# Thermodynamic databases for pure substances

**Thermodynamic databases**contain information about thermodynamic properties for substances, the most important being enthalpy, entropy, and Gibbs free energy. 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 standard pressure of 101.325 kPa (1 atm), or 100 kPa (1 bar). Unfortunately, both of these definitions for the standard condition for pressure are in use.

## Thermodynamic data

**Thermodynamic data**is usually presented as a table or chart of function values for one mole of a substance (or in the case of the steam tables, one kg). A

**thermodynamic datafile**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 on the state of aggregation of the substance, which must be defined for the value to have any meaning. The state of aggregation for thermodynamic purposes is the

*standard state*, sometimes called the

*reference state*, and defined by specifying certain conditions. The

*normal*standard state is commonly defined as the most stable physical form of the substance at the specified temperature 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

*physical*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 thermodynamically stable (for example, a supercooled liquid), it is called a

*metastable*state. A

*non*-

*physical*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 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 equation of state.

### Enthalpy, heat content and heat capacity

It is very difficult to measure the absolute amount of any thermodynamic quantity involving the internal energy (e.g. enthalpy), 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*change*in these functions that is of most interest. The isobaric change in enthalpy

*H*above the common reference temperature of 298.15 K (25 °C) is called the

*high temperature heat content*, the

*sensible heat*, or the

*relative high-temperature enthalpy*, and called henceforth the

**heat content**. Different databases designate this term in different ways; for example

*H*

_{T}-

*H*

_{298},

*H*°-

*H*°

_{298},

*H*°

_{T}-

*H*°

_{298}or

*H*°-

*H*°(T

_{r}), where T

_{r}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 ideal gas at the designated standard pressure. The SI 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 polynomial 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 reference temperature is 273.15 K (0 °C).

The

*heat capacity*C is the ratio of heat added to the temperature increase. For an incremental isobaric addition of heat:

*C*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).

_{p}### Enthalpy change of phase transitions

When heat is added to a condensed-phase substance, its temperature increases until a phase change temperature is reached. With further addition of heat, the temperature remains constant while the phase transition 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**isothermally**as it undergoes a physical change. The enthalpy change resulting from a phase transition is designated Δ

*H*. There are four types of enthalpy changes resulting from a phase transition. To wit:

- *
*Enthalpy of transformation*. This applies to the transformations from one solid phase to another, such as the transformation from α-Fe (bcc ferrite) to -Fe (fcc austenite). The transformation is designated Δ*H*_{tr}.

- *
*Enthalpy of fusion or melting*. This applies to the transition of a solid to a liquid and is designated Δ*H*_{m}.

- *
*Enthalpy of vaporization*. This applies to the transition of a liquid to a vapor and is designated Δ*H*_{v}.

- *
*Enthalpy of sublimation*. This applies to the transition of a solid to a vapor and is designated Δ*H*_{s}.

*C*is infinite at phase transition temperatures because the enthalpy changes isothermally. At the Curie temperature,

_{p}*C*shows a sharp discontinuity while the enthalpy has a change in slope.

_{p}Values of Δ

*H*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

*H*for a phase transition is a weak function of temperature. In some texts, the heats of phase transitions are called

*latent*heats (for example,

*latent heat of fusion*).

### Enthalpy change for a chemical reaction

An enthalpy change occurs during a chemical reaction. For the special case of the formation of a compound from the elements, the change is designated Δ*H*

_{form}and is a weak function of temperature. Values of Δ

*H*

_{form}are usually given where the elements and compound are in their normal standard states, and as such are designated

*standard heats*of formation, as designated by a superscript °. The Δ

*H*°

_{form}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

*H*°

_{rx}.

### Entropy and Gibbs energy

The entropy 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 Debye model leads to the result that the atomic heat capacity*C*

_{v}for solids should be proportional to

*T*

^{3}, and that for perfect crystalline solids it should become zero at absolute zero. Experimentally, the heat capacity is measured at temperature intervals to as low a temperature as possible. Values of

*C*

_{p}/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 third law of thermodynamics states that the entropy of a perfect crystalline substance becomes zero at 0 K. When

*S*

_{0}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

*C*

_{v}instead of

*C*

_{p}, the difference between the two at temperatures near 0 K is so small as to be negligible.

The absolute value of entropy for a substance in its standard state at the reference temperature of 298.15 K is designated

*S*°

_{298}. Entropy increases with temperature, and is discontinuous at phase transition temperatures. The change in entropy (Δ

*S*°) 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).

