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Enthalpy , a property of a
thermodynamic system A thermodynamic system is a body of matter and/or radiation, confined in space by walls, with defined permeabilities, which separate it from its surroundings. The surroundings may include other thermodynamic systems, or physical systems that a ...
, is the sum of the system's
internal energy The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinet ...
and the product of its pressure and volume. It is a
state function In the thermodynamics of equilibrium, a state function, function of state, or point function for a thermodynamic system is a mathematical function relating several state variables or state quantities (that describe equilibrium states of a sys ...
used in many measurements in chemical, biological, and physical systems at a constant pressure, which is conveniently provided by the large ambient atmosphere. The pressure–volume term expresses the
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an animal ...
required to establish the system's physical dimensions, i.e. to make room for it by displacing its surroundings. The pressure-volume term is very small for solids and liquids at common conditions, and fairly small for gases. Therefore, enthalpy is a stand-in for energy in chemical systems;
bond Bond or bonds may refer to: Common meanings * Bond (finance), a type of debt security * Bail bond, a commercial third-party guarantor of surety bonds in the United States * Chemical bond, the attraction of atoms, ions or molecules to form chemica ...
, lattice,
solvation Solvation (or dissolution) describes the interaction of a solvent with dissolved molecules. Both ionized and uncharged molecules interact strongly with a solvent, and the strength and nature of this interaction influence many properties of the ...
and other "energies" in chemistry are actually enthalpy differences. As a state function, enthalpy depends only on the final configuration of internal energy, pressure, and volume, not on the path taken to achieve it. In the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...
(SI), the unit of measurement for enthalpy is the
joule The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force appli ...
. Other historical conventional units still in use include the
calorie The calorie is a unit of energy. For historical reasons, two main definitions of "calorie" are in wide use. The large calorie, food calorie, or kilogram calorie was originally defined as the amount of heat needed to raise the temperature of o ...
and the
British thermal unit The British thermal unit (BTU or Btu) is a unit of heat; it is defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit. It is also part of the United States customary units. The modern SI ...
(BTU). The total enthalpy of a system cannot be measured directly because the internal energy contains components that are unknown, not easily accessible, or are not of interest in thermodynamics. In practice, a change in enthalpy is the preferred expression for measurements at constant pressure because it simplifies the description of
energy transfer In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of hea ...
. When transfer of matter into or out of the system is also prevented and no electrical or shaft work is done, at constant pressure the enthalpy change equals the energy exchanged with the environment by
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...
. In chemistry, the standard
enthalpy of reaction The standard enthalpy of reaction (denoted \Delta_ H^\ominus or \Delta H_^\ominus) for a chemical reaction is the difference between total reactant and total product molar enthalpies, calculated for substances in their standard states. This can i ...
is the enthalpy change when reactants in their
standard state In chemistry, the standard state of a material (pure substance, mixture or solution) is a reference point used to calculate its properties under different conditions. A superscript circle ° (degree symbol) or a Plimsoll (⦵) character is use ...
s (; usually ) change to products in their standard states. This quantity is the standard heat of reaction at constant pressure and temperature, but it can be measured by calorimetric methods even if the temperature does vary during the measurement, provided that the initial and final pressure and temperature correspond to the standard state. The value does not depend on the path from initial to final state because enthalpy is a
state function In the thermodynamics of equilibrium, a state function, function of state, or point function for a thermodynamic system is a mathematical function relating several state variables or state quantities (that describe equilibrium states of a sys ...
. Enthalpies of chemical substances are usually listed for pressure as a standard state. Enthalpies and enthalpy changes for reactions vary as a function of temperature, but tables generally list the standard heats of formation of substances at . For
endothermic In thermochemistry, an endothermic process () is any thermodynamic process with an increase in the enthalpy (or internal energy ) of the system.Oxtoby, D. W; Gillis, H.P., Butler, L. J. (2015).''Principle of Modern Chemistry'', Brooks Cole. ...
(heat-absorbing) processes, the change is a positive value; for
exothermic In thermodynamics, an exothermic process () is a thermodynamic process or reaction that releases energy from the system to its surroundings, usually in the form of heat, but also in a form of light (e.g. a spark, flame, or flash), electricit ...
(heat-releasing) processes it is negative. The enthalpy of an
ideal gas An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is ...
is independent of its pressure or volume, and depends only on its temperature, which correlates to its thermal energy. Real gases at common temperatures and pressures often closely approximate this behavior, which simplifies practical thermodynamic design and analysis.

