SLec4 - Lecture 4: Kinetic Theory of Gases and some math We...

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Lecture 4: Kinetic Theory of Gases and some math We have derived the Barometric formula From the point of individual molecules, the formula tells us what the probability is that a molecule is at the height z . It relates the potential energy of the molecule in the gravitational field to the average thermal energy k b T. The same kind of distribution holds for all other energy contributions, in particular, for the kinetic energy. So their probability distributions are where E v is the kinetic energy of the molecule or its internal rotational and vibrational energy. The above probability f(v) is called the Boltzmann distribution (its 3D integral over all v is normalized to 1, which gives C=(1/2 π m mol k b T) 3/2 ).
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Example: - it relates statistical theory to thermodynamics (chem 346). Let us try to calculate the pressure that the molecules exert on the walls. The number of molecules with velocities in the interval v and v+dv , which collide with the surface element dS in time dt is (without all the details)
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SLec4 - Lecture 4: Kinetic Theory of Gases and some math We...

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