Enthalpy

Enthalpy is the sum of a thermodynamic system's internal energy and the product of its pressure and volume. It is a state function in thermodynamics used in many measurements in chemical, biological, and physical systems at a constant external pressure, which is conveniently provided by Earth's ambient atmosphere. The pressure–volume term expresses the work that was done against constant external pressure to establish the system's physical dimensions from to some final volume , 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, lattice, solvation, and other chemical "energies" 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 unit of measurement for enthalpy is the joule. Other historical conventional units still in use include the calorie and the British thermal unit.
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 for the thermodynamic problem at hand. In practice, a change in enthalpy is the preferred expression for measurements at constant pressure, because it simplifies the description of energy transfer. When transfer of matter into or out of the system is also prevented and no electrical or mechanical work is done, at constant pressure the enthalpy change equals the energy exchanged with the environment by heat.
In chemistry, the standard enthalpy of reaction is the enthalpy change when reactants in their standard states change to products in their standard states.
This quantity is the standard heat of reaction at constant pressure and temperature, but it can be measured by calorimetric methods even if the temperature does vary during the measurement, provided that the initial and final pressure and temperature correspond to the standard state. The value does not depend on the path from initial to final state because enthalpy is a state function.
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 processes, the change is a positive value; for exothermic processes it is negative.
The enthalpy of an ideal gas 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.
The word "enthalpy" is derived from the Greek word enthalpein, which means "to heat".

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, and is the volume of the system; is sometimes referred to as the pressure energy.
Enthalpy is an extensive property; it is proportional to the size of the system. As intensive properties, the specific enthalpy is referenced to a unit of mass 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:
where
A closed system may lie in thermodynamic equilibrium in a static gravitational field, so that its pressure varies continuously with altitude, while, because of the equilibrium requirement, its temperature is invariant with altitude. Then the enthalpy summation becomes an integral:
where
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 of the simplest form, derived as follows. We start from the first law of thermodynamics for closed systems for an infinitesimal process:
where
In a homogeneous system in which only reversible processes or pure heat transfer are considered, the second law of thermodynamics gives with the absolute temperature and the infinitesimal change in entropy of the system. Furthermore, if only work is done, As a result,
Adding to both sides of this expression gives
or
So
and the coefficients of the natural variable differentials and are just the single variables and.

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:
where is the heat capacity at constant pressure, and is the coefficient of thermal expansion:
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 because is not a natural variable for the enthalpy.
At constant pressure, so that For an ideal gas, reduces to this form even if the process involves a pressure change, because
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 then becomes
where is the chemical potential per particle for a type particle, and is the number of such particles. The last term can also be written as or as .

Characteristic functions and natural state variables

The enthalpy expresses the thermodynamics of a system in the energy representation. As a function of state, its arguments include one intensive and several extensive state variables. The state variables , and are said to be the natural state variables in this representation. They are suitable for describing processes in which they are determined by factors in the surroundings. For example, when a virtual parcel of atmospheric air moves to a different altitude, the pressure surrounding it changes, and the process is often so rapid that there is too little time for heat transfer. This is the basis of the so-called adiabatic approximation that is used in meteorology.
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 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 at pressure and temperature, is created or brought to its present state from absolute zero, energy must be supplied equal to its internal energy plus, where is the work done in pushing against the ambient pressure.
In physics and statistical mechanics it may be more interesting to study the internal properties of a constant-volume system and therefore the internal energy is used.
In chemistry, experiments are often conducted at constant atmospheric pressure, 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, 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. We apply it to the special case with a constant pressure at the surface. In this case the work is given by . 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:
Now,
so
If the system is under constant pressure, and consequently, the increase in enthalpy of the system is equal to the heat added:
This is why the now-obsolete term heat content was used for enthalpy 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.
Energy must be supplied to remove particles from the surroundings to make space for the creation of the system, assuming that the pressure remains constant; this is the term. The supplied energy must also provide the change in internal energy, which includes activation energies, ionization energies, mixing energies, vaporization energies, chemical bond energies, and so forth. Together, these constitute the change in the enthalpy For systems at constant pressure, with no external work done other than the work, the change in enthalpy is the heat received by the system.
For a simple system with a constant number of particles at constant pressure, the difference in enthalpy is the maximum amount of thermal energy derivable from an isobaric thermodynamic process.