Gases - Ratios of Specific Heat
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 = cv dT (1)
where
du = change in internal energy
cv = specific heat capacity 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 capacity 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
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):
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 |
| Carbon Dioxide | 1.28 |
| Carbon Monoxide | 1.40 |
| Chlorine | 1.33 |
| Ethane | 1.18 |
| Helium | 1.66 |
| Helium | 1.66 |
| Hydrogen | 1.41 |
| Methane | 1.32 |
| Natural Gas (Methane) | 1.32 |
| Nitrogen | 1.40 |
| Oxygen | 1.40 |
| Propane | 1.12 |
| Steam (water) | 1.33 |
| Sulphur dioxide | 1.26 |
Since the ratio is dimensionless the value is the same in the SI and the imperial system of units.
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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.
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Related Documents
- Compression and Expansion of Gases - Isothermal and Isentropic processes
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