Enthalpy

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Enthalpy /ˈɛnθəlpi/ (listen) is a property of a thermodynamic system, and is defined as the sum of the system's internal energy and the product of its pressure and volume.^[1][2] It is a state function used in many measurements in chemical, biological, and physical systems at a constant pressure, that is conveniently provided by the large ambient atmosphere. The pressure–volume term expresses the work required to establish the system's physical dimensions, i.e. to make room for it by displacing its surroundings.^[3][4] 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.

The unit of measurement for enthalpy in the International System of Units (SI) 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 in thermodynamics. In practice, a change in enthalpy is the preferred expression for measurements at constant pressure, because it simplifies the description of energy transfer. When matter transfer into or out of the system is also prevented, 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, T = 298 K) change to products in their standard states.^[5] This quantity is the standard heat of reaction at constant pressure and temperature, but it can be measured by calorimetric methods in which the temperature does vary, 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 since enthalpy is a state function.

Calibration of enthalpy changes requires a reference point. Enthalpies for chemical substances at constant pressure usually refer to standard state: most commonly 1 bar (100 kPa) pressure. Standard state does not strictly specify a temperature, but expressions for enthalpy generally reference the standard heat of formation 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, and depends only on its temperature, which correlates to its internal 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 U and the work required to achieve its pressure and volume:^[6][7]

H = U + pV,

where p is pressure, and V is the volume of the system.

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 is H/n, where n is the number of moles. For inhomogeneous systems the enthalpy is the sum of the enthalpies of the composing subsystems:

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

where

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:

${\displaystyle H=\int (\rho h)\,dV,}$

where

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 natural state variables its entropy S[p] and its pressure p. A differential relation for it can be derived as follows. We start from the first law of thermodynamics for closed systems for an infinitesimal process:

${\displaystyle dU=\delta Q-\delta W,}$

where