Gases - Ratios of Specific Heat

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

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 = cv dT         (1)

where

du = change in internal energy

cv = specific heat for the gas in a constant volume process

dT = change in temperature

cv varies with temperature, but within a moderate temperature change the heat capacity - cv - can be regarded as constant.

Enthalpy

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

dh = cp dT         (2)

where

dh = change in enthalpy

cp= specific heat for the gas in a constant pressure process

cp 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

p = absolute pressure

ρ = density

Combining (3) and the Ideal Gas Law gives:

h = u + R T         (4)

where

R = the individual gas constant

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):

cp - cv = R         (7)

The difference cp - cv is constant for an ideal gas.

The Ratio of Specific Heats

The Ratio of Specific Heats can be expressed as:

k = cp / cv         (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 1.12
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.

Related Topics

  • Fluid Mechanics - The study of fluids - liquids and gases. Involves various properties of the fluid, such as velocity, pressure, density and temperature, as functions of space and time.

Related Documents

Search the Engineering ToolBox

Engineering ToolBox - SketchUp Edition - Online 3D modeling!

3D Engineering ToolBox - draw and model technical applications

Engineering ToolBox - SketchUp Edition - add standard and customized parametric components - like flange beams, lumbers, piping and more - to your SketchUp model - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro. Add from the Sketchup Extension Warehouse!

Translate the Engineering ToolBox!
About the Engineering ToolBox!