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lec15-equipart-energy-notes

lec15-equipart-energy-notes - 1 The Equipartition of Energy...

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1 The Equipartition of Energy Theorem. Annotated lecture notes by M. Croft ---------------------------------------------------------------------------------------------------------------------------- Note this material is important to this course and is not in the book. This material applies the macroscopic concepts of mechanical energy to microscopic collections of ~10 23 molecules. In so doing it casts the concepts of temperature and heat transfer in terms of physics you have already learned. ---------------------------------------------------------------------------------------------------------------------------- The equipartition (or equal division) of energy theorem involves the concept that, in thermal equilibrium, energy is shared equally among all of its various possible forms (or degree of freedom). Moreover the average amount of energy per degree of freedom is kT/2 per molecule or RT/2 per mole. [ Here k = Boltzman’s constant, R= k N A is the ideal gas constant and N A is Avagadro’s number.] Operationally a degree of freedom is identified with a quadratic term in the total mechanical energy. For this class this means a kinetic energy term involving a velocity component squared. {It is worth noting that it can also be a harmonic oscillator potential energy involving a quadratic displacement from equilibrium but this concept is not required for 203.} ---------------------------------------------------------------------------------------------------------------------------- This figure illustrates the application of the equipartition principal to a monatomic ideal gas. Note that there are three degrees of freedom associated with the <v x 2 >, <v y 2 > and <v z 2 > kinetic energy terms respectively. [Here <> denotes the average taken over all of the molecules of the gas].

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