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In thermodynamics and molecular chemistry, enthalpy (denoted as H, or specific enthalpy denoted as h) is a thermodynamic property of a thermodynamic system. It can be used to calculate the heat transfer during a quasistatic process taking place in a closed thermodynamic system under constant pressure (isobaric process). Change in enthalpy ΔH is frequently a more useful value than H itself. For quasistatic processes under constant pressure, ΔH is equal to the change in the internal energy of the system, plus the work that the system has done on its surroundings.[1] This means that the change in enthalpy under such conditions is the heat absorbed by a chemical reaction.

## Etymology

The term enthalpy comes from the prefix ἐν-, en-, meaning "to put into", and the Classical Greek verb θάλπειν, thalpein, meaning "to heat". The original definition is thought to have stemmed from the Neoclassical Greek adjective "enthalpos" (ἔνθαλπος).[note 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 Clausius-Clapeyron relation in The Mollier Steam Tables and Diagrams in 1827. Josiah Willard Gibbs introduced a "heat function for constant pressure" in 1875,[2] although the word enthalpy does not appear in any of Gibbs' work. In 1909, Keith Landler discussed Gibbs's work on this "heat function" and noted that Heike Kamerlingh Onnes had coined the modern name from the Greek word "enthalpos" (ενθαλπος) meaning "to put heat into."[note 1]

### Original definition

The thermodynamic potential H was introduced by the Dutch physicist Kamerlingh Onnes in early 20th century in the following form:

$H = E + pV,\,$

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:

$H = U + pV,\,$

where (all units given in SI)

H is the enthalpy (in joules),
U is the internal energy (in joules),
p is the pressure of the system, (in pascals), and
V is the volume, (in cubic meters).

The form pV (sometimes called "flow work") is motivated by the following example of an isobaric process. Gas producing heat (by, for example, a chemical reaction) in a cylinder pushes a piston, maintaining constant pressure p and adding to its thermal energy. The force is calculated from the area A of the piston and definition of pressure p = F/A: the force is F = pA. By definition, work W done is W = Fx, where x is the distance traversed. Combining gives W = pAx, and the product Ax is the volume traversed by the piston: Ax = V. Thus, the work done by the gas is W = pV, where p is a constant pressure and V the expansion of volume. Including this term allows the discussion of energy changes when not only temperature, but also volume or pressure are changed. The enthalpy change can be defined ΔH = ΔU + W = ΔU + Δ(pV), where ΔU is the thermal energy due to heating of the gas during the expansion, and W the work done on the piston.

## Difference between H and U: the additional term pV

If pV is an additional energy associated with the system (say, a gas), and is not in the internal energy U, then where is it? H is routinely used in chemistry as the energy of the system, so a convincing explanation for where this energy resides is in order. In a nutshell, the energy pV is in the surroundings (typically, the atmosphere). When a system (e.g., n moles of a gas of volume V at pressure P and temperature T) is created (brought to its present state from absolute zero), energy must be supplied equal to its internal energy U plus pV, where pV is the work done in pushing against the ambient (atmospheric) pressure. This additional energy is therefore stored in the surroundings (atmosphere) and can be recovered when the system collapses back to its initial state. In basic chemistry we are typically interested in experiments done at atmospheric pressure (or some ambient pressure P), and for reaction energy calculations care about the total energy in such (real) conditions and therefore typically need to use H. In basic physics / thermodynamics we may be more interested in the internal properties of the system and therefore in the internal energy U.

## 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, pV, differs based upon the constancy of conditions present at the creation of the thermodynamic system.

Internal energy, 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 (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 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.

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 pV 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;

$\mathrm{d}U=\delta Q-\delta W\,$

where, as defined by the law;

dU represents the infinitesimal increase of the systematic or internal energy,
δQ represents the infinitesimal amount of energy attributed or added to the system, and
δW represents the infinitesimal amount of energy acted out by the system on the surroundings.

As a differential expression, the value of H can be defined as[3]

\begin{align} \mathrm{d}H &= \mathrm{d}(U+ pV) \ &= \mathrm{d}U+\mathrm{d}(pV) \ &= \mathrm{d}U+(p\,\mathrm{d}V+V\,\mathrm{d}p) \ &= (\delta Q-p\,\mathrm{d}V)+(p\,\mathrm{d}V+V\,\mathrm{d}p) \ &= \delta Q+V\,\mathrm{d}p \ &= T\,\mathrm{d}S+V\,\mathrm{d}p \end{align}

where

δ represents the inexact differential,
U is the internal energy,
δQ = TdS is the energy added by heating during a reversible process,
δW = pdV is the work done by the system in a reversible process,
dS is the increase in entropy (joules per kelvin),
p is the constant pressure,
dV is an infinitesimal volume, and
T is the temperature (kelvins).

