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v t e

In thermodynamics, enthalpy /ˈɛnθəlpi/ ^ⓘ, is the sum of a thermodynamic system's internal energy and the product of its pressure and volume.^[1] It is a state function used in many measurements in chemical, biological, and physical systems at a constant external pressure, which is conveniently provided by the large ambient atmosphere. The pressure–volume term expresses the work ${\displaystyle W}$ that was done against constant external pressure ${\displaystyle P_{ext}}$ to establish the system's physical dimensions from ${\displaystyle V_{system,initial}=0}$ to some final volume ${\displaystyle V_{system,final}}$ (as ${\displaystyle W=P_{ext}\Delta V}$), i.e. to make room for it by displacing its surroundings.^[2][3] 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 (SI), the unit of measurement for enthalpy is the joule. Other historical conventional units still in use include the calorie and the British thermal unit (BTU).

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 (stirring shaft or lift pumping) 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 ( p = 1 bar ; usually T = 298 K ) change to products in their standard states.^[4] 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 1 bar (100 kPa) pressure as a standard state. Enthalpies and enthalpy changes for reactions vary as a function of temperature,^[5] but tables generally list the standard heats of formation of substances at 25 °C (298 K). For endothermic (heat-absorbing) processes, the change ΔH is a positive value; for exothermic (heat-releasing) 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.

Definition

The enthalpy H of a thermodynamic system is defined as the sum of its internal energy and the product of its pressure and volume:^[1]

H = U + p V ,

where U is the internal energy, p is pressure, and V is the volume of the system; p V is sometimes referred to as the pressure energy Ɛ_p .^[6]

Enthalpy is an extensive property; it is proportional to the size of the system (for homogeneous systems). As intensive properties, the specific enthalpy, h =  H /m , is referenced to a unit of mass m of the system, and the molar enthalpy, H_m =  H /n , where n is the number of moles. For inhomogeneous systems the enthalpy is the sum of the enthalpies of the component subsystems:

$${\displaystyle H=\sum _{k}H_{k}\;,}$$

H is the total enthalpy of all the subsystems,

k refers to the various subsystems,

H_k refers to the enthalpy of each subsystem.

A closed system may lie in thermodynamic equilibrium in a static gravitational field, so that its pressure p varies continuously with altitude, while, because of the equilibrium requirement, its temperature T is invariant with altitude. (Correspondingly, the system's gravitational potential energy density also varies with altitude.) Then the enthalpy summation becomes an integral:

$${\displaystyle H=\int \left(\rho \,h\right)\,\mathrm {d} V\;,}$$

ρ ("rho") is density (mass per unit volume),

h is the specific enthalpy (enthalpy per unit mass),

(ρh) represents the enthalpy density (enthalpy per unit volume),

dV denotes an infinitesimally small element of volume within the system, for example, the volume of an infinitesimally thin horizontal layer.

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 H( S, p ) , with its entropy S and its pressure p as natural state variables which provide a differential relation for dH of the simplest form, derived as follows. We start from the first law of thermodynamics for closed systems for an infinitesimal process:

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

where

δQ is a small amount of heat added to the system,

δW is a small amount of work performed by the system.

In a homogeneous system in which only reversible processes or pure heat transfer are considered, the second law of thermodynamics gives δQ = T dS , with T the absolute temperature and dS the infinitesimal change in entropy S of the system. Furthermore, if only p V work is done, δW = p dV . As a result,