THE MOLECULAR DYNAMICS of AIR

Dry air is a mixture of gases, primarily nitrogen and oxygen with a small amount of argon. Molecular nitrogen is composed of two nitrogen atoms joined by a covalent bond of length 1.09 Å. Molecular oxygen is similarly composed of two oxygen atoms with a bond length of 1.21 Å. Argon exists as a single isolated atom with a mean radius of 0.95Å. Typically 78 of 100 molecules of dry air are nitrogen, 21 are oxygen, and 1 is argon.

Air molecules are never at rest. They undergo constant random thermal motions of a variety of types. The simplest type is that of uniform translation. The mean speed is about 500 m/s which is greater than the speed of sound (340 m/s). Each molecule has three degrees of translational motion: up and down, left and right, and backward and forward..

Air molecules take up only 0.1% of the volume they occupy. Thus air is a very sparse gas in which 99.9% of the atmosphere is vacuum. However there are 2.7 x 1019 molecules in every cubic centimeter of air. This high number density coupled with the large translational speeds implies that the air molecules are constantly colliding with each other. The mean time between collisions is 0.2 x 10-9 s. Thus an average molecule undergoes 5 collisions every nanosecond. (One nanosecond corresponds to the time it takes light to travel 30 centimeters in a vacuum.) The mean free path is the average distance traveled by a molecule before it collides with another molecule in the gas. Typically this distance is about 10-5 cm or about 500 to 1000 molecular radii.

Other types of random thermal motions are possible for a molecule depending on its shape. Monatomic gases like argon can only translate. Diatomic molecules like nitrogen and oxygen can undergo rotations and a vibration. The two rotational degrees of freedom are degenerate in the sense that it is not possible to distinguish between the two. Energetically the single vibrational mode has two degrees of freedom: energy can be stored in the kinetic energy of the vibration or in the potential energy of the molecule associated with the interatomic bond or "spring."

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