# set3 - Department of Physics The Ohio State University Prof...

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Department of Physics Prof. R. Bundschuh The Ohio State University Third Problem Set for Physics 847 (Statistical Physics II) Winter quarter 2004 Important dates: Feb 10 10:30am-12:18pm midterm exam, Mar 16 9:30am-11:18am ±nal exam Due date: Tuesday, Jan 27 7. Ultra-relativistic gas 12 points If the particles of a gas have velocities close to the speed of light c , their energy has to be calculated relativistically. In the limit of massless particles (e.g., photons) which travel at the speed of light, this relation between the momentum ~ p i of particle i and its energy E i becomes E i = c | ~ p i | . Thus, the energy of a gas of N of these particles in a box of volume V is H ( ~x N ) = c N i =1 | ~ p i | all ~ r i inside volume V + otherwise . a) Calculate the partition function of such an ultra-relativistic gas. (Hint: R 0 x 2 exp( - x ) dx = Γ(3) = 2.) b) Calculate the free energy of the ultra-relativistic gas as a function of its natural variables temperature

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set3 - Department of Physics The Ohio State University Prof...

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