
1936:
1929:
1921:
1910:
1904:
1892:
1888:
1882:
1874:
1870:
1861:
1859:
1858:
1857:heat capacity
1852:
1849:
1844:
1840:
1827:
1823:
1815:
1807:
1799:
1795:
1788:
1781:
1777:
1773:
1769:
1768:
1767:sensible heat
1763:
1759:
1755:
1751:
1747:
1737:
1735:
1730:
1726:
1722:
1721:
1715:
1711:
1707:
1703:
1699:
1698:
1693:
1688:
1684:
1680:
1671:
1669:
1665:
1661:
1657:
1653:
1649:
1645:
1634:
1629:
1627:
1622:
1620:
1615:
1614:
1612:
1611:
1606:
1598:
1597:
1596:
1595:
1588:
1585:
1583:
1580:
1578:
1577:Self-assembly
1575:
1573:
1570:
1569:
1563:
1562:
1554:
1551:
1549:
1548:van der Waals
1546:
1544:
1541:
1539:
1536:
1534:
1531:
1529:
1526:
1524:
1521:
1519:
1516:
1514:
1511:
1509:
1506:
1504:
1501:
1499:
1496:
1494:
1491:
1489:
1486:
1484:
1481:
1479:
1476:
1474:
1473:von Helmholtz
1471:
1469:
1466:
1464:
1461:
1459:
1456:
1454:
1451:
1449:
1446:
1444:
1441:
1439:
1436:
1434:
1431:
1429:
1426:
1424:
1421:
1420:
1413:
1412:
1401:
1398:
1396:
1393:
1392:
1391:
1390:
1383:
1380:
1379:
1377:
1376:
1370:
1367:
1365:
1362:
1361:
1359:
1358:
1354:
1353:
1347:
1346:
1339:
1336:
1335:
1328:
1325:
1324:
1317:
1316:
1315:
1314:
1311:
1308:
1307:
1302:
1299:
1297:
1294:
1292:
1288:
1284:
1283:
1279:
1276:
1275:
1273:
1272:
1268:
1267:
1261:
1258:
1256:
1253:
1251:
1248:
1246:
1243:
1241:
1238:
1236:
1233:
1231:
1228:
1227:
1225:
1224:
1221:
1218:
1217:
1212:
1209:
1208:
1204:
1201:
1199:
1196:
1194:
1191:
1190:
1188:
1187:
1183:
1182:
1173:
1170:
1169:
1165:
1164:
1144:
1141:
1138:
1135:
1132:
1126:
1123:
1120:
1114:
1106:
1103:
1089:
1086:
1083:
1080:
1077:
1071:
1068:
1065:
1059:
1051:
1048:
1034:
1031:
1028:
1025:
1022:
1016:
1013:
1010:
1004:
996:
993:
976:
973:
970:
964:
956:
953:
952:
947:
944:
942:
939:
938:
934:
929:
928:
921:
920:
916:
914:
911:
909:
906:
904:
901:
900:
896:
895:Ideal gas law
893:
891:
888:
886:
883:
881:
878:
877:
873:
868:
867:
841:
831:
817:
810:
809:
794:
784:
770:
763:
762:
759:
745:
742:
735:
732:
729:
728:
709:
699:
685:
678:
677:
662:
652:
638:
631:
630:
627:
613:
610:
607:
600:
597:
594:
593:
574:
564:
550:
543:
542:
527:
517:
503:
496:
495:
492:
478:
475:
468:
465:
462:
461:
455:
452:
451:
448:
443:
442:
431:
428:
426:
425:Vapor quality
423:
421:
420:
415:
412:
410:
409:
404:
401:
398:
394:
393:
388:
385:
384:
383:
382:
379:
376:
375:
369:
366:
364:
361:
360:
358:
357:
354:
351:
350:
345:
342:
340:
337:
336:
335:
334:
330:
326:
319:
314:
313:
302:
299:
297:
294:
292:
289:
288:
287:
286:
283:
280:
279:
274:
271:
269:
266:
264:
263:Reversibility
261:
259:
256:
254:
251:
249:
246:
244:
241:
239:
236:
234:
231:
229:
226:
224:
221:
219:
216:
215:
214:
213:
210:
207:
206:
201:
198:
196:
193:
191:
188:
186:
183:
181:
178:
176:
173:
171:
168:
166:
163:
162:
161:
160:
157:
154:
153:
148:
145:
143:
140:
138:
137:Closed system
135:
134:
131:
126:
125:
117:
114:
112:
109:
107:
104:
102:
99:
98:
94:
89:
88:
81:
77:
74:
73:
69:
66:
64:
61:
59:
56:
54:
51:
50:
43:
42:
38:
32:
28:
27:
24:
21:
20:
4888:NIST WebBook
4862:
4854:
4846:
4842:
4833:
4829:
4820:
4816:
4807:
4803:
4784:
4765:
4746:
4726:
4706:
4641:
4631:
4619:
4607:
4596:
4585:
4574:
4563:
4552:
4541:
4530:
4519:
