# virtual temperature derivations

1. virtual temperature from temperature

   symbol | description | unit | variable name
   --- | --- | --- | ---
   \(M_{air}\) | molar mass of total air | \(\frac{g}{mol}\) | molar_mass {:}
   \(M_{dry\_air}\) | molar mass of dry air | \(\frac{g}{mol}\) |
   \(T\) | temperature | \(K\) | temperature {:}
   \(T_{v}\) | virtual temperature | \(K\) | virtual_temperature {:}

   The pattern : for the dimensions can represent {vertical}, {latitude,longitude}, {latitude,longitude,vertical}, {time}, {time,vertical}, {time,latitude,longitude}, {time,latitude,longitude,vertical}, or no dimensions at all.

   \[T_{v} = \frac{M_{dry\_air}}{M_{air}}T\]