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Engineering ToolBox > Compression and Expansion of Gases
The relationship between pressure and density when compressing or expanding gases depends on the nature of the process.
If the compression or expansion takes place under constant temperature conditions - the process is called isothermal. The isothermal process can on the basis of 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...)
suffix 1 denotes initial conditions and suffix 2 denotes final conditions
If the compression or expansion takes place under constant volume conditions - the process is called isentropic. The isentropic process can on the basis of 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)
An isothermal process must occur very slowly, so that the temperature in the gas remains constant. The adiabatic process must occur very rapidly so there is no flow of energy in or out of the system. In practice most expansion and compression processes are somewhere in between - polytropic.
The polytropic process can be expressed as
pVn= constant (3a)
or
p1V1n = p2V2n (3b)
where
n = polytropic index (lying between 1 and 1.4)