Perfect gas (ideal gas)

A perfect gas (or ideal gas) is defined as a gas that follows the laws of Boyle and Gay-Lussac. The perfect gas model explains the behavior of gases using the kinetic-molecular theory; here are the characteristics of an ideal gas:

  • the average kinetic energy of the gas molecules (thermal agitation motion) is directly proportional to the absolute temperature;
  • the gas molecules do not attract each other reciprocally; therefore the distance forces of interaction and any other type of energy other than kinetic energy are null. In a real gas, the situation is generally more complicated, because there are, even if weak, reciprocal cohesion forces between the gas molecules, and furthermore they also possess a particular potential (gravitational) energy. Moreover, in a real gas subject to compression, the distances between the molecules become too small to be able to neglect the reciprocal cohesion forces, while in gas at very low temperature the collisions between the particles become so sporadic that they are not significant. However, the behavior of a real gas, provided it is sufficiently rarefied, can be assimilated to that of a perfect gas. For this reason gases, unlike solids and liquids, have no shape of their own and tend to expand, occupying the entire volume of their container;
  • the volume occupied by the molecules is negligible, this feature is also valid for real gases since the particles are assumed as point-like;
  • the molecules interact with each other and with the walls of the container through perfectly elastic collisions (i.e., there is no dispersion of kinetic energy during impacts) the impacts against the walls determine the pressure exerted by the gas;
  • the ideal gas molecules are assumed as rigid spheres, having all identical mass and a negligible volume compared to that occupied by the entire gas;
  • the motion of molecules is random and disordered in every direction but subject to deterministic laws.

These approximations lead to formulate the law known as the ideal gas law, which describes, in thermodynamic equilibrium conditions, the relationship between pressure, volume and temperature of the gas:

\[PV=nRT\]

where \(P\) is the pressure, \(V\) is the volume occupied by the gas, \(n\) the amount of substance of the gas, \(R=8,314462618…\;\textrm{J} / \textrm{mol}\cdot \textrm{K}\) is the universal constant of perfect gases and \(T\) is the temperature.

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