# Virtual temperature

From Glossary of Meteorology

## virtual temperature

(

*Also called*density temperature.) The virtual temperature*T*_{v}=*T*(1 +*r*_{v}/ ε)/(1 +*r*_{v}), where*r*_{v}is the mixing ratio and ε is the ratio of the gas constants of air and water vapor, ≈ 0.622.The virtual temperature allows the use of the dry-air equation of state for moist air, except with

*T*replaced by*T*_{v}. Hence the virtual temperature is the temperature that dry dry air would have if its pressure and density were equal to those of a given sample of moist air. For typical observed values of*r*_{v}, the virtual temperature may be approximated by*T*_{v}= (1 + 0.61*r*_{v})*T*. Some authors incorporate the density increment due to liquid or solid water into virtual temperature, in which case the definition becomes*T*_{v}=*T*(1 +*r*_{v}/ε)/(1 +*r*_{v}+*r*_{l}) ≈*T*(1 + 0.61*r*_{v}-*r*_{l}), where*r*_{l}is the liquid or liquid plus solid water mixing ratio.