The standard enthalpy change for the formation of a compound from the elements, or for any standard reaction is designated Δ

*S*°

_{form}or Δ

*S*°

_{rx}. 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

*G*has no intrinsic value, so it is the change in

*G*that is of interest. Furthermore, there is no change in

*G*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 (Δ

*G*°

_{form}or Δ

*G*°

_{rx}). The SI units of Gibbs energy are the same as for enthalpy (J/mol).

### Additional functions

Compilers of thermochemical databases may contain some additional thermodynamic functions. For example, the absolute enthalpy of a substance*H*(

*T*) is defined in terms of its formation enthalpy and its heat content as follows:

For an element,

*H*(

*T*) and [

*H*

_{T}-

*H*

_{298}] are identical at all temperatures because Δ

*H*°

_{form}is zero, and of course at 298.15 K,

*H*(

*T*) = 0. For a compound:

Similarly, the absolute Gibbs energy

*G*(

*T*) is defined by the absolute enthalpy and entropy of a substance:

For a compound:

Some tables may also contain the Gibbs energy function (

*H*°

_{298.15}–

*G*°

_{T})/

*T*which is defined in terms of the entropy and heat content.

The Gibbs energy function has the same units as entropy, but unlike entropy, exhibits no discontinuity at normal phase transition temperatures.

The log

_{10}of the equilibrium constant

*K*

_{eq}is often listed, which is calculated from the defining thermodynamic equation.

## Thermodynamic databases

A**thermodynamic database**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 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.

Thermodynamic data comes from many types of experiments, such as calorimetry, phase equilibria, spectroscopy, composition measurements of chemical equilibrium mixtures, and emf 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

*internally consistent*. 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.

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 the isobaric heat content is:

Regardless of the equation format, the heat of formation of a compound at any temperature is Δ

*H*°

_{form}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

*C*

_{p}equation is obtained by taking the derivative of the heat content equation.

The entropy equation is obtained by integrating the

*C*

_{p}/T equation:

F' is a constant of integration obtained by inserting

*S*° at any temperature

*T*. The Gibbs energy of formation of a compound is obtained from the defining equation Δ

*G*°

_{form}= Δ

*H*°

_{form}– T(Δ

*S*°

_{form}), and is expressed as

For most substances, Δ

*G*°

_{form}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.

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 experimental data used to derive the equation parameters.

### Thermodynamic datafiles

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 example, the Excel-based thermodynamic database FREED[1] creates the following type of datafile, here for a standard pressure of 1 atm.- * Row 1. Molar mass of species, density at 298.15 K, Δ
*H*°_{form 298.15},*S*°_{298.15}. and the upper temperature limit for the file.

- * Row 2. Number of
*C*_{p}equations required. Here, three because of three species phases.

- * Row 3. Values of the five parameters for the first
*C*_{p}equation; temperature limit for the equation.

- * Row 4. Values of the five parameters for the second
*C*_{p}equation; temperature limit for the equation.

- * Row 5. Values of the five parameters for the third
*C*_{p}equation; temperature limit for the equation.

- * Row 6. Number of
*H*_{T}-*H*_{298}equations required.

- * Row 7. Values of the six parameters for the first
*H*_{T}-*H*_{298}equation; temperature limit for the equation, and Δ*H*°_{trans}for the first phase change.

- * Row 8. Values of the six parameters for the second
*H*_{T}-*H*_{298}equation; temperature limit for the equation, and Δ*H*°_{trans}for the second phase change.

- * Row 9. Values of the six parameters for the third
*H*_{T}-*H*_{298}equation; temperature limit for the equation, and Δ*H*°_{trans}for the third phase change.

- * Row 10. Number of Δ
*H*°_{form}equations required. Here five; three for species phases and two because one of the elements has a phase change.

- * Row 11. Values of the six parameters for the first Δ
*H*°_{form}equation; temperature limit for the equation.

- * Row 12. Values of the six parameters for the second Δ
*H*°_{form}equation; temperature limit for the equation.

- * Row 13. Values of the six parameters for the third Δ
*H*°_{form}equation; temperature limit for the equation.

- * Row 14. Values of the six parameters for the fourth Δ
*H*°_{form}equation; temperature limit for the equation.

- * Row 15. Values of the six parameters for the fifth Δ
*H*°_{form}equation; temperature limit for the equation.

- * Row 16. Number of Δ
*G*°_{form}equations required.

- * Row 17. Values of the seven parameters for the first Δ
*G*°_{form}equation; temperature limit for the equation.

- * Row 18. Values of the seven parameters for the second Δ
*G*°_{form}equation; temperature limit for the equation.

- * Row 19. Values of the seven parameters for the third Δ
*G*°_{form}equation; temperature limit for the equation.

