Thermodynamic Properties of Moist air
Perfect Gas Equation
In general, each molecular species in a mixture of gases at thermodynamic equilibrium will exert its own pressure and Dalton's law requires that these combine linearly to give the total pressure of the mixture. Similarly, in a fixed volume, the masses of each gas in the mixture are constant and sum to the total mass. Therefore, the densities
of the gas components are additive too. Each of the component gases are in thermal equilibrium with
each other and so are characterized by the same temperature. In our simplified description, moist air comprises two components - dry air and water vapour. If and are the partial pressure and density of
dry air respectively then the perfect gas equation states that:
where ) is the gas constant for dry air, is the universal gas constant and is the mean molecular mass of dry air. Similarly, if and are the partial pressure of water vapour and density respectively then:
where is the gas constant for water vapour. Therefore, the total pressure is given by:
.
Now defining the specific humidity and then:
where is called the virtual temperature. Since ,
and so for a saturated air parcel with , and , the difference between and is . A useful rough rule of thumb is that where is the specific humidity in (Ludlam, 1980).
Although small, the difference in density between moist and dry air is not negligible and needs to be accounted
for in the description of convective clouds -- particularly in the tropics where vapour mixing ratios are much higher.