Enthalpy

In thermodynamics, enthalpy is the sum of the internal energy U of a system and the product of pressure p and V of the system,

H = U + pV $$ Enthalpy used to be called "heat content", which is why it is conventionally indicated by H.

The work term pV has dimension energy, in SI units joule, and H has the same dimension. Enthalpy is a state function, a property of the state of the thermodynamic system and its value is determined entirely by the temperature T, pressure p, and composition NA, NB, ... (molar quantities of A, B, ...) of the system and not by its history.

Often one considers a system with thermal conducting walls, so that (small) amounts of heat  &Delta;Q  can go through the wall in either direction: if &Delta;Q > 0, heat enters the system and if &Delta;Q < 0 heat leaves the system. Also one usually considers one manner of performing (small) amount of work &Delta;W by or on the system:

\Delta W = p dV $$ If dV > 0 the volume of the system increases and work is performed by the system, if dV <0, work is performed on the system, hence the internal energy increase of the system by the work term obtains a minus sign:

dU = \Delta Q -\Delta W $$

To be continued