- * Row 20. Values of the seven parameters for the fourth Δ
*G*°_{form}equation; temperature limit for the equation.

- * Row 21. Values of the seven parameters for the fifth Δ
*G*°_{form}equation; temperature limit for the equation.

Most computerized databases will create a table of thermodynamic values using the values from the datafile. For MgCl

_{2}(c,l,g) at 1 atm pressure:

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 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

_{2}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.

## See also

- Chemical thermodynamics
- Physical chemistry
- Materials science
- Laws of thermodynamics
- Thermochemistry
- Standard temperature and pressure
- Dortmund Data Bank

## References

- Barin, Ihsan (2004).
*Thermochemical Data of Pure Substances*. Wiley-VCH. ISBN 3-527-30993-4. - Chase, M. W. (1998).
*NIST - JANAF Thermochemical Tables*, Fourth edition, Journal of Physical and Chemical Reference Data. ISBN 1-56396-831-2. - Cox, J. D.; Wagman, D.D. and V. A. Medvedev, V. A. (1989).
*CODATA Key Values for Thermodynamics*. John Benjamins Publishing Co. ISBN 0-89116-758-7. - Hummel, Wolfgang; Urs Berner, Enzo Curti, F. J. Pearson, and Tres Thoenen (2002).
*Nagra/Psi Chemical Thermodynamic Data Base*. Universal Publishers. ISBN 1-58112-620-4. - Lide, David R.; Henry V. Kehiaian (1994).
*CRC Handbook of Thermophysical and Thermochemical Data*, book & disk edition. ISBN 0-8493-0197-1. - Pankratz, L. B. (1982). "Thermodynamic Properties of Elements and Oxides".
*U. S. Bureau of Mines Bulletin***672**. - Pankratz, L. B. (1984). "Thermodynamic Properties of Halides".
*U. S. Bureau of Mines Bulletin***674**. - Pankratz, L. B.; A. D. Mah and S. W. Watson (1987). "Thermodynamic Properties of Sulfides".
*U. S. Bureau of Mines Bulletin***689**. - Pankratz, L. B. (1994). "Thermodynamic Properties of Carbides, Nitrides, and Other Selected Substances".
*U. S. Bureau of Mines Bulletin***696**. - Robie, Richard A., and Bruce S. Hemingway (1995).
*Thermodynamic Properties of Minerals . . . at Higher Temperatures*, U. S. Geological Survey Bulletin 2131. - Yaws, Carl L. (2007).
*Yaws Handbook of Thermodynamic Properties for Hydrocarbons & Chemicals*, Gulf Publishing Company. ISBN 1-933762-07-1.

## External links

- NIST WebBook A gateway to the data collection of the National Institute of Standards and Technology.
- THERMODATA Thermochemical Databases and Softwares.

**Thermodynamics**(from the Greek θερμη,

*therme,*meaning "heat" and δυναμις,

*dynamis,*meaning "power") is a branch of physics that studies the effects of changes in temperature, pressure, and volume on

**.....**Click the link for more information.

Here is a partial

**list of thermodynamic properties**of fluids:- temperature [K]
- density [kg/m
^{3}] - specific heat at constant pressure [J/kg·K]
- specific heat at constant volume [J/kg·K]
- dynamic viscosity [N/m²s]

**.....**Click the link for more information. In thermodynamics and molecular chemistry, the

**enthalpy**or*heat content*(denoted as**H**or**ΔH**, or rarely as*χ*) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the "useful" work**.....**Click the link for more information.**Ice melting**- a classic example of

*entropy increasing*

^{[1]}described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice.

**.....**Click the link for more information.

In thermodynamics, the

**Gibbs free energy**(IUPAC recommended name:**Gibbs energy**or**Gibbs function**) is a thermodynamic potential which measures the "useful" or process-initiating work obtainable from an isothermal, isobaric thermodynamic system.**.....**Click the link for more information. In chemistry and other sciences,

**STP**or**standard temperature and pressure**is a standard set of conditions for experimental measurements, to enable comparisons to be made between sets of data.**.....**Click the link for more information.**Atmospheric pressure**is the pressure at any point in the Earth's atmosphere. In most circumstances atmospheric pressure is closely approximated by the hydrostatic pressure caused by the weight of air above the measurement point.

**.....**Click the link for more information.

In physical chemistry, and in engineering,

**steam**refers to vaporized water. It is a pure, completely invisible gas (for mist see below). At standard atmospheric pressure, pure steam (unmixed with air, but in equilibrium with liquid water) occupies about 1,600 times the**.....**Click the link for more information. In the physical sciences, a

**phase**is a set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties (i.e. density, crystal structure, index of refraction, and so forth).**.....**Click the link for more information. In chemistry and other sciences,

**STP**or**standard temperature and pressure**is a standard set of conditions for experimental measurements, to enable comparisons to be made between sets of data.**.....**Click the link for more information.**trillion**fold).]]