# Definition

The enthalpy of a thermodynamic system is defined as the sum of its internal energy and the product of its pressure and volume: : , where is the
internal energy The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinet ...
, is
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
, and is the
volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...
of the system; is sometimes referred to as the pressure energy . Enthalpy is an extensive property; it is proportional to the size of the system (for homogeneous systems). As intensive properties, the specific enthalpy is referenced to a unit of
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different ele ...
of the system, and the molar enthalpy , where is the number of moles. For inhomogeneous systems the enthalpy is the sum of the enthalpies of the component subsystems: $H = \sum_k H_k,$ where * is the total enthalpy of all the subsystems, * refers to the various subsystems, * refers to the enthalpy of each subsystem. A closed system may lie in thermodynamic equilibrium in a static
gravitational field In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phen ...
, so that its pressure varies continuously with
altitude Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context ...
, while, because of the equilibrium requirement, its temperature is invariant with altitude. (Correspondingly, the system's
gravitational potential energy Gravitational energy or gravitational potential energy is the potential energy a massive object has in relation to another massive object due to gravity. It is the potential energy associated with the gravitational field, which is released (conv ...
density also varies with altitude.) Then the enthalpy summation becomes an
integral In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with ...
: $H = \int (\rho h) \, dV,$ where * (" rho") is
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematic ...
(mass per unit volume), * is the specific enthalpy (enthalpy per unit mass), * represents the enthalpy density (enthalpy per unit volume), * denotes an
infinitesimal In mathematics, an infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally refer ...
ly small element of volume within the system, for example, the volume of an infinitesimally thin horizontal layer, the integral therefore represents the sum of the enthalpies of all the elements of the volume. The enthalpy of a closed homogeneous system is its energy function , with its entropy and its pressure as natural state variables which provide a differential relation for $dH$ of the simplest form, derived as follows. We start from the
first law of thermodynamics The first law of thermodynamics is a formulation of the law of conservation of energy, adapted for thermodynamic processes. It distinguishes in principle two forms of energy transfer, heat and thermodynamic work for a system of a constant amo ...
for closed systems for an infinitesimal process: $dU = \delta Q - \delta W,$ where * is a small amount of heat added to the system, * is a small amount of work performed by the system. In a homogeneous system in which only reversible processes or pure heat transfer are considered, the
second law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unless ...
gives , with the
absolute temperature Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics. Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynami ...
and the infinitesimal change in
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...
of the system. Furthermore, if only work is done, . As a result, $dU = T\,dS - p\,dV.$ Adding to both sides of this expression gives $dU + d(pV) = T\,dS - p\,dV + d(pV),$ or $d(U + pV) = T\,dS + V\,dp.$ So $dH(S, p) = T\,dS + V\,dp.$ and the coefficients of the natural variable differentials $dS$ and $dp$ are just the single variables $T$ and $V$.

# Other expressions

The above expression of in terms of entropy and pressure may be unfamiliar to some readers. There are also expressions in terms of more directly measurable variables such as temperature and pressure: $dH = C_p\,dT + V(1 - \alpha T)\,dp.$ Here is the heat capacity at constant pressure and is the coefficient of (cubic) thermal expansion: $\alpha = \frac\left(\frac\right)_p.$ With this expression one can, in principle, determine the enthalpy if and are known as functions of and . However the expression is more complicated than $dH = T\,dS + V\,dp$ because T is not a natural variable for the enthalpy H. At constant pressure, $dP=0$ so that $dH = C_p\,dT.$ For an
ideal gas An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is ...
, $dH$ reduces to this form even if the process involves a pressure change, because ,$\alpha T=\frac\left\left(\frac\right\right)_p = \frac = 1$. In a more general form, the first law describes the internal energy with additional terms involving the
chemical potential In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species ...
and the number of particles of various types. The differential statement for then becomes $dH = T\,dS + V\,dp + \sum_i \mu_i\,dN_i,$ where is the chemical potential per particle for an -type particle, and is the number of such particles. The last term can also be written as (with the number of moles of component added to the system and, in this case, the molar chemical potential) or as (with the mass of component added to the system and, in this case, the specific chemical potential).

