Simplified form of the first law of thermodynamics for moist air
Consider an infinitesimal change in a cloudy air parcel for which all condensed water remains within ( i.e. ), eq.(9) gives:
or
Now using the Clausius-Clapeyron equation (12), eq.(3) and in the above gives:
and since and , a useful approximate form of the first law for cloudy air is:
or, following the motion of a saturated air parcel:
or
This reduced form of the first law of thermodynamics is often taken as the starting point in other texts.