Postulates

Postulates

The theory for ideal gases makes the following assumptions:

• The gas consists of very small particles, all with non-zero mass.
• The number of molecules is so large that statistical treatment can be applied.
• These molecules are in constant, random motion. The rapidly moving particles constantly collide with the walls of the container.
• The collisions of gas particles with the walls of the container holding them are perfectly elastic.
• Except during collisions, the interactions among molecules are negligible (they exert no forces on one another).
• The total volume of the individual gas molecules added up is negligible compared to the volume of the container. This is equivalent to stating that the average distance separating the gas particles is large compared to their size.
• The molecules are perfectly spherical in shape, and elastic in nature.
• The average kinetic energy of the gas particles depends only on the temperature of the system.
• Relativistic effects are negligible.
• Quantum-mechanical effects are negligible. This means that the inter-particle distance is much larger than the thermal de Broglie wavelength and the molecules are treated as classical objects.
• The time during collision of molecule with the container's wall is negligible as compared to the time between successive collisions.
• The equations of motion of the molecules are time-reversible.

More modern developments relax these assumptions and are based on the Boltzmann equation. These can accurately describe the properties of dense gases, because they include the volume of the molecules. The necessary assumptions are the absence of quantum effects, molecular chaos and small gradients in bulk properties. Expansions to higher orders in the density are known as virial expansions. The definitive work is the book by Chapman and Enskog but there have been many modern developments and there is an alternative approach developed by Grad based on moment expansions.^{[citation needed]} In the other limit, for extremely rarefied gases, the gradients in bulk properties are not small compared to the mean free paths. This is known as the Knudsen regime and expansions can be performed in the Knudsen number.