Sum of the internal energy math.E and the product of the pressure math.P and volume math.V of a thermodynamic system (see thermodynamics). So, enthalpy math.H = math.E + math.Pmath.V. Its value is determined by the temperature, pressure, and composition of the system at any given time. According to the law of conservation of energy (see conservation law), the change in internal energy is equal to the heat transferred to the system minus the work done by the system. If the only work done is a change of volume at constant pressure, the enthalpy change is exactly equal to the heat transferred to the system.
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In thermodynamics and molecular chemistry, the enthalpy (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).
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:
Internal energy, , 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 () 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 , 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 non-mechanical 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 is the work required to displace the surrounding atmosphere in order to vacate the space to be occupied by the system.
As a differential expression, the value of H can be defined as
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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:
It is seen that, if a thermodynamic process is isobaric (i.e., occurs at constant pressure), then is zero and thus
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 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 is then:
where is the chemical potential for an i-type particle, and is the number of such particles. It is seen that, not only must the term be set to zero by requiring the pressures of the initial and final states to be the same, but the 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.
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:
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.
where Uin is the average internal energy entering the system and Uout 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 work) and shaft work which may be performed on some mechanical device.
These two types of work are expressed in the equation:
Substitution into the equation above for the control volume cv yields:
The definition of enthalpy, H, permits us to use this thermodynamic potential to account for both internal energy and work in fluids for open systems:
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:
This expression is described by the diagram above.
Standard enthalpy change of reaction is defined as the enthalpy change observed in a constituent of a thermodynamic system when, one mole of substance reacts completely under standard conditions.
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 of combustion is defined as the enthalpy change observed in a constituent of a thermodynamic system, when one mole of a substance combusts completely with oxygen under standard conditions.
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 of atomization is defined as the enthalpy change required to atomize one mole of compound completely under standard conditions.
Standard enthalpy of solution 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 of fusion is 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 of vapourization is 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 of sublimation is 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 of denaturation is defined as the enthalpy change required to denature one mole of compound under standard conditions.
Lattice enthalpy is 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.