For a process that is not reversible, the above equation expressing dH in terms of dS and dp still holds because H is a thermodynamic state variable that can be uniquely specified by S and p. We thus have in general:

dH = TdS + Vdp

It is seen that, if a thermodynamic process is isobaric (i.e., occurs at constant pressure), then dp is zero and thus

dH = TdS ≥ δQ

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 dH over any isobar in state space is the maximum thermal energy attainable from the system.

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 dH is then:

$dH = T\mathrm{d}S+V\mathrm{d}p + \sum_i \mu_i \,\mathrm{d}N_i\,$

where μi is the chemical potential for an i-type particle, and Ni is the number of such particles. It is seen that, not only must the Vdp term be set to zero by requiring the pressures of the initial and final states to be the same, but the μidNi 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:

ΔH = HfinalHinitial

where

ΔH  is the enthalpy change
Hfinal is the final enthalpy of the system, expressed in joules. In a chemical reaction, Hfinal is the enthalpy of the products.
Hinitial is the initial enthalpy of the system, expressed in joules. In a chemical reaction, Hinitial 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:

dU = dUin − dUout + δQ − δW

where Uin is the average internal energy entering the system and Uout is the average internal energy leaving the system

During steady, continuous operation, an energy balance applied to an open system equates shaft work performed by the system to heat added plus net enthalpy added.

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 pV work) and shaft work which may be performed on some mechanical device.

These two types of work are expressed in the equation:

δW = d(poutVout) − d(pinVin) + δWshaft.

Substitution into the equation above for the control volume cv yields:

dUcv = dUin + d(pinVin) − dUout − d(poutVout) + δQ − δWshaft.

The definition of enthalpy, H, permits us to use this thermodynamic potential to account for both internal energy and pV work in fluids for open systems:

dUcv = dHin − dHout + δQ − δWshaft.

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, 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:

$\frac{\delta W_{shaft}}{\mathrm{d}t}=\frac{\mathrm{d}H_{in}}{\mathrm{d}t}- \frac{\mathrm{d}H_{out}}{\mathrm{d}t}+\frac{\delta Q}{\mathrm{d}t}. \,$

This expression is described by the diagram above.

### Specific enthalpy

The specific enthalpy of a working mass is a property of that mass used in thermodynamics. It is defined as h = u + pv, where u is the specific internal energy, p is the pressure, and v is specific volume. In other words, h = H/m where m is the mass of the system. The SI unit for specific enthalpy is joules per kilogram.

## 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 change of vaporization, for example gives the enthalpy change when going from liquid to gas. These enthalpies are reversible; the enthalpy change of going from gas to liquid is the negative of the enthalpy change of vaporization. A common standard enthalpy change is the standard enthalpy change of formation, which has been determined for a large 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

#### Physical Properties

• Standard enthalpy change of solution, 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, defined as the enthalpy change required to completely change the state of one mole of substance between solid and liquid states under standard conditions.
• Standard enthalpy change of vapourization, defined as the enthalpy change required to completely change the state of one mole of substance between liquid and gaseous states under standard conditions.
• Standard enthalpy change of sublimation, defined as the enthalpy change required to completely change the state of one mole of substance between solid and gaseous states under standard conditions.
• Standard enthalpy change of denaturation, defined as the enthalpy change required to denature one mole of compound under standard conditions.
• Lattice enthalpy, defined as the enthalpy 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.

## Notes

1. ^ a b 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.

## 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; S.R Furphy and Company, New York, 1980; p246
• DeHoff, R. Thermodynamics in Materials Science: 2nd ed.; Taylor and Francis Group, New York, 2006.
1. ^ G.J. Van Wylen and R.E. Sonntag (1985), Fundamentals of Classical Thermodynamics, Section 5.5 (3rd edition), John Wiley & Sons Inc. New York, NY. ISBN 0 471 82933 1
2. ^ Henderson, Douglas; Eyring, Henry; Jost, Wilhelm (1967). Physical Chemistry: An Advanced Treatise. Academic Press.
3. ^ DeHoff p 57

# Simple English

Enthalpy is a concept used in science and engineering when heat and work need to be calculated.

In the study of heat, both in engineering and chemistry, enthalpy (written as H) is a useful measure that scientists have developed to find out how much work has been done, or heat absorbed, when a gas changes its size at a constant pressure.

The name comes from the Greek word "enthalpos" (ενθαλπος), meaning "to put heat into". The idea and the word was made up by the Dutch scientist Heike Kamerlingh Onnes in 1909.