Editing Enthalpy (section)

== Relationship to heat ==
In order to discuss the relation between the enthalpy increase and heat supply, we return to the first law for closed systems, with the physics sign convention: {{math|d''U'' {{=}} ''δQ'' − ''δW''}}, where the heat {{mvar|δQ}} is supplied by conduction, radiation, [[Joule heating]]. We apply it to the special case with a constant pressure at the surface. In this case the work is given by {{nobr|{{math|''p''{{tsp}}d''V''}}}} (where {{mvar|p}} is the pressure at the surface, {{math|d''V''}} is the increase of the volume of the system). Cases of long-range electromagnetic interaction require further state variables in their formulation and are not considered here. In this case the first law reads:
<math display="block">
 \mathrm{d}U = \delta Q - p \,\mathrm{d}V.
</math>
Now,
<math display="block">
 \mathrm{d}H = \mathrm{d}U + \mathrm{d}(pV),
</math>
so
<math display="block">\begin{align}
 \mathrm{d}H &= \delta Q + V \,\mathrm{d}p + p \,\mathrm{d}V - p \,\mathrm{d}V \\
             &= \delta Q + V \,\mathrm{d}p.
\end{align}</math>

If the system is under [[isobaric system|constant pressure]], {{nobr|{{math|d''p'' {{=}} 0}}}} and consequently, the increase in enthalpy of the system is equal to the [[heat]] added:
<math display="block">
 \mathrm{d}H = \delta Q.
</math>
This is why the now-obsolete term ''heat content'' was used for enthalpy in the 19th century.