Ideal gas

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Ideal gas (also called perfect gas) is a hypothetical fluid which obeys the gas laws exactly. It consists of molecules which occupy negligible space and undergo perfect elastic collisions with each other, with no intermolecular forces and no intramolecular storage of energy.

At low density and high temperature, real fluids roughly approximate the behavior of an ideal gas. However, at lower temperature and high density, a real fluid deviates strongly from the behavior of an ideal gas, particularly as it condenses from a gas into a liquid or solid. These deviations are often approximated through quantum-mechanical statistic methods. At extremely low temperatures, the ideal gas concept may be extended to that of an ideal Fermi gas or Bose gas.

The ideal gas law relates physical conditions as follows:

<math>

PV = n_{\mbox{moles}}RT = 1000 mRT/u = n_{\mbox{molecules}}kT <math>

where

P is the pressure of the gas
V is the volume containing the gas
<math>n_{\mbox{moles}}<math> is the number of moles of the gas, and <math>n_{\mbox{molecules}}kT<math> the number of molecules
R = 8.314 J K^-1 mol^-1 is the universal gas constant
k = 1.381 × 10⁻²³ J/K is the Boltzmann constant
T is the temperature of the gas
m is the mass in kg
u is the molecular mass

The translational kinetic energy is

<math>E = 1.5 PV = 12.47 n_{\mbox{moles}}T =

12 470 mT/u = 2.07 \times 10^{-23} n_{\mbox{molecules}}T<math> Thus the kinetic energy per Kelvin is:

per mole 12.47 J
per molecule 20.7 yJ = 129 μeV

At standard temperature (273.15 K) we get:

<math>E = 3406 n_{\mbox{moles}} =

3 406 000 m/u = 5.65 \times 10^{-21} n_{\mbox{molecules}}<math> Thus the kinetic energy is:

per mole 3406 J
per molecule 5.65 zJ = 35.2 meV

At standard pressure (101 325 Pa) we get:

E = 151 988 V

Thus the energy is ca. 152 kJ/m³.

At standard temperature and pressure (273.15 K, 101 325 Pa) we get:

<math>V = 0.0224 n_{\mbox{moles}} =

22.4 m/u = 3.72 \times 10^{-26} n_{\mbox{molecules}}<math>

Thus:

the volume per mole is 22.4 litre, and conversely, a cubic metre contains 1000/22.4 = 44.6 mole
the density in kg/m³ is 0.0446 times the average molecular mass, hence between 0.0892 and ca. 10 (see also density of gas)
the volume of space available per molecule is 37.2 nm³

cs:Ideální plyn de:Ideales Gas eo:Ideala gaso fr:Gaz parfait he:גז אידאלי nl:Ideaal gas ja:理想気体 pt:Gás perfeito sl:Idealni plin sv:Perfekt klassisk gas pl:Gaz dooskonały