4508:
4497:
4486:
4475:
4468:
4461:
4450:
4443:
4436:
4425:
4418:
4411:
4401:
4394:
4384:
4374:
4364:
4354:
4343:
4335:
4320:
4304:
4295:
4201:
4199:
3887:
3879:
3871:
3867:
3863:
3861:
3662:
3660:
3512:
3504:
3502:
3344:
3339:
3328:spectroscopy
3317:
3311:
3309:
3194:
3185:
3182:
3054:
3046:
3038:
3036:
2897:
2826:
2822:
2820:
2679:
2675:
2667:
2663:
2659:
2657:
2554:
2550:
2548:
2533:
2521:
2409:
2395:
2387:
2382:
2378:
2374:
2366:
2358:
2356:
2350:
2340:
2332:
2330:
2322:
2315:
2308:
2297:
2289:
2282:
2271:
2256:
2242:
2234:
2230:
2223:
2216:
2206:
2195:
2191:
2187:
2177:
2171:
2166:
2162:
2160:
2152:
2141:
2140:
2129:
2123:Enthalpy of
2122:
2113:
2109:vaporization
2107:Enthalpy of
2106:
2097:
2090:
2081:
2057:
2048:
2045:isothermally
2044:
2033:
2018:
2003:
1990:
1989:
1855:
1853:
1825:
1821:
1813:
1805:
1797:
1793:
1786:
1779:
1776:heat content
1775:
1771:
1765:
1761:
1757:
1753:
1743:
1728:
1724:
1718:
1713:
1705:
1701:
1695:
1686:
1678:
1677:
1670:are in use.
1643:
1642:
1438:Carathéodory
1369:Heat engines
1341:
1330:
1319:
1301:Motive power
1286:
946:Free entropy
917:
453:
417:
416: /
406:
405: /
397:introduction
390:
389: /
328:
291:Heat engines
78: /
4340:form 298.15
3320:calorimetry
2321:instead of
2279:Debye model
2161:Values of Δ
2125:sublimation
1710:temperature
1260:Synergetics
941:Free energy
387:Temperature
248:Quasistatic
243:Isenthalpic
200:Instruments
190:Equilibrium
142:Open system
76:Equilibrium
58:Statistical
4699:References
2532:(771 K). Δ
1848:polynomial
1832:), where T
1723:state. A
1720:metastable
1572:Nucleation
1416:Scientists
1220:Philosophy
933:Potentials
296:Heat pumps
253:Polytropic
238:Isentropic
228:Isothermal
4912:DIPPR 801
4282:χ
4270:
4258:β
4249:α
4241:∘
4219:Δ
4183:∘
4158:Δ
4149:Δ
4124:Δ
4110:−
4060:Δ
4043:−
4029:Δ
3993:Δ
3990:−
3981:
3966:Δ
3963:−
3946:Δ
3943:−
3937:Δ
3926:∘
3904:Δ
3783:−
3768:−
3757:−
3705:
3688:∘
3612:−
3576:−
3562:−
3430:−
3366:−
3272:∘
3250:Δ
3247:−
3220:
3148:−
3132:−
3127:∘
3098:∘
3085:−
3080:∘
2977:∑
2974:−
2930:∘
2908:Δ
2872:×
2866:−
2761:∑
2758:−
2714:∘
2692:Δ
2631:−
2610:∘
2582:Δ
2466:⇒
2068:γ
1960:∂
1952:∂
1927:Δ
1919:Δ
1908:→
1902:Δ
1839:ideal gas
1770:, or the
1553:Waterston
1503:von Mayer
1458:de Donder
1448:Clapeyron
1428:Boltzmann
1423:Bernoulli
1384:Education
1355:Timelines
1139:−
1084:−
872:Equations
839:∂
792:∂
743:α
707:∂
660:∂
614:−
608:β
572:∂
525:∂
233:Adiabatic
223:Isochoric
209:Processes
170:Ideal gas
53:Classical
4940:Category
4652:See also
4634:for MgCl
4323:for MgCl
3953:′
3845:′
2213:elements
1750:enthalpy
1729:physical
1714:physical
1652:enthalpy
1605:Category
1543:Thompson
1453:Clausius
1433:Bridgman
1287:Vis viva
1269:Theories
1203:Gas laws
995:Enthalpy
403:Pressure
218:Isobaric
175:Real gas
63:Chemical
46:Branches
3285:19.1448
3190:of the
3186:The log
2274:entropy
2259:of ZnBr
2093:melting
1690:on the
1656:entropy
1528:Smeaton
1523:Rankine
1513:Onsager
1498:Maxwell
1493:Massieu
1198:Entropy
1193:General
1184:History
1174:Culture
1171:History
395: (
392:Entropy
329:italics
130:Systems
4870:
4791:
4772:
4753:
4734:
4713:
4348:298.15
3043:298.15
2172:latent
1764:, the
1754:change
1748:(e.g.
