Enthalpy

Enthalpy, symbol $H$, is a property in thermodynamics defined as the internal energy of a system plus the product of its pressure and volume: $H=U+pV$. It is especially useful for describing constant-pressure processes and energy transport by flowing fluids. Although historically called “heat content,” enthalpy is not heat stored inside a substance; under specified conditions, its change equals the heat transferred to the system. (goldbook.iupac.org)

Definition and properties

In the defining equation,

$U$ denotes internal energy, $p$ pressure, and $V$ volume. The pressure–volume term has the dimensions of energy. Enthalpy is a state function: its value depends on the system’s state, rather than the route by which that state was reached. Accordingly,

depends only on the endpoints. Heat and work, by contrast, describe energy transfers associated with a particular process. (goldbook.iupac.org)

Enthalpy is extensive: for equivalent samples at the same conditions, it scales with the amount of material. Its SI unit is the joule. Molar enthalpy, $H_m=H/n$, is expressed in joules per mole, while specific enthalpy, $h=H/m$, is expressed in joules per kilogram. Tabulated enthalpies use reference conventions; calculations normally require differences rather than an independently measured absolute value. (openstax.org)

Constant-pressure heat transfer

For a closed system, using the convention that work done on the system is positive, the first law gives

If the only work is expansion or compression against a constant external pressure, $w=-p_{\mathrm{ext}}\Delta V$. When the initial and final system pressures equal that external pressure,

where $q_p$ is the heat transferred at constant pressure. Changes in the system’s bulk kinetic and gravitational potential energies are excluded or assumed negligible. (openstax.org)

This equality is conditional, not the definition of enthalpy. Electrical work, shaft work, or other non-expansion work can prevent constant-pressure heat from equalling $\Delta H$. Under the stated conditions, a process with $\Delta H<0$ releases heat and is exothermic; one with $\Delta H>0$ absorbs heat and is endothermic. The sign refers to the system, so the surroundings experience the opposite heat transfer. (openstax.org)

Temperature dependence and phase changes

For fixed composition within a single phase, the constant-pressure heat capacity is

Consequently, heating between two temperatures at constant pressure produces

If $C_p$ varies little across the interval, this becomes approximately $C_p(T_2-T_1)$. The integral expression preserves temperature dependence when that approximation is unsuitable. (ocw.mit.edu)

For an ideal gas of fixed composition, enthalpy depends only on temperature, so $dh=c_p(T)\,dT$ applies even when pressure changes. This special result does not hold generally for real fluids. (ocw.mit.edu)

A phase transition also changes enthalpy. At the equilibrium transition temperature and pressure, melting or vaporization can absorb energy without raising temperature. This energy is associated with latent heat; reversing the transition reverses the sign of the enthalpy change. For example, liquid water and water vapour have different enthalpies at the same coexistence conditions. Heating calculations that cross a phase boundary must include both temperature-dependent contributions and the transition enthalpy. (ocw.mit.edu)

Chemical reaction enthalpies

In chemistry, reaction enthalpy compares products and reactants for a specified chemical reaction. Hess’s law states that the enthalpy change of an overall process equals the sum of the changes for steps that produce the same overall transformation. Reversing a step changes its sign; multiplying its chemical equation multiplies its enthalpy change accordingly. (openstax.org)

The standard enthalpy of formation, $\Delta_fH^\circ$, describes formation of one mole of a substance from its constituent elements in their reference states. Those reference-state elements have standard formation enthalpies of zero by convention. A reaction value can therefore be calculated as

where $\nu_i$ are the positive coefficients in the balanced equation. Physical states must be specified because different phases have different enthalpies. (openstax.org)

The superscript $\circ$ indicates standard-state conditions, not a particular temperature. IUPAC’s standard pressure is $10^5$ pascals, or 1 bar; older sources may use 1 atmosphere. Values are commonly tabulated at 298.15 kelvin, but their stated temperature and reference conventions remain essential. (goldbook.iupac.org)

Thermodynamic potentials and fluid flow

For a simple compressible system of fixed composition, the fundamental enthalpy relation is

where $S$ is entropy. Enthalpy is related to Gibbs free energy by $G=H-TS$. At constant temperature and pressure, $\Delta G=\Delta H-T\Delta S$; therefore, enthalpy alone does not determine whether a process is thermodynamically spontaneous. Under these constraints, equilibrium corresponds to minimum Gibbs free energy for the permitted changes. (ocw.mit.edu)

In chemical engineering and power systems, specific enthalpy combines a flowing fluid’s internal energy with the pressure work needed to move it across a boundary. For steady flow with one inlet and one outlet,

with all terms expressed per unit mass. Here $w_s$ is shaft work delivered by the fluid, $c$ speed, and $z$ elevation. This balance describes equipment such as turbines, compressors, and nozzles, while keeping fluid enthalpy distinct from bulk kinetic and potential energy. (live.ocw.mit.edu)