In thermodynamics, the quantity enthalpy, symbolized by H, also called heat content, is the sum of the internal energy of a thermodynamic system plus the energy associated with work done by the system on the atmosphere which is the product of the pressure times the volume. The term enthalpy is composed of the prefix en-, meaning to "put into", plus the Greek suffix -thalpein, meaning "to heat".

History

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The function H was introduced by the Dutch physicist Kamerlingh Onnes in late 19th century in the following form:

$H\; =\; E\; +\; PV\; \backslash ,$

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:

$H\; =\; U\; +\; PV\; \backslash ,$

where (all units given in SI)

• H is the enthalpy
• U is the internal energy, (joule)
• P is the pressure of the system, (pascal)
• V is the volume, (cubic metre)

Overview

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Enthalpy is a quantifiable state function, and the total enthalpy of a system cannot be measured directly; the enthalpy change of a system is measured instead. A possible interpretation of enthalpy is as follows. Imagine we are to create the system out of nothing, then, in addition to supplying the internal energy U for the system, we need to do work to push the atmosphere away in order to make room for the system. Assuming the environment is at some constant pressure P, this mechanical work required is just PV where V is the volume of the system. Therefore, colloquially, enthalpy is the total amount of energy one needs to provide to create the system and then place it in the atmosphere. Conversely, if the system is annihilated, the energy extracted is not just U, but also the work done by the atmosphere as it collapses to fill the space previously occupied by the system, which is PV.

Enthalpy is a thermodynamic potential, and is useful particularly for nearly-constant pressure processes, where any energy input to the system must go into internal energy or the mechanical work of expanding the system. For systems at constant pressure, the change in enthalpy is the heat received by the system plus the non-mechanical work that has been done. In other words, when considering change in enthalpy, one can ignore the compression/expansion mechanical work. Therefore, 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.

Some useful relationships

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From the first law of thermodynamics:

$dU\; =\; \backslash delta\; Q\; -\; \backslash delta\; W\backslash ,$

And differentiating the expression for H  we have:

$dH\; =\; dU\; +\; (PdV+VdP)\; \backslash !$

$=\; \backslash delta\; Q\; -\; PdV\; +\; PdV+VdP\; =\; \backslash delta\; Q\; +VdP\; =\; TdS\; +\; VdP\; \backslash !$

$U$ is the internal energy,

$\backslash delta\; Q=TdS\; \backslash !$ is the energy added by heating during a reversible process,

$\backslash delta\; W=PdV\; \backslash !$ is the work done by the system in a reversible process.

T is the Temperature,

dS is the increase in entropy,

P is the constant pressure,

dV is an infintesimal volume, and

$\backslash delta$ represents the inexact differential.

where

For a process that is not reversible, the second law of thermodynamics states that the increase in heat $\backslash delta\; Q$ is less than or equal to the product $TdS$ of temperature $T$ and the increase in entropy $dS$; thus

$dH\; =\; \backslash delta\; Q\; +\; VdP\; \backslash le\; TdS+VdP\backslash ,$

It is seen that, if a thermodynamic process is isobaric (i.e., occurs at constant pressure), then dP = 0  and thus

$dH\; =\; \backslash delta\; Q\; \backslash le\; TdS\; \backslash ,$

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.

If, in addition, the entropy is held constant as well, i.e., $dS\; =\; 0$, the above equation becomes:

$dH\; \backslash le\; 0\backslash ,$

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 equilbrium.

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:

$dH\; =\; \backslash delta\; Q\; +\; VdP\; +\; \backslash sum\_i\; \backslash mu\_i\; dN\_i\; \backslash le\; TdS+VdP\; +\; \backslash sum\_i\; \backslash mu\_i\; dN\_i\backslash ,$

where $\backslash mu\_i$ is the chemical potential for an i-type particle, and $N\_i$ 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 $\backslash mu\_i\; dN\_i$ 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.

Applications

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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:

$\backslash Delta\; H\; =\; H\_\{final\}\; -\; H\_\{initial\}\; \backslash ,$

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 enthlapy than the reactants. The product of an endothermic reaction will be cold to the touch. 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. The product of an exothermic reaction will be warm to the touch.

Although Enthalpy is commonly used in engineering and science, being impossible to measure directly, 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 two or more closed systems cannot be compared using enthalpy as a basis, although sometime this is done, erroneously.

Open systems

Open systems provide additional possibilities for performing work—by rotating a steam turbine for example. This "shaft work" is separate from work done on the fluid itself (called PV work):

$\backslash delta\; W\; =\; dW\_\{PV\}\; +\; \backslash delta\; W\_\{shaft\}\; =\; d(PV)\; +\; \backslash delta\; W\_\{shaft\}\backslash ,$

The incorporation of the PV term into enthalpy is very useful for these systems. From the first law:

$\backslash frac\{dU\}\{dt\}\; =\; \backslash frac\{\backslash delta\; Q\}\{dt\}\; -\; \backslash frac\{d(PV)\}\{dt\}\; -\; \backslash frac\{\backslash delta\; W\_\{shaft\}\}\{dt\}\backslash ,$

and the definition of enthalpy:

$dH\; =\; dU\; +\; d(PV)\backslash ,$

we obtain a version of the first law for shaft work in open systems with no chemical reaction:

$\backslash frac\{dH\}\{dt\}\; =\; \backslash frac\{\backslash delta\; Q\}\{dt\}\; -\; \backslash frac\{\backslash delta\; W\_\{shaft\}\}\{dt\}\backslash ,$

This expression, like the first law expressed in terms of U, is not limited to reversible processes or any assumptions about the thermodynamic path taken by the process.

Standard enthalpy

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The standard enthalpy change of reaction (denoted H° or H^o) is the enthalpy change that occurs in a system when 1 equivalent of matter is transformed by a chemical reaction under standard conditions.

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. Other reactions with standard enthalpy change values include combustion (standard enthalpy change of combustion) and neutralisation (standard enthalpy change of neutralisation).

Specific enthalpy

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The specific enthalpy of a working mass is a property of that mass used in thermodynamics, defined as $h=u+P*v$ 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/kilogram.

See also

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• Calorimetry
• Calorimeter
• Isenthalpic process

External links

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• Enthalpy - Eric Weisstein's World of Physics
• Enthalpy - Georgia State University
• Enthalpy - KnowAllAbout.com
• Enthalpy (example calculations) - Texas A&M University (Chemistry Department)

Enthalpy | Thermodynamics | Chemistry

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