In atmospheric thermodynamics, the virtual temperature
Contents
Description
In atmospheric thermodynamic processes, it is often useful to assume air parcels behave approximately adiabatic, and thus approximately ideally. The specific gas constant for the standardized mass of one kilogram of a particular gas is variable, and described mathematically as:
where
with
Purpose
Rather than carry out these calculations, it is convenient to scale another quantity within the ideal gas law to equate the pressure and density of a dry parcel to a moist parcel. The only variable quantity of the ideal gas law independent of density and pressure is temperature. This scaled quantity is known as virtual temperature, and it allows for the use of the dry-air equation of state for moist air. Temperature has an inverse proportionality to density. Thus, analytically, a higher vapor pressure would yield a lower density, which should yield a higher virtual temperature in turn.
Derivation
Consider a moist air parcel containing masses
where
Solving for the densities in each equation and combining with the law of partial pressures yields:
Then, solving for
where the virtual temperature
We now have a non-linear scalar for temperature dependent purely on the unitless value
Variations
Often the more easily accessible atmospheric parameter is the mixing ratio
which allows:
Algebraic expansion of that equation, ignoring higher orders of
An approximate conversion using
Uses
Virtual temperature is used in adjusting CAPE soundings for assessing available convective potential energy from Skew-T log-P diagrams. The errors associated with ignoring virtual temperature correction for smaller CAPE values can be quite significant. Thus, in the early stages of convective storm formation, a virtual temperature correction is significant in identifying the potential intensity in tropical cyclogenesis.