Compression and Expansion of Gases

Isothermal and Isentropic processes

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 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

p = absolute pressure

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

Isentropic (or adiabatic) Compression/Expansion Process

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 / ρ^k = constant (2)

where

k = c_p / c_v - the ratio of specific heats - the ratio of specific heat at constant pressure - c_p - to the specific heat at constant volume - c_v

The isentropic or adiabatic process can also be expressed as

pV^k= constant (2a)

or

p₁V₁^k  = p₂V₂^k (2b)

Polytropic Compression/Expansion Process

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)

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