1706:normal
1658:, and
1518:Planck
1508:Nernst
1483:Kelvin
1443:Carnot
733:
598:
466:
408:Volume
323:Note:
282:Cycles
111:Second
101:Zeroth
4906:DIPPR
4480:trans
4455:trans
4430:trans
4308:Excel
3886:– T(Δ
2520:The Δ
2174:heats
1683:steam
1566:Other
1533:Stahl
1488:Lewis
1478:Joule
1468:Gibbs
1463:Duhem
156:State
116:Third
106:First
4868:ISBN
4789:ISBN
4770:ISBN
4751:ISBN
4732:ISBN
4711:ISBN
4612:form
4601:form
4590:form
4579:form
4568:form
4557:form
4546:form
4535:form
4524:form
4513:form
4502:form
4491:form
4206:form
3892:form
3884:form
3876:form
3509:form
2672:form
2394:or Δ
2392:form
2365:or Δ
2363:form
2272:The
2239:form
2227:form
2220:form
1854:The
1538:Tait
368:Heat
363:Work
93:Laws
4847:696
4834:689
4821:674
4808:672
4472:298
4447:298
4422:298
4405:298
4178:298
3878:= Δ
3615:0.5
3455:0.5
3374:298
3336:emf
3211:log
3156:298
3075:298
2639:298
2605:298
2337:298
2180:).
1898:lim
1828:°(T
1820:or
1818:298
1802:298
1790:298
1725:non
1381:Art
327:in
4942::
4845:.
4832:.
4819:.
4806:.
4467:-
4442:-
4417:-
4400:-
4342:,
4267:ln
3978:ln
3702:ln
3326:,
3322:,
3310:A
3215:10
3198:eq
3188:10
3053:)/
3045:–
2538:rx
2526:rx
2400:rx
2386:(Δ
2371:rx
2249:.
2247:rx
2151:,
2085:tr
1843:SI
1824:°-
1804:,
1796:°-
1792:,
1736:.
1654:,
4874:.
4849:.
4836:.
4823:.
4810:.
4797:.
4778:.
4759:.
4740:.
4719:.
4645:2
4636:2
4622:2
4610:°
4608:G
4599:°
4597:G
4588:°
4586:G
4577:°
4575:G
4566:°
4564:G
4555:°
4553:G
4544:°
4542:H
4533:°
4531:H
4522:°
4520:H
4511:°
4509:H
4500:°
4498:H
4489:°
4487:H
4478:°
4476:H
4469:H
4465:T
4462:H
4453:°
4451:H
4444:H
4440:T
4437:H
4428:°
4426:H
4419:H
4415:T
4412:H
4402:H
4398:T
4395:H
4388:p
4385:C
4378:p
4375:C
4368:p
4365:C
4358:p
4355:C
4346:°
4344:S
4338:°
4336:H
4325:2
4279:+
4276:)
4273:T
4264:T
4261:(
4255:+
4252:T
4246:=
4236:m
4233:r
4230:o
4227:f
4223:G
4204:°
4202:G
4175:m
4172:r
4169:o
4166:f
4162:H
4155:+
4152:F
4146:+
4143:)
4138:3
4134:T
4130:(
4127:E
4119:2
4116:1
4088:)
4080:2
4077:1
4070:T
4066:(
4063:D
4057:2
4054:+
4051:)
4046:1
4039:T
4035:(
4032:C
4024:2
4021:1
4015:+
4012:)
4007:2
4003:T
3999:(
3996:B
3987:)
3984:T
3975:T
3972:(
3969:A
3960:T
3957:)
3950:F
3940:A
3934:(
3931:=
3921:m
3918:r
3915:o
3912:f
3908:G
3890:°
3888:S
3882:°
3880:H
3874:°
3872:G
3868:T
3864:S
3842:F
3838:+
3835:)
3830:2
3826:T
3822:(
3819:E
3814:2
3811:1
3805:1
3802:+
3799:)
3791:2
3788:1
3778:T
3774:(
3771:D
3765:)
3760:2
3753:T
3749:(
3746:C
3741:2
3738:1
3732:+
3729:)
3726:T
3723:(
3720:B
3717:2
3714:+
3711:)
3708:T
3699:(
3696:A
3693:=
3683:T
3679:S
3666:p
3663:C
3645:)
3640:2
3636:T
3632:(
3629:E
3626:3
3623:+
3620:)
3608:T
3604:(
3601:D
3596:2
3593:1
3587:+
3584:)
3579:2
3572:T
3568:(
3565:C
3559:)
3556:T
3553:(
3550:B
