Compression and Expansion of Gases
Isothermal and Isentropic processes
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The relationship between pressure and density when compressing or expanding gases depends on the nature of the process.
- isothermal
- isentropic or adiabatic
- polytropic
Isothermal Compression/Expansion Processes
If a compression or expansion takes place under constant temperature conditions - the process is said to be isothermal. The isothermal process can with the Ideal Gas Law be expressed as
p / ρ = constant (1)
where
ρ = density
The isothermal process can also be expressed as
pV = constant (1a)
or
p1V1 = p2V2 (1b)
where
V = gas volume (m3, ft3...)
suffix1 denotes initial conditions and suffix2 denotes final conditions
Isentropic (or adiabatic) Compression/Expansion Processes
If a compression or expansion takes place under constant volume conditions - the process is said to be isentropic. The isentropic process can with the Ideal Gas Law be expressed as
p / ρk = constant (2)
where
k = cp / cv - the ratio of specific heats - the ratio of specific heat at constant pressure - cp - to the specific heat at constant volume - cv
The isentropic or adiabatic process can also be expressed as
pVk= constant (2a)
or
p1V1k = p2V2k (2b)
Polytropic Compression/Expansion Process
An isothermal process must occur very slowly to keep the temperature in the gas constant. The adiabatic process must occur very rapidly without any flow of energy in or out of the system. In practice most expansion and compression processes are somewhere in between, or said to be polytropic.
The polytropic process can be expressed as
pVn= constant (3a)
or
p1V1n = p2V2n (3b)
where
n = polytropic index (ranging 1 to 1.4)
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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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