Ideal gas: Statistical mechanics

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Presentation transcript:

Ideal gas: Statistical mechanics Temperature is related to averaged kinetic energy For each of projections (degrees of freedom):

Theorem of Equipartition of Energy: Statistical mechanics Theorem of Equipartition of Energy: Each degree of freedom contributes ½kT to the energy of a system, where possible degrees of freedom are those associated with translation, rotation and vibration of molecules

Boltzmann Distribution: Statistical mechanics Boltzmann Distribution: Distribution function (number density) nV(E): It is defined so that nV(E) dE is the number of molecules per unit volume with energy between E and E + dE Probability P(E): It is defined so that P(E) dE is the probability to find a particular molecule between E and E + dE

Statistical mechanics Free particle: Harmonic oscillator:

Averaged values: Averaged energy: Averaged velocity: Usually: Statistical mechanics Averaged values: Averaged energy: Averaged velocity: Usually: