Enthalpy

Enthalpy H = U + PV is the internal energy of a system plus the work PV needed to make room for it against the surrounding pressure. At constant pressure the heat absorbed or released by a process equals the change in enthalpy, ΔH, which is why reaction enthalpies and latent heats are tabulated as enthalpy changes: most chemistry and metallurgy happens open to the atmosphere at fixed pressure.

Formally, enthalpy is the Legendre transform of the internal energy that swaps volume for pressure as the natural variable: from dU = T dS − P dV one obtains dH = T dS + V dP. Enthalpy is therefore the potential whose natural variables are entropy and pressure, and it is minimised at equilibrium when those are the quantities held fixed.

Differences in enthalpy, not absolute values, carry physical meaning. A negative ΔH marks an exothermic process that releases heat; a positive ΔH marks an endothermic one that absorbs it.

The concept dates to the nineteenth-century study of heat at constant pressure; the name 'enthalpy', from the Greek for 'to warm within', was popularised by Heike Kamerlingh Onnes around 1909, though the underlying function H = U + PV was used earlier by Gibbs and others.