## Characteristic functions and natural state variables

The enthalpy, , expresses the thermodynamics of a system in the ''energy representation''. As a function of state, its arguments include both one intensive and several extensive state variables. The state variables , , and are said to be the ''natural state variables'' in this representation. They are suitable for describing processes in which they are determined by factors in the surroundings. For example, when a virtual parcel of atmospheric air moves to a different altitude, the pressure surrounding it changes, and the process is often so rapid that there is too little time for heat transfer. This is the basis of the so-called adiabatic approximation that is used in
meteorology Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did no ...
. Conjugate with the enthalpy, with these arguments, the other characteristic function of state of a thermodynamic system is its entropy, as a function, , of the same list of variables of state, except that the entropy, , is replaced in the list by the enthalpy, . It expresses the ''entropy representation''. The state variables , , and are said to be the ''natural state variables'' in this representation. They are suitable for describing processes in which they are experimentally controlled. For example, and can be controlled by allowing heat transfer, and by varying only the external pressure on the piston that sets the volume of the system.

# Physical interpretation

The term is the energy of the system, and the term can be interpreted as the
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an animal ...
that would be required to "make room" for the system if the pressure of the environment remained constant. When a system, for example, moles of a gas of
volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...
at
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
and
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied ...
, is created or brought to its present state from
absolute zero Absolute zero is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibrati ...
, energy must be supplied equal to its internal energy plus , where is the
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an animal ...
done in pushing against the ambient (atmospheric) pressure. In
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
and
statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic b ...
it may be more interesting to study the internal properties of a constant-volume system and therefore the internal energy is used. In
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, proper ...
, experiments are often conducted at constant
atmospheric pressure Atmospheric pressure, also known as barometric pressure (after the barometer), is the pressure within the atmosphere of Earth. The standard atmosphere (symbol: atm) is a unit of pressure defined as , which is equivalent to 1013.25 millibars, ...
, and the pressure–volume work represents a small, well-defined energy exchange with the atmosphere, so that is the appropriate expression for the heat of reaction. For a
heat engine In thermodynamics and engineering, a heat engine is a system that converts heat to mechanical energy, which can then be used to do mechanical work. It does this by bringing a working substance from a higher state temperature to a lower state ...
, the change in its enthalpy after a full cycle is equal to zero, since the final and initial state are equal.

# Relationship to heat

In order to discuss the relation between the enthalpy increase and heat supply, we return to the first law for closed systems, with the physics sign convention: , where the heat is supplied by conduction, radiation,
Joule heating Joule heating, also known as resistive, resistance, or Ohmic heating, is the process by which the passage of an electric current through a conductor produces heat. Joule's first law (also just Joule's law), also known in countries of former US ...
. We apply it to the special case with a constant pressure at the surface. In this case the work is given by (where is the pressure at the surface, is the increase of the volume of the system). Cases of long range electromagnetic interaction require further state variables in their formulation, and are not considered here. In this case the first law reads: $dU = \delta Q - p\,dV.$ Now, $dH = dU + d(pV).$ So $\begin dH &= \delta Q + V\,dp + p \,dV - p\,dV\\ &= \delta Q + V\,dp. \end$ If the system is under constant pressure, and consequently, the increase in enthalpy of the system is equal to the
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...
added: $dH = \delta Q.$ This is why the now-obsolete term ''heat content'' was used in the 19th century.

# Applications

In thermodynamics, one can calculate enthalpy by determining the requirements for creating a system from "nothingness"; the mechanical work required, , differs based upon the conditions that obtain during the creation of the
thermodynamic system A thermodynamic system is a body of matter and/or radiation, confined in space by walls, with defined permeabilities, which separate it from its surroundings. The surroundings may include other thermodynamic systems, or physical systems that a ...
.
Energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of he ...
must be supplied to remove particles from the surroundings to make space for the creation of the system, assuming that the pressure remains constant; this is the term. The supplied energy must also provide the change in internal energy, , which includes activation energies, ionization energies, mixing energies, vaporization energies, chemical bond energies, and so forth. Together, these constitute the change in the enthalpy . For systems at constant pressure, with no external work done other than the work, the change in enthalpy is the heat received by the system. For a simple system with a constant number of particles at constant pressure, the difference in enthalpy is the maximum amount of thermal energy derivable from an isobaric thermodynamic process.

