# Gases - Ratios of Specific Heat

### 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.

## Related Topics

### • Fluid Mechanics

The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

## Related Documents

### Air - Specific Heat Ratio

Specific Heat Ratio of air at temperatures ranging -40 - 1000 degC (-40 - 1500 degF) at standard atmospheric pressure - Imperial and SI Units.

### Compression and Expansion of Gases

Isothermal and isentropic gas compression and expansion processes.

### Gases - Dynamic Viscosities

Absolute (dynamic) viscosities of some common gases.

### Gases - Molar Specific Heats

Molar specific heats for some common gases at constant volume.

### Gases - Specific Heats and Individual Gas Constants

Specific heat at constant volume, specific heat at constant pressure, specific heat ratio and individual gas constant - *R* - common gases as argon, air, ether, nitrogen and many more.

### Heat Capacity

The amount of heat required to change the temperature of a substance by one degree.

### Hydrogen - Thermophysical Properties

Chemical, Physical and Thermal Properties of Hydrogen - H2.

### Methane - Thermophysical Properties

Chemical, Physical and Thermal Properties of Methane - *CH _{4}*. Phase diagram included.

### Non-ideal gas - Van der Waal's Equation and Constants

The van der Waals constants for more than 200 gases used to correct for non-ideal behavior of gases caused by intermolecular forces and the volume occupied by the gas particles.

### Nozzles

Gas flow through nozzles and sonic chokes.

### Specific Heat - Online Unit Converter

Online specific heat converter with the most commonly used units.

### Speed of Sound - Equations

Calculate the speed of sound (the sonic velocity) in gases, fluids or solids.

### The Ideal Gas Law

The relationship between volume, pressure, temperature and quantity of a gas, including definition of gas density.

### Total and Partial Pressure - Dalton's Law of Partial Pressures

How to calculate total pressure and partial pressures for gas mixtures from Ideal Gas Law.

### Units of Heat - BTU, Calorie and Joule

The most common units of heat BTU - British Thermal Unit, Calorie and Joule.

### Universal and Individual Gas Constants

The Universal and Individual Gas Constants in fluid mechanics and thermodynamics. Individual gas constants for the most common gases.