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Additional resources for Britannica Discovery Library Volume 6 - Colors
Since the ideal gas equation of state relates pressure, molar volume, and temperature as pv = rt, the temperature t must be related to the average kinetic energy of the molecules as (19) 41 7 The Britannica Guide to Matter 7 This expression is often written in molecular (rather than molar) terms as (1/2)[mv2] = (3/2)kT, where k = R/N0 is called Boltzmann’s constant, named after Ludwig Boltzmann, a 19th-century Austrian physicist who substantially contributed to the foundation and development of statistical mechanics.
Two limitations of the model are briefly discussed below. Free-Molecule Gas The mean free path in a gas may easily be increased by decreasing the pressure. If the pressure is halved, the mean free path doubles in length. Thus, at low enough pressures the mean free path can become sufficiently large that collisions of the gas molecules with surfaces become more important than collisions with other gas molecules. In such a case, the molecules can be envisioned as moving freely through space until they encounter some solid surface; hence, they are termed free-molecule gases.
Two other facts are especially important. The first is that the lengths involved, especially the mean free path, are minute compared with ordinary lengths, even with the diameter of a capillary tube. This means that gas behaviour and properties are dominated by collisions between molecules and that collisions with walls play only a secondary (though important) role. The second is that the mean free path is much larger than the molecular diameter. Thus, collisions between pairs of molecules are of paramount importance in determining ordinary gas behaviour, while collisions that involve three or more molecules at the same time can basically be ignored.