## Heat of reaction

The total enthalpy of a system cannot be measured directly; the ''enthalpy change'' of a
system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and expres ...
is measured instead. Enthalpy change is defined by the following equation: $\Delta H = H_\mathrm - H_\mathrm,$ where * is the "enthalpy change", * is the final enthalpy of the system (in a chemical reaction, the enthalpy of the products or the system at equilibrium), * is the initial enthalpy of the system (in a chemical reaction, the enthalpy of the reactants). For an
exothermic reaction In thermochemistry, an exothermic reaction is a "reaction for which the overall standard enthalpy change Δ''H''⚬ is negative." Exothermic reactions usually release heat. The term is often confused with exergonic reaction, which IUPAC defines ...
at constant
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
, the system's change in enthalpy, , is negative due to the products of the reaction having a smaller enthalpy than the reactants, and equals the heat released in the reaction if no electrical or shaft work is done. In other words, the overall decrease in enthalpy is achieved by the generation of heat. Conversely, for a constant-pressure
endothermic In thermochemistry, an endothermic process () is any thermodynamic process with an increase in the enthalpy (or internal energy ) of the system.Oxtoby, D. W; Gillis, H.P., Butler, L. J. (2015).''Principle of Modern Chemistry'', Brooks Cole. ...
reaction, is positive and equal to the heat ''absorbed'' in the reaction. From the definition of enthalpy as , the enthalpy change at constant pressure is . However for most chemical reactions, the work term is much smaller than the internal energy change , which is approximately equal to . As an example, for the combustion of carbon monoxide 2 CO(g) + O2(g) → 2 CO2(g), and . Since the differences are so small, reaction enthalpies are often described as reaction energies and analyzed in terms of
bond energies In chemistry, bond energy (''BE''), also called the mean bond enthalpy or average bond enthalpy is the measure of bond strength in a chemical bond. IUPAC defines bond energy as the average value of the gas-phase bond-dissociation energy (usually a ...
.

## Specific enthalpy

The specific enthalpy of a uniform system is defined as where is the mass of the system. The
SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...
for specific enthalpy is joule per kilogram. It can be expressed in other specific quantities by , where is the specific
internal energy The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinet ...
, is the pressure, and is specific volume, which is equal to , where is the
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematic ...
.

## Enthalpy changes

An enthalpy change describes the change in enthalpy observed in the constituents of a thermodynamic system when undergoing a transformation or chemical reaction. It is the difference between the enthalpy after the process has completed, i.e. the enthalpy of the
products Product may refer to: Business * Product (business), an item that serves as a solution to a specific consumer problem. * Product (project management), a deliverable or set of deliverables that contribute to a business solution Mathematics * Prod ...
assuming that the reaction goes to completion, and the initial enthalpy of the system, namely the reactants. These processes are specified solely by their initial and final states, so that the enthalpy change for the reverse is the negative of that for the forward process. A common standard enthalpy change is the enthalpy of formation, which has been determined for a large number of substances. Enthalpy changes are routinely measured and compiled in chemical and physical reference works, such as the
CRC Handbook of Chemistry and Physics The ''CRC Handbook of Chemistry and Physics'' is a comprehensive one-volume reference resource for science research. First published in 1914, it is currently () in its 103rd edition, published in 2022. It is sometimes nicknamed the "Rubber Bible ...
. The following is a selection of enthalpy changes commonly recognized in thermodynamics. When used in these recognized terms the qualifier ''change'' is usually dropped and the property is simply termed ''enthalpy of 'process. Since these properties are often used as reference values it is very common to quote them for a standardized set of environmental parameters, or standard conditions, including: * A
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
of one atmosphere (1 atm or 101.325 kPa) or 1 bar * A
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied ...
of 25 °C or 298.15 K * A
concentration In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', '' molar concentration'', '' number concentration'', ...
of 1.0 M when the element or compound is present in solution * Elements or compounds in their normal physical states, i.e.
standard state In chemistry, the standard state of a material (pure substance, mixture or solution) is a reference point used to calculate its properties under different conditions. A superscript circle ° (degree symbol) or a Plimsoll (⦵) character is use ...
For such standardized values the name of the enthalpy is commonly prefixed with the term ''standard'', e.g. ''standard enthalpy of formation''. Chemical properties: *
Enthalpy of reaction The standard enthalpy of reaction (denoted \Delta_ H^\ominus or \Delta H_^\ominus) for a chemical reaction is the difference between total reactant and total product molar enthalpies, calculated for substances in their standard states. This can i ...
, defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of substance reacts completely. * Enthalpy of formation, defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of a compound is formed from its elementary antecedents. * Enthalpy of combustion, defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of a substance burns completely with oxygen. * Enthalpy of hydrogenation, defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of an unsaturated compound reacts completely with an excess of hydrogen to form a saturated compound. * Enthalpy of atomization, defined as the enthalpy change required to separate one mole of a substance into its constituent
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, g ...
s completely. * Enthalpy of neutralization, defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of water is formed when an acid and a base react. * Standard
Enthalpy of solution In thermochemistry, the enthalpy of solution ( heat of solution or enthalpy of solvation) is the enthalpy change associated with the dissolution of a substance in a solvent at constant pressure resulting in infinite dilution. The enthalpy of so ...
, defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of a solute is dissolved completely in an excess of solvent, so that the solution is at infinite dilution. * Standard enthalpy of
Denaturation (biochemistry) In biochemistry, denaturation is a process in which proteins or nucleic acids lose the quaternary structure, tertiary structure, and secondary structure which is present in their native state, by application of some external stress or comp ...
, defined as the enthalpy change required to denature one mole of compound. * Enthalpy of hydration, defined as the enthalpy change observed when one mole of gaseous ions are completely dissolved in water forming one mole of aqueous ions. Physical properties: *
Enthalpy of fusion In thermodynamics, the enthalpy of fusion of a substance, also known as (latent) heat of fusion, is the change in its enthalpy resulting from providing energy, typically heat, to a specific quantity of the substance to change its state from ...
, defined as the enthalpy change required to completely change the state of one mole of substance from solid to liquid. *
Enthalpy of vaporization The enthalpy of vaporization (symbol ), also known as the (latent) heat of vaporization or heat of evaporation, is the amount of energy (enthalpy) that must be added to a liquid substance to transform a quantity of that substance into a gas. T ...
, defined as the enthalpy change required to completely change the state of one mole of substance from liquid to gas. *
Enthalpy of sublimation In thermodynamics, the enthalpy of sublimation, or heat of sublimation, is the heat required to sublimate (change from solid to gas) one mole of a substance at a given combination of temperature and pressure, usually standard temperature and ...
, defined as the enthalpy change required to completely change the state of one mole of substance from solid to gas. * Lattice enthalpy, defined as the energy required to separate one mole of an ionic compound into separated gaseous ions to an infinite distance apart (meaning no force of attraction). * Enthalpy of mixing, defined as the enthalpy change upon mixing of two (non-reacting) chemical substances.

