TheInfoList

Enthalpy , a property of a
thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, whic ...
, is the sum of the system's
internal energy The internal energy of a thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that ca ...
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 is a function defined for a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form ...
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 * Work (physics), the product of ...

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) In finance Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of ...
, lattice,
solvation Solvation (or dissolution) describes the interaction of solvent A solvent (from the Latin language, Latin ''wikt:solvo#Latin, solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usual ...

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 Pleonasm#Acronyms_and_initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wi ...
(SI), the unit of measurement for enthalpy is the
joule The joule ( ; symbol: J) is a SI derived unit, derived unit of energy in the International System of Units. It is equal to the energy transferred to (or work (physics), work done on) an object when a force of one Newton (unit), newton acts on th ...

. Other historical conventional units still in use include the
calorie The calorie is a unit of energy Unit may refer to: Arts and entertainment * UNIT Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a di ...
and the
British thermal unit The British thermal unit (BTU or Btu) is a unit of heat In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physica ...
(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 is the physical quantity, quantitative physical property, property that must be #Energy transfer, transferred to a physical body, body or physical system to perform Work (thermodynamics), work on the body, or to heat it. En ...

. 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 Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these ...

. In chemistry, the standard
enthalpy of reaction The standard enthalpy of reaction (denoted \Delta H_^\ominus or \Delta H_^\ominus) is the difference between total reactant and total product enthalpy, enthalpies due to a chemical reaction, from reactants in their standard states to products in the ...
is the enthalpy change when reactants in their
standard state In chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds composed of atoms, ...
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 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 is a function defined for a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form ...
. 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 Thermochemistry is the study of the heat energy which is associated with chemical reactions and/or physical transformations. A reaction may release or absorb energy, and a phase change may do the same, such as in melting and bo ...
(heat-absorbing) processes, the change is a positive value; for
exothermic In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these qu ...

(heat-releasing) processes it is negative. The enthalpy of an
ideal gas An ideal gas is a theoretical gas Gas is one of the four fundamental states of matter In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion ...
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, is
pressure Pressure (symbol: ''p'' or ''P'') is the force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving fr ...

, and is the
volume Volume is a scalar quantity expressing the amount Quantity or amount is a property that can exist as a multitude Multitude is a term for a group of people who cannot be classed under any other distinct category, except for their shared fact ...
of the system. Enthalpy is an
extensive property Extensive may refer to: * Extensive property * Extensive function * Extensional See also * Extension (disambiguation) {{Dab ...
; it is proportional to the size of the system (for homogeneous systems). As
intensive properties Physical properties A physical property is any property Property (''latin: Res Privata'') in the Abstract and concrete, abstract is what belongs to or with something, whether as an attribute or as a component of said thing. In the context of ...
, the
specific enthalpy Enthalpy , a property of a , is the sum of the system's and the product of its pressure and volume. It is a used in many measurements in chemical, biological, and physical systems at a constant pressure, which is conveniently provided by the la ...
is referenced to a unit of
mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value ...
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 Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "P ...

, 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 and a point or object. The exact definition and reference datum varies according to the context (e.g. ...

, 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 In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or othe ...
density also varies with altitude.) Then the enthalpy summation becomes an
integral In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...

: $H = \int (\rho h) \, dV,$ where * ("
rho Rho (uppercase Ρ, lowercase ρ or ; el, ῥῶ) is the 17th letter of the Greek alphabet The Greek alphabet has been used to write the Greek language since the late ninth or early eighth century BC. It is derived from the earlier Phoenician ...
") is
density The density (more precisely, the volumetric mass density; also known as specific mass), of a substance is its per unit . The symbol most often used for density is ''ρ'' (the lower case Greek letter ), although the Latin letter ''D'' can also ...

(mass per unit volume), * is the specific enthalpy (enthalpy per unit mass), * represents the (enthalpy per unit volume), * denotes an
infinitesimal In mathematics, infinitesimals or infinitesimal numbers are quantities that are closer to zero than any standard real number, but are not zero. They do not exist in the standard real number system, but do exist in many other number systems, such a ...
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 version of the law of conservation of energy, adapted for thermodynamic processes, distinguishing three kinds of transfer of energy, as heat, as thermodynamic work, and as energy associated with matter tran ...
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 establishes the concept of 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 an ...
gives , with the
absolute temperature Thermodynamic temperature is a quantity defined in thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of ...
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 thermodynamic ...

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 Gas is one of the four fundamental states of matter In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion ...
, 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 Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, radiation, and physical properties of matter. The behavior of these quantities is governed ...

