  The specific thermal enthalpy of a moist-air parcel is defined analytically
following a method in which specific moist entropy is derived from the Third
Law of thermodynamics. Specific thermal enthalpy is computed by integrating
specific heat content with respect to absolute temperature and including the
impacts of various latent heats (i.e., solid condensation, sublimation,
melting, and evaporation). It is assumed that thermal enthalpies can be set to
zero at $0$ K for the solid form of the main chemically inactive components of
the atmosphere (solid-$\alpha$ oxygen and nitrogen, hexagonal ice). The moist
thermal enthalpy is compared to already existing formulations of moist static
energy (MSE). It is shown that the differences between thermal enthalpy and the
thermal part of MSE may be quite large. This prevents the use of MSE to
evaluate the enthalpy budget of a moist atmosphere accurately, a situation that
is particularly true when dry-air and cloud parcels mix because of
entrainment/detrainment processes along the edges of cloud. Other differences
are observed when MSE or moist-air thermal enthalpy is plotted on a
psychrometric diagram or when vertical profiles of surface deficit are plotted.
