# The Individual and Universal Gas Constants

## The Individual and Universal Gas Constants used in fluid mechanics and thermodynamics

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The Individual and Universal Gas Constants are known from the Ideal Gas Law.

### The Individual Gas Constant - *R*

The Individual Gas Constant depends on the particular gas and is related to the molecular weight of the gas. The value is independent of temperature.

In the imperial system the units for the individual gas constant are *ft lb/slug ^{o}R*. In the SI system the units are

*J/kg K*.

The Individual Gas Constant for some gases:

Gas | Individual Gas Constant - R | ||
---|---|---|---|

Imperial Units(ft lb/slug ^{o}R) | SI Units(J/kg K) | Molecular Weight(g/mole) | |

Argon, Ar | 208 | 39.94 | |

Acetylene | 319 | 26 | |

Ammonia | 488 | 17 | |

Carbon Dioxide, CO_{2} | 1130 | 188.9 | 44.01 |

Carbon Monoxide, CO | 297 | 28.01 | |

Carbonic acid | 189 | 44 | |

Helium, He | 12420 | 2077 | 4.003 |

Hydrogen, H_{2} | 24660 | 4124 | 2.016 |

Methane - natural gas, CH_{4} | 3099 | 518.3 | 16.04 |

Nitrogen, N_{2} | 1775 | 296.8 | 28.02 |

Oxygen, O_{2} | 1554 | 259.8 | 32 |

Propane, C_{3}H_{8} | 189 | 44.09 | |

Sulfur dioxide, SO_{2 }(sulfuric acid) | 130 | 64.07 | |

Air | 1716 | 286.9 | 28.97 |

Water vapor | 2760 | 461.5 | 18.02 |

### The Universal Gas Constant - *R*_{u}

_{u}

The **Universal Gas Constant** - ** R_{u}** - appears in the ideal gas law and can be expressed as the product between the

*Individual Gas Constant - R -*for the particular gas - and the

*Molecular Weight*-

*M*- for the gas, and is

_{gas}**the same for all ideal or perfect gases**:

R_{u}= M_{gas}R(1)

where

R_{u }= universal gas constant

M_{gas}= molecular weight of the ideal gas or mixture of gases

### The Molar Weight of a Gas

The molar weight of a gas can be calculated like

1 / M_{gas}= (f_{1 }/ M_{1}+ .... + f_{n }/ M_{n}) (2)

where

f = mass of the gas relative to the total mass of the mixture

M = molecular weight of the gas

### The Universal Gas Constant - *R*_{u} - in alternative Units

_{u}-

*atm.cm*^{3}/(mol.K) : 82.0575*atm.ft*^{3}/(lbmol.K) : 1.31443*atm.ft*^{3}/(lbmol.^{o}R) : 0.73024*atm.l/(mol.K) : 0.08206**bar.cm*^{3}/(mol.K) : 83.14472*bar.l/(mol.K) : 0.08314472**Btu/(lbmol.*^{o}R) : 1.9859*cal/(mol.K) : 1.9859**erg/(mol.K) : 83144720**hp.h/(lbmol.*^{o}R) : 0.0007805*inHg.ft*^{3}/(lbmol.^{o}R) : 21.85**J/(mol.K) : 8.3144598****kJ/(kmol.K) : 8.3144598***J/(kmol.K) : 8314.472**(kgf/cm*^{2}).l/(mol.K) : 0.084784*kPa.cm*^{3}/(mol.K) : 8314.472*kWh/(lbmol.*^{o}R) : 0.000582**lbf.ft/(lbmol.**^{o}**R) : 1545.349***mmHg.ft*^{3}/(lbmol.K) : 999*mmHg.ft*^{3}/(lbmol.^{o}R) : 555*mmHg.l/(mol.K) : 62.364**Pa.m*^{3}/(mol.K) : 8.314472*psf.ft*^{3}/(lbmol.^{o}R) : 1545.349*psi.ft*^{3}/(lbmol.^{o}R) : 10.73*Torr.cm*^{3}/(mol.K) : 62364

- The Ideal Gas Law - Gases are highly compressible with changes in density directly related to changes in temperature and pressure.
- A Mixture of Gases - Properties of mixtures of gases.
- More about temperature

### The Universal Constant defined in Terms of the Boltzmann's Constant

The universal gas constant cab be defined in terms of Boltzmann's constant *k* as:

R_{u}= k N_{A}(2)

where

k= Boltzmann's constant = 1.381 x 10^{-23}(J/K)

N_{A}=Avogadro Number = 6.022 x 10^{23}(1/mol)

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