**Temperature**is a physical property of a system that underlies the common notions of hot and cold; something that is hotter generally has the greater temperature. Temperature is one of the principal parameters of thermodynamics.

**.....**Click the link for more information.

In the physical sciences, a

**phase**is a set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties (i.e. density, crystal structure, index of refraction, and so forth).**.....**Click the link for more information.**equation of state**is a relation between state variables.<ref name="Perrot" >Perrot, Pierre (1998).

*A to Z of Thermodynamics*. Oxford University Press. ISBN 0-19-856552-6.

**.....**Click the link for more information.

In thermodynamics, the

**internal energy**of a thermodynamic system, or a body with well-defined boundaries, denoted by*U*, or sometimes*E*, is the total of the kinetic energy due to the motion of molecules (translational, rotational, vibrational) and**.....**Click the link for more information. In thermodynamics and molecular chemistry, the

**enthalpy**or*heat content*(denoted as**H**or**ΔH**, or rarely as*χ*) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the "useful" work**.....**Click the link for more information.**Sensible heat**is potential energy in the form of thermal energy or heat. The thermal body must have a temperature higher than its surroundings, (also see: latent heat). The thermal energy can be transported via conduction, convection, radiation or by a combination thereof.

**.....**Click the link for more information.

An

**ideal gas**or**perfect gas**is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces. Additionally, the constituent atoms or molecules undergo perfectly elastic collisions with the walls of the container.**.....**Click the link for more information.**International System of Units**(abbreviated

**SI**from the French

*Le*) is the modern form of the metric system.

**S**ystème**i**nternational d'unités**.....**Click the link for more information.

In mathematics, a

**polynomial**is an expression that is constructed from one or more variables and constants, using only the operations of addition, subtraction, multiplication, and constant positive whole number exponents. is a polynomial.**.....**Click the link for more information. In the physical sciences, a

**phase**is a set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties (i.e. density, crystal structure, index of refraction, and so forth).**.....**Click the link for more information.**phase transition**or

**phase change**is the transformation of a thermodynamic system from one phase to another. The distinguishing characteristic of a phase transition is an abrupt change in one or more physical properties, in particular the heat capacity, with a small change in

**.....**Click the link for more information.

**Melting**is a process that results in the phase change of a substance from a solid to a liquid. The internal energy of a solid substance is increased (typically by the application of heat) to a specific temperature (called the melting point) at which it changes to the liquid phase.

**.....**Click the link for more information.

**Evaporation**is the process by which molecules in a liquid state (e.g. water) spontaneously become gaseous (e.g. water vapor), without being heated to boiling point. It is the opposite of condensation.

**.....**Click the link for more information.

**Sublimation**can have several meanings:

- Sublimation (chemistry), the change from solid to gas, while at no point becoming a liquid.
- Sublimation (psychology), the transformation of emotions.

**.....**Click the link for more information.

The

**Curie point**(**T**), or_{c}**Curie temperature**, is a term in physics and materials science, named after Pierre Curie (1859-1906), and refers to a characteristic property of a ferromagnetic or piezoelectric material.**.....**Click the link for more information. In thermochemistry,

**latent heat**is the amount of energy in the form of heat released or absorbed by a substance during a change of phase (i.e. solid, liquid, or gas), - also called a phase transition.**.....**Click the link for more information.**chemical reaction**is a process that results in the interconversion of chemical substances.

^{[1]}The substance or substances initially involved in a chemical reaction are called reactants.

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**chemical element**, or

**element**, is a type of atom that is defined by its atomic number; that is, by the number of protons in its nucleus. The term is also used to refer to a pure chemical substance composed of atoms with the same number of protons.

**.....**Click the link for more information.

**Ice melting**- a classic example of

*entropy increasing*

^{[1]}described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice.

**.....**Click the link for more information.

In thermodynamics and solid state physics, the

**Debye model**is a method developed by Peter Debye in 1912^{[1]}for estimating the phonon contribution to the specific heat (heat capacity) in a solid.**.....**Click the link for more information.This article is copied from an article on Wikipedia.org - the free encyclopedia created and edited by online user community. The text was not checked or edited by anyone on our staff. Although the vast majority of the wikipedia encyclopedia articles provide accurate and timely information please do not assume the accuracy of any particular article. This article is distributed under the terms of GNU Free Documentation License.