## Open systems

In
thermodynamic Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...
open systems, mass (of substances) may flow in and out of the system boundaries. The first law of thermodynamics for open systems states: The increase in the internal energy of a system is equal to the amount of energy added to the system by mass flowing in and by heating, minus the amount lost by mass flowing out and in the form of work done by the system: $dU = \delta Q + dU_\text - dU_\text - \delta W,$ where is the average internal energy entering the system, and is the average internal energy leaving the system. The region of space enclosed by the boundaries of the open system is usually called a control volume, and it may or may not correspond to physical walls. If we choose the shape of the control volume such that all flow in or out occurs perpendicular to its surface, then the flow of mass into the system performs work as if it were a piston of fluid pushing mass into the system, and the system performs work on the flow of mass out as if it were driving a piston of fluid. There are then two types of work performed: ''flow work'' described above, which is performed on the fluid (this is also often called '' work''), and ''shaft work'', which may be performed on some mechanical device such as a turbine or pump. These two types of work are expressed in the equation $\delta W = d(p_\textV_\text) - d(p_\textV_\text) + \delta W_\text.$ Substitution into the equation above for the control volume (cv) yields: $dU_\text = \delta Q + dU_\text + d(p_\textV_\text) - dU_\text - d(p_\textV_\text) - \delta W_\text.$ The definition of enthalpy, , permits us to use this thermodynamic potential to account for both internal energy and work in fluids for open systems: $dU_\text = \delta Q + dH_\text - dH_\text - \delta W_\text.$ If we allow also the system boundary to move (e.g. due to moving pistons), we get a rather general form of the first law for open systems. In terms of time derivatives it reads: $\frac = \sum_k \dot Q_k + \sum_k \dot H_k - \sum_k p_k\frac - P,$ with sums over the various places where heat is supplied, mass flows into the system, and boundaries are moving. The terms represent enthalpy flows, which can be written as $\dot H_k = h_k\dot m_k = H_\mathrm\dot n_k,$ with the mass flow and the molar flow at position respectively. The term represents the rate of change of the system volume at position that results in power done by the system. The parameter represents all other forms of power done by the system such as shaft power, but it can also be, say, electric power produced by an electrical power plant. Note that the previous expression holds true only if the kinetic energy flow rate is conserved between system inlet and outlet. Otherwise, it has to be included in the enthalpy balance. During steady-state operation of a device (''see
turbine A turbine ( or ) (from the Greek , ''tyrbē'', or Latin ''turbo'', meaning vortex) is a rotary mechanical device that extracts energy from a fluid flow and converts it into useful work. The work produced by a turbine can be used for generatin ...
,
pump A pump is a device that moves fluids (liquids or gases), or sometimes slurries, by mechanical action, typically converted from electrical energy into hydraulic energy. Pumps can be classified into three major groups according to the method they ...
, and
engine An engine or motor is a machine designed to convert one or more forms of energy into mechanical energy. Available energy sources include potential energy (e.g. energy of the Earth's gravitational field as exploited in hydroelectric powe ...
''), the average may be set equal to zero. This yields a useful expression for the average
power Power most often refers to: * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power * Power (social and political), the ability to influence people or events ** Abusive power Power may ...
generation for these devices in the absence of chemical reactions: $P = \sum_k \left\langle \dot Q_k \right\rangle + \sum_k \left\langle \dot H_k \right\rangle - \sum_k \left\langle p_k\frac \right\rangle,$ where the
angle bracket A bracket is either of two tall fore- or back-facing punctuation marks commonly used to isolate a segment of text or data from its surroundings. Typically deployed in symmetric pairs, an individual bracket may be identified as a 'left' or 'r ...
s denote time averages. The technical importance of the enthalpy is directly related to its presence in the first law for open systems, as formulated above.

