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# Compression and Expansion of Gases

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. Involving velocity, pressure, density and temperature as functions of space and time.

## Related Documents

### Density vs. Specific Weight and Specific Gravity

An introduction to density, specific weight and specific gravity.

### Gases - Ratios of Specific Heat

Ratios of specific heat for gases with constant pressure and volume processes.

### Gases - Specific Heats and Individual Gas Constants

Specific heat at constant volume, specific heat at constant pressure, specific heat ratio and individual gas constant - R - common gases as argon, air, ether, nitrogen and many more.

### Isentropic Flow

Fluid flow with constant entropy is also called isentropic flow.

### Molecular Weight of Substances

Definition and molecular weight (molar mass) of some common substances.

### Non-ideal gas - Van der Waal's Equation and Constants

The van der Waals constants for more than 200 gases used to correct for non-ideal behavior of gases caused by intermolecular forces and the volume occupied by the gas particles.

### Pressure

Introduction to pressure - online pressure units converter.

### The Ideal Gas Law

The relationship between volume, pressure, temperature and quantity of a gas, including definition of gas density.

### Total and Partial Pressure - Dalton's Law of Partial Pressures

How to calculate total pressure and partial pressures for gas mixtures from Ideal Gas Law.

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