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# Compression and Expansion of Gases

## Isothermal and isentropic gas compression and expansion processes.

The relationship between pressure and density when compressing - or expanding - a gas depends on the nature of the process. The process can be

• isothermal,
• polytropic

### Isothermal Compression/Expansion Processes

If compression or expansion of gas takes place under constant temperature conditions - the process is said to be isothermal. The isothermal process can be expressed with the Ideal Gas Law as

p / ρ = constant                         (1)

where

p = absolute pressure (Pa, N/m2)

ρ = density (kg/m3)

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 compression or expansion of gas takes place with no flow of heat energy either into or out of the gas - the process is said to be isentropic or adiabatic. The isentropic (adiabatic) process can be expressed with the Ideal Gas Law 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 ideal isothermal process must occur very slowly to keep the gas temperature constant. An ideal 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 or exponent (ranging 1 to 1.4)

## Related Topics

• Fluid Mechanics - The study of fluids - liquids and gases. Involves velocity, pressure, density and temperature as functions of space and time

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Temperature

oC
oF

Length

m
km
in
ft
yards
miles
naut miles

Area

m2
km2
in2
ft2
miles2
acres

Volume

m3
liters
in3
ft3
us gal

Weight

kgf
N
lbf

Velocity

m/s
km/h
ft/min
ft/s
mph
knots

Pressure

Pa (N/m2)
bar
mm H2O
kg/cm2
psi
inches H2O

Flow

m3/s
m3/h
US gpm
cfm

1 14