# Diagrams

The enthalpy values of important substances can be obtained using commercial software. Practically all relevant material properties can be obtained either in tabular or in graphical form. There are many types of diagrams, such as diagrams, which give the specific enthalpy as function of temperature for various pressures, and diagrams, which give as function of for various . One of the most common diagrams is the temperature–specific entropy diagram ( diagram). It gives the melting curve and saturated liquid and vapor values together with isobars and isenthalps. These diagrams are powerful tools in the hands of the thermal engineer.

## Some basic applications

The points a through h in the figure play a role in the discussion in this section. : Points e and g are saturated liquids, and point h is a saturated gas.

## Throttling

One of the simple applications of the concept of enthalpy is the so-called throttling process, also known as Joule–Thomson expansion. It concerns a steady adiabatic flow of a fluid through a flow resistance (valve, porous plug, or any other type of flow resistance) as shown in the figure. This process is very important, since it is at the heart of domestic
refrigerator A refrigerator, colloquially fridge, is a commercial and home appliance consisting of a thermally insulated compartment and a heat pump (mechanical, electronic or chemical) that transfers heat from its inside to its external environment so th ...
s, where it is responsible for the temperature drop between ambient temperature and the interior of the refrigerator. It is also the final stage in many types of liquefiers. For a steady state flow regime, the enthalpy of the system (dotted rectangle) has to be constant. Hence $0 = \dot m h_1 - \dot m h_2.$ Since the mass flow is constant, the specific enthalpies at the two sides of the flow resistance are the same: $h_1 = h_2,$ that is, the enthalpy per unit mass does not change during the throttling. The consequences of this relation can be demonstrated using the diagram above.

### Example 1

Point c is at 200 bar and room temperature (300 K). A Joule–Thomson expansion from 200 bar to 1 bar follows a curve of constant enthalpy of roughly 425 kJ/kg (not shown in the diagram) lying between the 400 and 450 kJ/kg isenthalps and ends in point d, which is at a temperature of about 270 K. Hence the expansion from 200 bar to 1 bar cools nitrogen from 300 K to 270 K. In the valve, there is a lot of friction, and a lot of entropy is produced, but still the final temperature is below the starting value.

### Example 2

Point e is chosen so that it is on the saturated liquid line with = 100 kJ/kg. It corresponds roughly with = 13 bar and = 108 K. Throttling from this point to a pressure of 1 bar ends in the two-phase region (point f). This means that a mixture of gas and liquid leaves the throttling valve. Since the enthalpy is an extensive parameter, the enthalpy in f () is equal to the enthalpy in g () multiplied by the liquid fraction in f () plus the enthalpy in h () multiplied by the gas fraction in f . So $h_\mathbf = x_\mathbf h_\mathbf + (1 - x_\mathbf)h_\mathbf.$ With numbers: , so = 0.64. This means that the mass fraction of the liquid in the liquid–gas mixture that leaves the throttling valve is 64%.

