Ideal gas Totally Explained

Everything about Ideal Gas totally explained

An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces, where the constituent atoms or molecules undergo perfectly elastic collisions with the walls of the container and each other and are in constant random motion. Real gases don't behave according to these exact properties, although the approximation is often good enough to describe real gases.
   These four properties that constitute an ideal gas can be easily remembered by the acronym PRIE, which stands for;
   - Point masses (molecules occupy no volume)
   - Random Motion (molecules are in constant random motion)
   - Intermolecular forces (there are NO intermolecular forces between the particles)
   - Elastic collisions (the collisions involving the gas molecules are totally elastic)
   The concept of ideal gas is useful in technology because one mole (6.02214 particles) of an ideal gas has a volume of 22.4 liters at the standard conditions for temperature and pressure and many common real gases approach this behaviour in these conditions.
   The conditions in which a real gas will behave more and more like an ideal gas is either at very high temperatures (as the molecules of the gas have so much energy that the intermolecular forces and energy lost in collisions is negligable) and at very low pressures (as the molecules of the gas rarely collide or come into close enough proximity for intermolecular forces to be significant).

Types of ideal gases

There exist three basic types of ideal gas:

the classical or Maxwell-Boltzmann ideal gas,
the ideal quantum Bose gas, composed of bosons, and
the ideal quantum Fermi gas, composed of fermions.

The classical ideal gas can be separated into two types: The classical thermodynamic ideal gas and the ideal quantum Boltzmann gas. Both are essentially the same, except that the classical thermodynamic ideal gas is based on classical thermodynamics alone, and certain thermodynamic parameters such as the entropy are only specified to within an undetermined additive constant. The ideal quantum Boltzmann gas overcomes this limitation by taking the limit of the quantum Bose gas and quantum Fermi gas in the limit of high temperature to specify these additive constants. The behavior of a quantum Boltzmann gas is the same as that of a classical ideal gas except for the specification of these constants. The results of the quantum Boltzmann gas are used in a number of cases including the Sackur-Tetrode equation for the entropy of an ideal gas and the Saha ionization equation for a weakly ionized plasma.

Classical thermodynamic ideal gas

The thermodynamic properties of an ideal gas can be described by two equations :
The equation of state of a classical ideal gas is given by the ideal gas law. ť

pV = N k_B T = nRT.,

The internal energy of an ideal gas is given by:
ť

U = hat

where Λ is the thermal de Broglie wavelength of the gas and g is the degeneracy of states.

Ideal Bose and Fermi gases

An ideal gas of bosons (for example a photon gas) will be governed by Bose-Einstein statistics and the distribution of energy will be in the form of a Bose-Einstein distribution. An ideal gas of fermions will be governed by Fermi-Dirac statistics and the distribution of energy will be in the form of a Fermi-Dirac distribution.

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