Enthalpy
Statistical mechanics 
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Key topics 
Statistical thermodynamics Kinetic theory 
Particle Statistics 
MaxwellBoltzmann BoseEinstein · FermiDirac 
Ensembles 
Microcanonical · Canonical Grand canonical Isothermal–isobaric Isoenthalpic–isobaric 
Thermodynamics 
Gas laws · Carnot cycle · DulongPetit 
Models 
Debye · Einstein · Ising 
Potentials 
Internal energy · Enthalpy Helmholtz free energy Gibbs free energy 
Scientists

In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H, h, or rarely as χ) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the "useful" work obtainable from a closed thermodynamic system under constant pressure and entropy.
The term enthalpy was composed of the prefix en, meaning to "put into" and the Greek word thalpein, meaning "to heat", although the original definition is thought to have stemmed from the word "enthalpos" (ἐνθάλπος).^{[1]}
History
Over the history of thermodynamics, several terms have been used to denote what is now known as the enthalpy of a system. Originally, it was thought that the word "enthalpy" was created by Benoit Paul Émile Clapeyron and Rudolf Clausius through the publishing of the ClausiusClapeyron relation in "The Mollier Steam Tables and Diagrams" in 1827, but it was later published that the earliest recording of the word was in 1875, by Josiah Willard Gibbs in the publication "Physical Chemistry: an Advanced Treatise"^{[2]}, although it is not referenced in Gibbs' works directly^{[3]}. In 1909, Keith Landler discussed Gibbs' work on the 'heat function for constant pressure' and noted that Heike Kamerlingh Onnes had coined its modern name from the Greek word "enthalpos" (ενθαλπος) meaning "to put heat into." ^{[1]}
Original definition
This is the heat change which occurs when 1 mol of a substance reacts completely with oxygen to form products at 298 K and 1 atm. The function H was introduced by the Dutch physicist Heike Kamerlingh Onnes in early 20th century in the following form:
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): H = E + pV,\,
where E represents the energy of the system. In the absence of an external field, the enthalpy may be defined, as it is generally known, by:
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): H = U + pV,\,
where (all units given in SI)
 H is the enthalpy (joules)
 U is the internal energy, (joules)
 p is the pressure of the system, (pascals)
 V is the volume, (cubic metres)
Application and extended formula
Overview
In terms of thermodynamics, enthalpy can be calculated by determining the requirements for creating a system from "nothingness"; the mechanical work required, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): pV differs, based upon the constancy of conditions present at the creation of the thermodynamic system.
Internal energy, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): U , must be supplied to remove particles from a surrounding in order to allow space for the creation of a system, providing that environmental variables, such as pressure (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): p ) remain constant. This internal energy also includes the energy required for activation and the breaking of bonded compounds into gaseous species.
This process is calculated within enthalpy calculations as Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): U + pV , to label the amount of energy or work required to "set aside space for" and "create" the system; describing the work done by both the reaction or formation of systems, and the surroundings. For systems at constant pressure, the change in enthalpy is the heat received by the system plus the nonmechanical work that has been done.
Therefore, the change in enthalpy can be devised or represented without the need for compressive or expansive mechanics; for a simple system, with a constant number of particles, the difference in enthalpy is the maximum amount of thermal energy derivable from a thermodynamic process in which the pressure is held constant.
The term Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): p Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): V is the work required to displace the surrounding atmosphere in order to vacate the space to be occupied by the system.
Relationships
As an expansion of the first law of thermodynamics, enthalpy can be related to several other thermodynamic formulae. As with the original definition of the first law;
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \mathrm{d}U = \delta Q + \delta W\,
 Where, as defined by the law;
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \mathrm{d}U represents the infinitesimal increase of the systematic or internal energy.
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \delta Q represents the infinitesimal amount of energy attributed or added to the system.
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \delta W represents the infinitesimal amount of energy acted out by the system on the surroundings.
As a differentiating expression, the value of H can be defined as
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \mathrm{d}H = \mathrm{d}U + (p\,\mathrm{d}V + V\mathrm{d}p) \!
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): = (\delta Q  p\,\mathrm{d}V) + (p\,\mathrm{d}V + V\mathrm{d}p) \!
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): = \delta Q +V\mathrm{d}p = T\mathrm{d}S + V\mathrm{d}p \!