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 In the Thermodynamics#Equilibrium_thermodynamics, thermodynamics of equilibrium, a state function, function of state, or point function is a function defined for a system relating several state variables or state quantities that depends only on the ...
, its arguments include both one intensive and several extensive
state variable A state variable is one of the set of variables that are used to describe the mathematical "state"of a dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of ...
s. 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 In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, radiation, and physical properties of matter. The behavior of these quantities is govern ...
that is used in
meteorology Meteorology is a branch of the (which include and ), with a major focus on . The study of meteorology dates back , though significant progress in meteorology did not begin until the 18th century. The 19th century saw modest progress in the f ...
. 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 * Work (physics), the product of ...
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 scalar quantity expressing the amount Quantity or amount is a property that can exist as a multitude Multitude is a term for a group of people who cannot be classed under any other distinct category, except for their shared fact ...
at
pressure Pressure (symbol: ''p'' or ''P'') is the force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving fr ...

and
temperature Temperature ( ) is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy refers to several distinct physical concept ...

, is created or brought to its present state from
absolute zero Absolute zero is the lowest limit of the thermodynamic temperature Thermodynamic temperature is the measure of ''absolute temperature'' and is one of the principal parameters of thermodynamics. A thermodynamic temperature reading of zero deno ...
, 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 * Work (physics), the product of ...

done in pushing against the ambient (atmospheric) pressure. In
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical scie ...

and
statistical mechanics In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
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 Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in the real world. T ...

, experiments are often conducted at constant
atmospheric pressure Atmospheric pressure, also known as barometric pressure (after the barometer A barometer is a scientific instrument that is used to measure air pressure Atmospheric pressure, also known as barometric pressure (after the barometer), is the ...
, 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 work (physics), mechanical work. It does this by bringing a working substance from a higher state temperature to ...

, 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 An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical condu ...
, or friction from stirring by a shaft with paddles or by an externally driven magnetic field acting on an internal rotor (which is surroundings-based work, but contributes to system-based heat Schmidt-Rohr, K. (2014). "Expansion Work without the External Pressure, and Thermodynamics in Terms of Quasistatic Irreversible Processes", ''J. Chem. Educ.'' 91: 402-409. http://dx.doi.org/10.1021/ed3008704 ). 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 Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these ...

added or given off: $dH = \delta Q.$ 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 In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, whic ...
.
Energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regula ...

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 , 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 Interaction, 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 purp ...
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 of reaction, standard enthalpy change Δ''H''⚬ is negative." Exothermic reactions usually release heat and entail the replacement of weak bonds wi ...
at constant
pressure Pressure (symbol: ''p'' or ''P'') is the force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving fr ...

, 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 Thermochemistry is the study of the heat energy which is associated with chemical reactions and/or physical transformations. A reaction may release or absorb energy, and a phase change may do the same, such as in melting and bo ...
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 The metric system is a that succeeded the decimal ...
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 A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that ca ...
, is the pressure, and is
specific volumeIn thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantiti ...
, which is equal to , where is the
density The density (more precisely, the volumetric mass density; also known as specific mass), of a substance is its per unit . The symbol most often used for density is ''ρ'' (the lower case Greek letter ), although the Latin letter ''D'' can also ...

.

## 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 * Produc ...
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 formationThe standard enthalpy of formation or standard heat of formation of a compound is the change of enthalpy Enthalpy is a property of a thermodynamic system A thermodynamic system is a body of matter and/or radiation, confined in space by walls, wi ...
, 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 102nd edition, published in 2021. 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 Standard temperature and pressure (STP) are standard Standard may refer to: Flags * Colours, standards and guidons * Standard (flag), a type of flag used for personal identification Norm, convention or requirement * Standard (metrology), a ...
, including: * A
pressure Pressure (symbol: ''p'' or ''P'') is the force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving fr ...

of one atmosphere (1 atm or 101.325 kPa) or 1 bar * A
temperature Temperature ( ) is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy refers to several distinct physical concept ...

of 25 °C or 298.15 K * A
concentration In chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in t ...