## Compressors

A power is applied e.g. as electrical power. If the compression is adiabatic, the gas temperature goes up. In the reversible case it would be at constant entropy, which corresponds with a vertical line in the diagram. For example, compressing nitrogen from 1 bar (point a) to 2 bar (point b) would result in a temperature increase from 300 K to 380 K. In order to let the compressed gas exit at ambient temperature , heat exchange, e.g. by cooling water, is necessary. In the ideal case the compression is isothermal. The average heat flow to the surroundings is . Since the system is in the steady state the first law gives $0 = -\dot Q + \dot m h_1 - \dot m h_2 + P.$ The minimal power needed for the compression is realized if the compression is reversible. In that case the
second law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unless ...
for open systems gives $0 = -\frac + \dot m s_1 - \dot m s_2.$ Eliminating gives for the minimal power $\frac = h_2 - h_1 - T_\mathrm(s_2 - s_1).$ For example, compressing 1 kg of nitrogen from 1 bar to 200 bar costs at least . With the data, obtained with the diagram, we find a value of 476 kJ/kg. The relation for the power can be further simplified by writing it as $\frac = \int_1^2(dh - T_\mathrm\,ds).$ With , this results in the final relation $\frac = \int_1^2 v\,dp.$

# History and etymology

The term ''enthalpy'' was coined relatively late in the history of thermodynamics, in the early 20th century.
Energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of he ...
was introduced in a modern sense by Thomas Young in 1802, while
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...
was coined by
Rudolf Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Sadi Carnot's principle ...
in 1865. ''Energy'' uses the root of the
Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...
word (''ergon''), meaning "work", to express the idea of capacity to perform work. ''Entropy'' uses the Greek word (''tropē'') meaning ''transformation'' or ''turning''. ''Enthalpy'' uses the root of the Greek word (''thalpos'') "warmth, heat". The term expresses the obsolete concept of ''heat content'', as refers to the amount of heat gained in a process at constant pressure only, but not in the general case when pressure is variable.
Josiah Willard Gibbs Josiah Willard Gibbs (; February 11, 1839 – April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in t ...
used the term "a heat function for constant pressure" for clarity.''The Collected Works of J. Willard Gibbs, Vol. I'' do not contain reference to the word enthalpy, but rather reference the "heat function for constant pressure". See: Introduction of the concept of "heat content" is associated with Benoît Paul Émile Clapeyron and
Rudolf Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Sadi Carnot's principle ...
(
Clausius–Clapeyron relation The Clausius–Clapeyron relation, named after Rudolf Clausius and Benoît Paul Émile Clapeyron, specifies the temperature dependence of pressure, most importantly vapor pressure, at a discontinuous phase transition between two phases of matt ...
, 1850). The term ''enthalpy'' first appeared in print in 1909. It is attributed to
Heike Kamerlingh Onnes Heike Kamerlingh Onnes (21 September 1853 – 21 February 1926) was a Dutch physicist and Nobel laureate. He exploited the Hampson–Linde cycle to investigate how materials behave when cooled to nearly absolute zero and later to liquefy heliu ...
, who most likely introduced it orally the year before, at the first meeting of the Institute of Refrigeration in Paris. It gained currency only in the 1920s, notably with the '' Mollier Steam Tables and Diagrams'', published in 1927. Until the 1920s, the symbol was used, somewhat inconsistently, for "heat" in general. The definition of as strictly limited to enthalpy or "heat content at constant pressure" was formally proposed by Alfred W. Porter in 1922.; see p. 140.

* Standard enthalpy change of formation (data table) *
Calorimetry In chemistry and thermodynamics, calorimetry () is the science or act of measuring changes in '' state variables'' of a body for the purpose of deriving the heat transfer associated with changes of its state due, for example, to chemical rea ...
*
Calorimeter A calorimeter is an object used for calorimetry, or the process of measuring the heat of chemical reactions or physical changes as well as heat capacity. Differential scanning calorimeters, isothermal micro calorimeters, titration calorimete ...
* Departure function * Hess's law * Isenthalpic process *
Laws of thermodynamics The laws of thermodynamics are a set of scientific laws which define a group of physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems in thermodynamic equilibrium. The laws also use various paramet ...
* Stagnation enthalpy * Thermodynamic databases for pure substances

* * * * * * *