Where








For a process that is not reversible, the second law of thermodynamics states that the increase in heat Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \delta Q is less than or equal to the product Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): T\mathrm{d}S of temperature Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): T and the increase in entropy Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \mathrm{d}S ; thus
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \mathrm{d}H = \delta Q + V\mathrm{d}p \le T\mathrm{d}S+V\mathrm{d}p\,
It is seen that, if a thermodynamic process is isobaric (i.e., occurs at constant pressure), then Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \mathrm{d}p is zero and thus
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \mathrm{d}H = \delta Q \le T\mathrm{d}S \,
The difference in enthalpy is the maximum thermal energy attainable from the system in an isobaric process. This explains why it is sometimes called the heat content. That is, the integral of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \mathrm{d}H over any isobar in state space is the maximum thermal energy attainable from the system.
If, in addition, the entropy is held constant as well, i.e., Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \mathrm{d}S = 0 , the above equation becomes:
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \mathrm{d}H \le 0\,
with the equality holding at equilibrium. It is seen that the enthalpy for a general system will continuously decrease to its minimum value, which it maintains at equilibrium.
In a more general form, the first law describes the internal energy with additional terms involving the chemical potential and the number of particles of various types. The differential statement for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \mathrm{d}H is then:
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): dH = \delta Q + V\mathrm{d}p + \sum_i \mu_i \,\mathrm{d}N_i \le T\mathrm{d}S+V\mathrm{d}p + \sum_i \mu_i \,\mathrm{d}N_i\,
where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \mu_i is the chemical potential for an itype particle, and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): N_i is the number of such particles. It is seen that, not only must the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): V\mathrm{d}p term be set to zero by requiring the pressures of the initial and final states to be the same, but the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \mu_i \mathrm{d}N_i terms must be zero as well, by requiring that the particle numbers remain unchanged. Any further generalization will add even more terms whose extensive differential term must be set to zero in order for the interpretation of the enthalpy to hold.
Heats of reaction
The total enthalpy of a system cannot be measured directly; the enthalpy change of a system is measured instead. Enthalpy change is defined by the following equation:
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \Delta H = H_\mathrm{final}  H_\mathrm{initial} \,
where
 ΔH is the enthalpy change
 H_{final} is the final enthalpy of the system, measured in joules. In a chemical reaction, H_{final} is the enthalpy of the products.
 H_{initial} is the initial enthalpy of the system, measured in joules. In a chemical reaction, H_{initial} is the enthalpy of the reactants.
For an exothermic reaction at constant pressure, the system's change in enthalpy is equal to the energy released in the reaction, including the energy retained in the system and lost through expansion against its surroundings. In a similar manner, for an endothermic reaction, the system's change in enthalpy is equal to the energy absorbed in the reaction, including the energy lost by the system and gained from compression from its surroundings. A relatively easy way to determine whether or not a reaction is exothermic or endothermic is to determine the sign of ΔH. If ΔH is positive, the reaction is endothermic, that is heat is absorbed by the system due to the products of the reaction having a greater enthalpy than the reactants. On the other hand if ΔH is negative, the reaction is exothermic, that is the overall decrease in enthalpy is achieved by the generation of heat.
Although enthalpy is commonly used in engineering and science, it is impossible to measure directly, as enthalpy has no datum (reference point). Therefore enthalpy can only accurately be used in a closed system. However, few real world applications exist in closed isolation, and it is for this reason that two or more closed systems cannot be compared using enthalpy as a basis, although sometimes this is done erroneously.
Open systems
In thermodynamic open systems, matter 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 matter flowing in and by heating, minus the amount lost by matter flowing out and in the form of work done by the system. The first law for open systems is given by:
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \mathrm{d}U= \mathrm{d}U_{in}\mathrm{d}U_{out}+\delta Q\delta W\,
where U_{in} is the average internal energy entering the system and U_{out} is the average internal energy leaving the system
The region of space enclosed by open system boundaries 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 matter 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 matter 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): pV work) and shaft work which may be performed on some mechanical device.
These two types of work are expressed in the equation:
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \delta W=\mathrm{d}(p_{out}V_{out})\mathrm{d}(p_{in}V_{in})+\delta W_{shaft}\,
Substitution into the equation above for the control volume cv yields:
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \mathrm{d}U_{cv}=\mathrm{d}U_{in}+\mathrm{d}(p_{in}V_{in})  \mathrm{d}U_{out}\mathrm{d}(p_{out}V_{out})+\delta Q\delta W_{shaft}\,
The definition of enthalpy, H, permits us to use this thermodynamic potential to account for both internal energy and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): pV work in fluids for open systems:
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \mathrm{d}U_{cv}=\mathrm{d}H_{in}\mathrm{d}H_{out}+\delta Q\delta W_{shaft}\,
During steadystate operation of a device (see turbine, pump, and engine), the expression above may be set equal to zero. This yields a useful expression for the power generation or requirement for these devices in the absence of chemical reactions:
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \frac{\delta W_{shaft}}{\mathrm{d}t}=\frac{\mathrm{d}H_{in}}{\mathrm{d}t} \frac{\mathrm{d}H_{out}}{\mathrm{d}t}+\frac{\delta Q}{\mathrm{d}t} \,
This expression is described by the diagram above.
