Compression and Expansion of Gases

Isothermal and Isentropic processes

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

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...)

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 / 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 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