# C230 – Solartron RD Appendix A Calculation

## Description

This function calculates the anticipated density and the relative density of the calibration and sample gases.

## References

Solartron 3096 Specific Gravity Transducer Technical Manual – 30960015 July 1989

Solartron 3098 Specific Gravity Transducer Technical Manual – 30985000

R recommended by the Committee on Data for Science and Technology (CODATA) for international use

Kelton calculation reference C230

FLOCALC calculation reference F017

KIMS calculation reference K207

## Options

### Gas Constant R

- Solartron

- AGA 8

- CODATA

- User Entered

Select option based on value you wish to use for the molar gas constant.

### Velocity of Sound Correction

- Simplified

- Entended

Select option based on which velocity of sound correction you wish to employ.

### Transducer Model

- 3096

- 3098

Select option based on the transducer model being used, if applicable.

## Constants

Molecular weight of Methane – M_{x} = 16.043g/mol

Molecular eight of Nitrogen – M_{y} = 28.014 g/mol

Value of gas constant provided by Solartron – 8.31434 Jmol^{-1}K^{-1}

Value of gas constant provided by AGA 8 – 8.31451 Jmol^{-1}K^{-1}

Value of gas constant provided by CODATA – 8.3144621 Jmol^{-1}K^{-1}

## Calculation

All calculations are performed in SI units unless otherwise stated.

### Anticipated density

The anticipated density for each gas is found by

Where | ||

ρ | = | Density of gas |

Δ | = | Anticipated error |

### Velocity of sound correction factor

#### Simplified Version

For Solartron 3096 Specific Gravity Transducer

Where | ||

M | = | Molecular weight |

γ | = | Ratio of specific heats |

For Solartron 3098 Specific Gravity Transducer

Where | ||

M | = | Molecular weight |

γ | = | Ratio of specific heats |

#### Extended Version

Where | ||

K_{3} |
= | Velocity of sound coefficient |

τ | = | Sensor periodic time in μs |

γ | = | Ratio of specific heats |

P | = | Pressure |

ρ | = | Density of gas |

### Total factor

Where | ||

Z_{F} |
= | Compressibity factor |

V_{F} |
= | Velocity of sound correction factor |

#### Total factor for sample gas using calibration gases as reference

Where | ||

E_{Fx} |
= | Total factor of methane |

E_{Fy} |
= | Total factor of nitrogen |

ρ_{s} |
= | Base density of sample gas |

ρ_{sx} |
= | Base density of methane |

ρ_{sy} |
= | Base density of nitrogen |

#### Total factor for nitrogen using methane and sample gas as reference

Where | ||

E_{Fx} |
= | Total factor of methane |

E_{F} |
= | Total factor of sample gas |

ρ_{s} |
= | Base density of sample gas |

ρ_{sx} |
= | Base density of methane |

ρ_{sy} |
= | Base density of nitrogen |