# Gases - Ratios of Specific Heat

## Ratios of specific heat for gases with constant pressure and volume processes.

### Internal Energy

For an ideal gas the internal energy - *u* - is a function of temperature. A change in internal energy can be expressed as

du =c_{v}dT(1)

where

du= change in internal energy (kJ/kg)

c_{v}= specific heat for gas in a constant volume process(kJ/kgK)

dT= change in temperature (K)

Specific heat* c _{v}* varies with temperature but within moderate temperature changes the specific heat -

*c*- can be regarded as constant.

_{v}### Enthalpy

For an ideal gas the enthalpy - *h* - is a function of temperature. Change of enthalpy can be expressed as

dh = c_{p}dT(2)

where

dh= change in enthalpy (kJ/kg)

c_{p}= specific heat for gas in a constant pressure process(kJ/kgK)

Specific heat* c_{p}* can within moderate temperature changes be regarded as constant.

The enthalpy in a fluid is defined as:

h = u + p / ρ(3)

where

h= enthalpy (kJ/kg)

u= internal energy (kJ/kg)

p= absolute pressure(Pa)

ρ= density(kg/m^{3})

Combining* (3)* and the Ideal Gas Law:

h = u + R T(4)

where

R= the individual gas constant(kJ/kgK)

Change in enthalpy can be expressed by differentiating *(4)*:

dh = du + R dT(5)

Dividing* (5)* with *dT*:

(dh / dT) - (du / dT) = R(6)

Modifying *(6)* with* (1)* and *(2)*:

c_{p}- c_{v}= R(7)

The difference *c _{p} - c_{v}* is constant for an ideal gas.

### Ratio of Specific Heat

The Ratio of Specific Heat can be expressed as:

k=c_{p}/ c_{v}(8)

where

k= Ratio of Specific Heat

Ratio of Specific Heat for some gases:

Gas | Ratio of Specific Heat- k - |

Acetylene | 1.30 |

Air, Standard | 1.40 |

Ammonia | 1.32 |

Argon | 1.66 |

Benzene | 1.12 |

N-butane | 1.18 |

Iso-butane | 1.19 |

Carbon Dioxide | 1.28 |

Carbon Disulphide | 1.21 |

Carbon Monoxide | 1.40 |

Chlorine | 1.33 |

Ethane | 1.18 |

Ethyl alcohol | 1.13 |

Ethyl chloride | 1.19 |

Ethylene | 1.24 |

Helium | 1.66 |

N-heptane | 1.05 |

Hexane | 1.06 |

Hydrochloric acid | 1.41 |

Hydrogen | 1.41 |

Hydrogen chloride | 1.41 |

Hydrogen sulphide | 1.32 |

Methane | 1.32 |

Methyl alcohol | 1.20 |

Methyl butane | 1.08 |

Methyl chloride | 1.20 |

Natural Gas (Methane) | 1.32 |

Nitric oxide | 1.40 |

Nitrogen | 1.40 |

Nitrous oxide | 1.31 |

N-octane | 1.05 |

Oxygen | 1.40 |

N-pentane | 1.08 |

Iso-pentane | 1.08 |

Propane | 1.13 |

R-11 | 1.14 |

R-12 | 1.14 |

R-22 | 1.18 |

R-114 | 1.09 |

R-123 | 1.10 |

R-134a | 1.20 |

Steam (water) | 1.33 |

Sulphur dioxide | 1.26 |

Toluene | 1.09 |

The Ratio of Specific Heat is dimensionless and the value is the same in the SI and the Imperial system of units.