# Gases - Ratios of Specific Heats

## Heat capacity of a gas in a constant pressure process - to heat capacity in a constant volume process

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### Internal Energy

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

du =c_{v}dT(1)

where

du= change in internal energy

c_{v}= specific heat for the gas in a constant volume process

dT= change in temperature

*c _{v}* varies with temperature, but within a moderate temperature change the heat capacity -

*c*- can be regarded as constant.

_{v}### Enthalpy

For an ideal gas the enthalpy - *h* - is function of temperature and the change in enthalpy can be expressed as

dh = c_{p}dT(2)

where

dh= change in enthalpy

c_{p}= specific heat for the gas in a constant pressure process

*c _{p}* can within a moderate temperature change be regarded as constant.

The enthalpy in a fluid is defined as:

h = u + p / ρ(3)

where

h= enthalpy

u= internal energy

ρ= density

Combining (3) and the Ideal Gas Law gives:

h = u + R T(4)

where

The change in enthalpy can be expressed by differentiating (4):

dh = du + R dT(5)

Dividing (5) with *dT* gives:

(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.

### The Ratio of Specific Heats

The Ratio of Specific Heats can be expressed as:

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

where

k= the ratio of specific heats

Ratio of Specific Heats for some common gases:

Gas | Ratio of Specific Heats |

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 |

Toulene | 1.09 |

Since the ratio is dimensionless the value is the same in the SI and the imperial system of units.

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