Enthalpy

Why define enthalpy?

Many real thermal processes occur at approximately constant pressure. Chemical reactions in open containers, boiling water in the atmosphere, and many biological and engineering processes happen while pressure remains near atmospheric pressure.

In constant-pressure situations, it is useful to combine internal energy with the energy associated with making room for the system's volume. This combined quantity is enthalpy, defined as

$H=U+PV$

Enthalpy is a state function because $U$, $P$, and $V$ are state variables.

Heat at constant pressure

Start with the first law using work done by the system:

$Delta U=Q-W$

For pressure-volume work at constant pressure,

$W=PDelta V$

so

$Q=Delta U+PDelta V$

If pressure is constant, then

$Delta(PV)=PDelta V$

Therefore

$Q_P=Delta U+Delta(PV)=Delta H$

At constant pressure, the heat added equals the change in enthalpy:

$Q_P=Delta H$

This is the main reason enthalpy is useful.

Enthalpy of an ideal gas

For an ideal gas,

$PV=nRT$

so

$H=U+nRT$

For a monatomic ideal gas,

U=rac{3}{2}nRT

so

H=rac{5}{2}nRT

More generally, ideal gas enthalpy depends only on temperature. For a temperature change at constant pressure,

$Delta H=nC_PDelta T$

Enthalpy and phase changes

Phase changes at constant pressure are commonly described using enthalpy. The heat required to vaporize a liquid at constant pressure is the enthalpy of vaporization. The heat required to melt a solid is the enthalpy of fusion.

For a mass $m$ undergoing a phase change,

$Q=mL$

At constant pressure, this heat is also an enthalpy change:

$Delta H=mL$

The enthalpy change includes changes in internal energy and any expansion work done during the phase change.

Boiling and expansion work

When water vaporizes, the vapor occupies much more volume than the liquid. At atmospheric pressure, the system must push back the atmosphere to make room for the vapor. The energy required includes both molecular separation and expansion work.

This is why enthalpy is often more convenient than internal energy in chemistry and phase-change tables.

Enthalpy in chemical reactions

Chemical reaction energy changes measured at constant pressure are enthalpy changes. An exothermic reaction releases heat, so

$Delta H<0$

An endothermic reaction absorbs heat, so

$Delta H>0$

Combustion, dissolving salts, metabolism, and industrial chemical processes are often described using enthalpy.

Flow systems

In fluid flow, enthalpy naturally appears because fluid entering or leaving a device carries internal energy and flow work. Turbines, compressors, nozzles, heat exchangers, and engines are often analyzed using enthalpy.

The quantity $PV$ per mole or per mass accounts for the work needed to push fluid into or out of a control volume.

The big idea

Enthalpy is defined by $H=U+PV$ and is especially useful for constant-pressure processes. At constant pressure, heat transfer equals enthalpy change. Enthalpy simplifies analysis of phase changes, chemical reactions, and flowing fluids by including both internal energy and pressure-volume effects.