# C033 – Density of Moist Air

## Description

This calculates the density of moist air from temperature, pressure, carbon dioxide content and one other parameter depending on the option selected.

## References

Revised formula for the density of moist air (CIPM-2007) – A Picard, R S Davis, M Glaser and K Fujii

Kelton calculation reference C033

FLOCALC calculation reference F043

## Options

### Calculate from

- Relative Humidity

- Dew-point Temperature

- Vapour Mol Fraction

This option group allows the selection of the final parameter for calculating the density of moist air.

## Constants

Molar gas constant – R = 8.314472 J mol^{-1}K^{-1}

Molar mass of water – M_{v} = 18.015 kg kmol^{-1}

Constituent | Molar mass, M_{i} (kg kmol^{-1}) |
Mole fraction, x_{i} |
M_{i}·x_{i} |
---|---|---|---|

N_{2} |
28.0134 | 0.780848 | 21.874207 |

O_{2} |
31.9988 | 0.209390 | 6.700229 |

Ar | 39.948 | 0.009332 | 0.372795 |

CO_{2} |
44.01 | 0.0004 | 0.017604 |

Ne | 20.18 | 18.2 x 10^{-6} |
0.000367 |

He | 4 | 5.2 x 10^{-6} |
21 x 10^{-6} |

CH_{4} |
16 | 1.5 x 10^{-6} |
24 x 10^{-6} |

Kr | 83.8 | 1.1 x 10^{-6} |
92 x 10^{-6} |

H_{2} |
2 | 0.5 x 10^{-6} |
1 x 10^{-6} |

N_{2}O |
44 | 0.3 x 10^{-6} |
13 x 10^{-6} |

CO | 28 | 0.2 x 10^{-6} |
6 x 10^{-6} |

Xe | 131 | 0.1 x 10^{-6} |
13 x 10^{-6} |

Σ | 28.96546 |

## Calculation

### Corrected Molar Mass of Air

The corrected molar mass of air is calculated from:

Where | ||
---|---|---|

x_{CO2} |
= | Carbon dioxide concentration |

### Mole Fraction of Water Vapour

The mole fraction of water vapour is calculated from the formulae below. Use the appropriate one depending on the inputs available i.e. use equation on the far right if using dew point temperature as an input.

Where | ||
---|---|---|

h | = | Relative humidity |

P | = | Pressure |

P_{sv} |
= | Saturated vapour pressure of moist air |

f | = | Enhancement factor |

### Saturated Vapour Pressure of Moist Air

The vapour pressure at saturation, P_{sv} is calculated from:

Where | ||
---|---|---|

T | = | Temperature in Kelvin |

A | = | 1.2378847 x 10^{-5} K^{-2} |

B | = | 1.9121316 x 10^{-2} K^{-1} |

C | = | 33.93711047 |

D | = | -6.3431645 x 10^{3} K |

### Enhancement Factor

The enhancement factor, f, is calculated from:

Where | ||
---|---|---|

t | = | Temperature in °C |

α | = | 1.0062 |

β | = | 3.14 x 10^{-8} Pa ^{-1} |

γ | = | 5.6 x 10^{-7} K^{-2} |

### Compressibility

The compressibility, Z, is calculated from:

Where | ||

a_{0} |
= | 1.58123 x 10^{-6} K Pa^{-1} |

a_{1} |
= | -2.9331 x 10^{-8} Pa^{-1} |

a_{2} |
= | 1.1043 x 10^{-10} K^{-1} Pa^{-1} |

b_{0} |
= | 5.707 x 10^{-6} K Pa^{-1} |

b_{1} |
= | -2.051 x 10^{-8} Pa^{-1} |

c_{0} |
= | 1.9898 x 10^{-4} K Pa^{-1} |

c_{1} |
= | -2.376 x 10^{-6} Pa^{-1} |

d | = | 1.83 x 10^{-11} K^{2} Pa^{-2} |

e | = | -0.765 x 10^{-8} K^{2} Pa^{-2} |

### Density of Moist Air

The density of moist air, ρ_{a} is calculated from: