# partial pressure derivations

1. partial pressure from number density and temperature

symbol

description

unit

variable name

$$k$$

Boltzmann constant

$$\frac{kg m^2}{K s^2}$$

$$n_{x}$$

number density of air component x (e.g. $$n_{O_{3}}$$)

$$\frac{molec}{m^3}$$

<species>_number_density {:}

$$p_{x}$$

partial pressure of air component x (e.g. $$p_{O_{3}}$$)

$$Pa$$

<species>_partial_pressure {:}

$$T$$

temperature

$$K$$

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.

$p_{x} = n_{x}kT$
2. partial pressure from volume mixing ratio

symbol

description

unit

variable name

$$p$$

pressure

$$Pa$$

pressure {:}

$$p_{x}$$

partial pressure of air component x (e.g. $$p_{O_{3}}$$)

$$Pa$$

<species>_partial_pressure {:}

$$\nu_{x}$$

volume mixing ratio of air component x (e.g. $$\nu_{O_{3}}$$)

$$ppv$$

<species>_volume_mixing_ratio {:}

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.

$p_{x} = \nu_{x}p$
3. partial pressure from volume mixing ratio dry air

symbol

description

unit

variable name

$$p_{x}$$

partial pressure of air component x (e.g. $$p_{O_{3}}$$)

$$Pa$$

<species>_partial_pressure {:}

$$\bar{\nu}_{x}$$

volume mixing ratio of air component x (e.g. $$\nu_{O_{3}}$$)

$$ppv$$

<species>_volume_mixing_ratio_dry_air {:}

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.

$p_{x} = \bar{\nu}_{x}p_{dry\_air}$