Standard enthalpy changes
Standard enthalpy changes describe the change in enthalpy observed in the constituents of a thermodynamic system when going between different states under standard conditions. The standard enthalpy of vaporization, for example gives the enthaply change when going from liquid and gas, these entalpies are reversible, then enthalpy of going from gas to liquid is negative of the enthalpy of vaporization. A common standard enthalpy change is the standard enthalpy change of formation, which has been determined for a vast number of substances. The enthalpy change of any reaction under any conditions can be computed, given the standard enthalpy change of formation of all of the reactants and products.
Definitions
Chemical Properties
Standard enthalpy change of reaction
“  Standard enthalpy change of reaction is defined as the enthalpy change observed in a constituent of a themodynamic system when, one mole of substance reacts completley under under standard conditions.  ” 
Standard enthalpy change of formation
“  Standard enthalpy change of formation is 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 under standard conditions.  ” 
Standard enthalpy change of combustion
“  Standard enthalpy of combustion is defined as the enthalpy change observed in a constituent of a thermodynamic system, when one mole of a substance combusts completley with oxygen under standard conditions.  ” 
Standard enthalpy change of hydrogenation
“  Standard enthalpy of hydrogenation is 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 under standard conditions to form a saturated compound.  ” 
Standard enthalpy change of atomization
“  Standard enthalpy of hydrogenation is defined as the enthalpy change required to atomize one mole of compound completley under standard conditions.  ” 
Physical Properties
Standard enthalpy change of solution
“  Standard enthalpy of hydrogenation is defined as the enthalpy change observed in a constituent of a thermodynamic system, when one mole of an solute is dissolved completely in an excess of solvent under standard conditions.  ” 
Standard enthalpy change of fusion
“  Standard enthalpy of hydrogenation is defined as the enthalpy change required to completley change the state of one mole of substance between solid and liquid states under standard conditions.  ” 
Standard enthalpy change of vapourization
“  Standard enthalpy of hydrogenation is defined as the enthalpy change required to completley change the state of one mole of substance between liquid and gaseous states under standard conditions.  ” 
Standard enthalpy change of denaturation
“  Standard enthalpy of hydrogenation is defined as the enthalpy change required to denature one mol of compound under standard conditions.  ” 
“  Lattice enthalpy is defined as the enthalpy required required to separate one mole of an ionic compound into separated gaseous ions to an infinite distance apart (meaning no force of attraction) under standard conditions.  ” 
Specific enthalpy
The specific enthalpy of a working mass is a property of that mass used in thermodynamics, defined as Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): h=u+p \cdot v where u is the specific internal energy, p is the pressure, and v is specific volume. In other words, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): h = H/m where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): m is the mass of the system. The SI unit for specific enthalpy is joules per kilogram.
See also
 Calorimetry
 Calorimeter
 Departure function
 Entropy
 Hess's law
 Isenthalpic process
 Thermodynamic databases for pure substances
Notes
 ↑ ^{1.0} ^{1.1} The World of Chemistry noted that whilst ruminating on the origin being credited to Gibbs, the original word was created by Onnes, who had specified its derivation.
 ↑ Physical Chemistry: An Advanced Treatise States that the original creator of the word was Josiah Willard Gibbs, who noted "the familiar definition of enthalpy as introduced by Gibbs in 1875 (‘heat function for constant pressure’)”"
 ↑ 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.
References
 Haase, R. In Physical Chemistry: An Advanced Treatise; Jost, W., Ed.; Academic: New York, 1971; p 29.
 Gibbs, J. W. In The Collected Works of J. Willard Gibbs, Vol. I; Yale University Press: New Haven, CT, reprinted 1948; p 88.
 Laidler, K. The World of Physical Chemistry; Oxford University Press: Oxford, 1995; p 110.
 C.Kittel, H.Kroemer In Thermal Physics; W.H.Freeman and Company, New York, 1980; p246
External links
 Enthalpy  Eric Weisstein's World of Physics
 Enthalpy  Georgia State University
 Enthalpy  KnowAllAbout.com
 Enthalpy (example calculations)  Texas A&M University (Chemistry Department)
 Enthalpy  Water and Steam Enthalpy
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