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 =cv dT (1)
where
du = change in internal energy (kJ/kg)
cv = specific heat for gas in a constant volume process (kJ/kgK)
dT = change in temperature (K)
Specific heat cv varies with temperature but within moderate temperature changes the specific heat - cv - can be regarded as constant.
Enthalpy
For an ideal gas the enthalpy - h - is a function of temperature. Change of enthalpy can be expressed as
dh = cp dT (2)
where
dh = change in enthalpy (kJ/kg)
cp= specific heat for gas in a constant pressure process (kJ/kgK
Specific heat cp 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/m3)
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):
cp - cv = R (7)
The difference cp - cv is constant for an ideal gas.
Ratio of Specific Heat
The Ratio of Specific Heat can be expressed as:
k = cp / cv (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.
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