Enthalpy

Enthalpy is a combination property, also known as the “total heat”.

$$\begin{array}{rl}h& =u+Pv\text{(Intensive property)}\\ H& =U+PV\text{(Extensive property)}\end{array}$$

The heat required to heat up a close system isobarically (constant pressure) is the change in enthalpy:

$$Q_{\text{in}}=\Delta H$$

This can be split up to:

$$dh=du+Pdv+vdP$$