Dilute gas hypothesis

The phrase dilute gas indicates that the physical volume n[ 7rt/ ] occupied by the gas particles (molecules) is small compared to the container volume V available to the gas. Mathematically this condition can be expressed as  

A real gas is also considered dilute provided that the mean free path I is much larger than the particle size, i.e., I d. 

Assuming that the molecules are rigid elastic spheres a typical value for the mean free path for a gas, say oxygen, can be calculated from (2.611). Consider a typical room temperature at 300 (K) and a pressure of 101325 (Pa). The collision diameter of molecular oxygen can be set to 3.57 x 10 ° (m) in accordance with the data given by Laidler [80], example 1.4. We can then calculate the mean free path I for oxygen from (2.611)  

Since the molecular diameters for the different gases are of the same order, the mean free path in any gas at the given temperature and pressure is of the order 10 (cm). In this case it follows that the mean free path is about hundred times the diameter of the molecule, thus the gas is dilute. However, it is noted that at higher gas pressure, say 10132500 (Pa), the mean free path is reduced and comparable with the dimensions of a molecule. In this case the assumption of molecular chaos may not be valid so the gas cannot be considered dilute [20]. 

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