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 Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds composed of atoms, ...
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) is the difference between total reactant and total product enthalpy, enthalpies due to a chemical reaction, from reactants in their standard states to products in the ...
, defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of substance reacts completely. *
Enthalpy of formationThe standard enthalpy of formation or standard heat of formation of a compound is the change of enthalpy Enthalpy is a property of a thermodynamic system A thermodynamic system is a body of matter and/or radiation, confined in space by walls, wi ...
, 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 The heating value (or energy value or calorific value) of a substance Substance may refer to: * Substance (Jainism), a term in Jain ontology to denote the base or owner of attributes * Chemical substance, a material with a definite chemical composi ...
, 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 The enthalpy of atomization (also atomisation in British English) is the enthalpy change that accompanies the total separation of all atoms An atom is the smallest unit of ordinary matter that forms a chemical element Image:Simple Periodi ...
, defined as the enthalpy change required to separate one mole of a substance into its constituent
atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of ato ...

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 The enthalpy of solution, enthalpy of dissolution, or heat of solution is the enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function ...
, 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) Denaturation is a process in which protein Proteins are large biomolecule , showing alpha helices, represented by ribbons. This poten was the first to have its suckture solved by X-ray crystallography by Max Perutz and Sir John Cowde ...
, 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 The enthalpy of fusion of a substance, also known as (latent) heat of fusion is the change in its enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It ...
, 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 Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy an ...
, defined as the enthalpy change required to completely change the state of one mole of substance from liquid to gas. *
Enthalpy of sublimation The enthalpy of sublimation, or heat of sublimation, is the heat required to change one mole of a substance from solid state to gaseous state at a given combination of temperature Temperature is a physical quantity that expresses hot an ...
, 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 The enthalpy of mixing (or heat of mixing or excess enthalpy) is the enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in m ...
, defined as the enthalpy change upon mixing of two (non-reacting) chemical substances.

## Open systems

In
thermodynamic Thermodynamics is a branch of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related ent ...
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 In continuum mechanics and thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, radiation, and physical properties of matter. The behavior of the ...

, 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 A thermodynamic potential (or more accurately, a thermodynamic potential energy)ISO/IEC 80000-5, Quantities an units, Part 5 - Thermodynamics, item 5-20.4 Helmholtz energy, Helmholtz functionISO/IEC 80000-5, Quantities an units, Part 5 - Thermodyn ...
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 In systems theory, a system or a Process theory, process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those pro ...
operation of a device (''see
turbine A turbine ( or ) (from the Greek , ''tyrbē'', or Latin Latin (, or , ) is a classical language A classical language is a language A language is a structured system of communication Communication (from Latin ''communicare'', ...

,
pump A pump is a device that moves fluids (liquid A liquid is a nearly incompressible In fluid mechanics or more generally continuum mechanics, incompressible flow (isochoric process, isochoric flow) refers to a fluid flow, flow in which the ...

, and
engine An engine or motor is a machine A machine is any physical system with ordered structural and functional properties. It may represent human-made or naturally occurring device molecular machine that uses Power (physics), power to apply For ...

''), the average may be set equal to zero. This yields a useful expression for the average
power Power most often refers to: * Power (physics) In physics, power is the amount of energy In , energy is the that must be to a or to perform on the body, or to it. Energy is a ; the law of states that energy can be in form, bu ...
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 Punctuation (or sometimes interpunction) is the use of spacing, conventional signs (called punctuation marks), and certain typographical devices as aids to the understanding ...
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 A home appliance, also referred to as a domestic appliance, an electric appliance or a household appliance, is a machine which assists in household A household co ...

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. 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. 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 , 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 establishes the concept of 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 an ...
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 Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regula ...

was introduced in a modern sense by 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 thermodynamic ...

was coined by
Rudolf Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German German(s) may refer to: Common uses * of or related to Germany * Germans, Germanic ethnic group, citizens of Germany or people of German ancestry * For citize ...
in 1865. ''Energy'' uses the root of the
Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximately 10.7 million as of ...
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 tr ...

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 Benoît Paul Émile Clapeyron (; 26 January 1799 – 28 January 1864) was a French engineer Engineers, as practitioners of engineering, are Professional, professionals who Invention, invent, design, analyze, build and test Machine, machines, co ...
and
Rudolf Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German German(s) may refer to: Common uses * of or related to Germany * Germans, Germanic ethnic group, citizens of Germany or people of German ancestry * For citize ...
(
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 matter o ...
, 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 A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, are ...
, 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 Calorimetry is the science or act of measuring changes in '' state variables'' of a body for the purpose of deriving the heat transfer Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and ...
*
Calorimeter A calorimeter is an object used for calorimetry, or the process of measuring the heat of chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classicall ...

* Departure function * Hess's law * Isenthalpic process * Laws of thermodynamics * Stagnation enthalpy * Thermodynamic databases for pure substances

* * * * * * *