hwk11 - M 1 and M 2 interact via an attractive potential...

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PH421 - Thermal and Statistical Physics Assignment 11 - Apr 4, 2008 1. Maxwell’s distribution of speeds - 1 Consider an ideal gas in equilibrium at temperature T , and composed of molecules of mass m . Show that: < v > = r 8 kT πm (1) v max = r 2 kT m (2) < v 2 > = 3 kT m (3) where v max is the most probable speed. 2. Maxwell’s distribution of speeds - 2 (a) Show that the distribution of kinetic energies ± in an ideal gas that obeys the Maxwellian distribution of speeds is: F ( ± ) = 2 π ± 1 πkT ² 3 / 2 ± 1 / 2 e - ± kT (4) (b) Calculate the most probable kinetic energy in a Maxwellian gas. 3. Application of the equipartition theorem Consider a diatomic molecule in which two atoms of mass
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Unformatted text preview: M 1 and M 2 interact via an attractive potential. Assume that: • The attractive potential can be approximated as a square term of the scalar distance r between the two atoms; • The molecule moves freely in 3-D space; • The atoms’ motion relative to the center of mass can be described by three variables r , θ and φ . Recall that the corresponding terms in the Hamiltonian are square terms in these variables. Find the specific heat capacity at constant volume C V for a diffuse gas composed of these molecules....
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