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Enthalpy /ˈɛnθəlpi/ (About this soundlisten) is a property of a thermodynamic system, defined as the sum of the system's internal energy and the product of its pressure and volume.[1][2] It is a convenient state function preferred in many measurements in chemical, biological, and physical systems at a constant pressure. 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, and 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 British thermal unit (BTU) and the calorie.

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 (ΔH) 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, the enthalpy change equals the energy exchanged with the environment by heat. For calibration of enthalpy changes a specific and convenient reference point is established. 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 processes, the change ΔH is a positive value, and is negative in exothermic (heat-releasing) processes.

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.

Schematic diagram of a compressor in the steady state. Fluid enters the system (dotted rectangle) at point 1 and leaves it at point 2. The mass flow is . A power P is applied and a heat flow is released to the surroundings at ambient temperature Ta.

A power P is applied e.g. as electrical power. If the compression is adiabatic, the gas temperature goes up. In the reversible case it would be at constant entropy, which corresponds with a vertical line in the Ts diagram. For example, compressing nitrogen from 1 bar (point a) to 2 bar (point bA power P is applied e.g. as electrical power. If the compression is adiabatic, the gas temperature goes up. In the reversible case it would be at constant entropy, which corresponds with a vertical line in the Ts diagram. For example, compressing nitrogen from 1 bar (point a) to 2 bar (point b) would result in a temperature increase from 300 K to 380 K. In order to let the compressed gas exit at ambient temperature Ta, heat exchange, e.g. by cooling water, is necessary. In the ideal case the compression is isothermal. The average heat flow to the surroundings is . Since the system is in the steady state the first law gives

second law of thermodynamics for open systems gives

gives for the minimal power

(hcha) − Ta(scsa). With the data, obtained with the Ts diagram, we find a value of (430 − 461) − 300 × (5.16 − 6.85) = 476 kJ/kg.

The relation for the power can be further simplified by writing it as

With dh = Tds + vdp, this results in the final relation

The relation for the power can be further simplified by writing it as

With dh = Tds + vdp, this results in the final relation

History

The term enthalpy was coined relatively late in the history of thermodynamics, in the early 20th centur

The term enthalpy was coined relatively late in the history of thermodynamics, in the early 20th century. Energy was introduced in a modern sense by Thomas Young in 1802, while entropy was coined by Rudolf Clausius in 1865. Energy uses the root of the Greek word ἔργον (ergon), meaning "work", to express the idea of capacity to perform work. Entropy uses the Greek word τροπή (tropē) meaning transformation. Enthalpy uses the root of the Greek word θάλπος (thalpos) "warmth, heat"[21]

The term expresses the obsolete concept of heat content,[22] as dH refers to the amount of heat gained in a process at constant pressure only,[23] but not in the general case when pressure is variable.[24] Josiah Willard Gibbs used the term "a heat function for constant pressure" for clarity.[note 2]

Introduction of the concept of "heat content" H is associated with Benoît Paul Émile Clapeyron and Rudolf Clausius (Clausius–Clapeyron relation, 1850).

The term enthalpy first appeared in print in 1909.[25] It is attributed to Heike Kamerlingh Onnes, who most likely introduced it orally the year before, at the first meeting of the Institute of Refrigeration in Paris.[26] It gained currency only in the 1920s, notably with the Mollier Steam Tables and Diagrams, published in 1927.

Until the 1920s, the symbol [22] as dH refers to the amount of heat gained in a process at constant pressure only,[23] but not in the general case when pressure is variable.[24] Josiah Willard Gibbs used the term "a heat function for constant pressure" for clarity.[note 2]

Introduction of the concept of "heat content" H is associated with Benoît Paul Émile Clapeyron and Rudolf Clausius (Clausius–Clapeyron relation, 1850).

The term enthalpy first appeared in print in 1909.[25] It is attributed to Heike Kamerlingh Onnes, who most likely introduced it orally the year before, at the first meeting of the Institute of Refrigeration in Paris.[26] It gained currency only in the 1920s, notably with the Mollier Steam Tables and Diagrams, published in 1927.

Until the 1920s, the symbol H was used, somewhat inconsistently, for "heat" in general. The definition of H as strictly limited to enthalpy or "heat content at constant pressure" was formally proposed by Alfred W. Porter in 1922.[27][28]