  We derived a new formula for calculating the moist adiabatic temperature
profile of an atmosphere consisting of ideal gases with multiple condensing
species. This expression unifies various formulas published in the literature
and can be generalized to account for chemical reactions. Unlike previous
methods, it converges to machine precision independent of mesh size. It
accounts for any ratio of condensable vapors to dry gas, from zero to infinity,
and for variable heat capacities as a function of temperature. Because the
derivation is generic, the new formula is not only applicable to planetary
atmosphere in the solar system, but also to hot Jupiters and brown dwarfs in
which a variety of alkali metals, silicates and exotic materials condense. We
demonstrate that even though the vapors are ideal gases, they interact in their
effects on the moist adiabatic lapse rate. Finally, we apply the new
thermodynamic model to study the effects of downdrafts on the distribution of
minor constituents and thermal profile in the Galileo probe hotspot. We find
that the Galileo Probe measurements can be interpreted as a strong downdraft
that displaces an air parcel from 1 bar to the 4 bar level.