3547:2
3544:+
3541:A
3538:=
3533:P
3529:C
3516:p
3513:C
3507:°
3505:H
3488:F
3485:+
3482:)
3477:3
3473:T
3469:(
3466:E
3463:+
3460:)
3451:T
3447:(
3444:D
3441:+
3438:)
3433:1
3426:T
3422:(
3419:C
3416:+
3413:)
3408:2
3404:T
3400:(
3397:B
3394:+
3391:)
3388:T
3385:(
3382:A
3379:=
3370:H
3361:T
3357:H
3291:)
3288:T
3282:(
3278:/
3267:m
3264:r
3261:o
3258:f
3254:G
3244:=
3240:)
3235:q
3232:e
3228:K
3224:(
3195:K
3169:T
3165:/
3161:)
3152:H
3143:T
3139:H
3135:(
3122:T
3118:S
3114:=
3111:T
3107:/
3103:)
3093:T
3089:G
3071:H
3067:(
3055:T
3051:T
3049:°
3047:G
3041:°
3039:H
3022:}
3018:s
3015:t
3012:n
3009:e
3006:m
3003:e
3000:l
2997:e
2994:)
2991:T
2988:(
2985:G
2981:{
2971:d
2968:n
2965:u
2962:o
2959:p
2956:m
2953:o
2950:c
2947:)
2944:T
2941:(
2938:G
2935:=
2925:m
2922:r
2919:o
2916:f
2912:G
2884:)
2881:T
2878:(
2875:S
2869:T
2863:)
2860:T
2857:(
2854:H
2851:=
2848:)
2845:T
2842:(
2839:G
2827:T
2825:(
2823:G
2806:}
2802:s
2799:t
2796:n
2793:e
2790:m
2787:e
2784:l
2781:e
2778:)
2775:T
2772:(
2769:H
2765:{
2755:d
2752:n
2749:u
2746:o
2743:p
2740:m
2737:o
2734:c
2731:)
2728:T
2725:(
2722:H
2719:=
2709:m
2706:r
2703:o
2700:f
2696:H
2680:T
2678:(
2676:H
2670:°
2668:H
2664:T
2662:(
2660:H
2644:]
2635:H
2626:T
2622:H
2618:[
2615:+
2602:,
2599:m
2596:r
2593:o
2590:f
2586:H
2579:=
2576:)
2573:T
2570:(
2567:H
2555:T
2553:(
2551:H
2536:°
2534:G
2530:2
2524:°
2522:H
2507:)
2504:g
2501:(
2496:2
2492:H
2488:+
2483:2
2479:l
2475:C
2472:b
2469:P
2463:)
2460:g
2457:(
2454:l
2451:C
2448:H
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2442:+
2439:)
2436:l
2433:,
2430:c
2427:(
2424:b
2421:P
2398:°
2396:G
2390:°
2388:G
2383:G
2379:G
2375:G
2369:°
2367:S
2361:°
2359:S
2341:S
2335:°
2333:S
2326:p
2323:C
2319:v
2316:C
2312:0
2309:S
2301:p
2298:C
2290:T
2286:v
2283:C
2261:2
2245:°
2243:H
2237:°
2235:H
2224:H
2217:H
2196:H
2192:H
2167:H
2163:H
2155:p
2153:C
2144:p
2142:C
2135:.
2133:s
2130:H
2119:.
2117:v
2114:H
2103:.
2101:m
2098:H
2087:.
2082:H
2049:H
2023:2
2008:2
1993:p
1991:C
1974:p
1969:)
1963:T
1955:H
1946:(
1941:=
1937:}
1930:T
1922:H
1911:0
1905:T
1893:{
1889:=
1886:)
1883:T
1880:(
1875:P
1871:C
1834:r
1830:r
1826:H
1822:H
1816:°
1814:H
1812:-
1810:T
1808:°
1806:H
1800:°
1798:H
1794:H
1787:H
1785:-
1783:T
1780:H
1758:H
1727:-
1632:e
1625:t
1618:v
1145:S
1142:T
1136:H
1133:=
1130:)
1127:p
1124:,
1121:T
1118:(
1115:G
1090:S
1087:T
1081:U
1078:=
1075:)
1072:V
1069:,
1066:T
1063:(
1060:A
1035:V
1032:p
1029:+
1026:U
1023:=
1020:)
1017:p
1014:,
1011:S
1008:(
1005:H
980:)
977:V
974:,
971:S
968:(
965:U
842:T
818:V
795:V
771:1
746:=
710:p
686:V
663:V
639:1
611:=
575:T
551:N
528:S
504:T
479:=
476:c
399:)
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