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**Unformatted text preview: **Physics 404 (Prof. Hu) Final Examination Dec. 18, 2007 (Total 7 problems, 200 points. Write YOUR NAME on your exam book NOW!) 1. (24 pts) Consider a non-interacting gas of spin 1/2 fermions each of mass m initially confined in a volume V i at temperature T = 0. Let this gas expand irreversibly into a vac- uum to a final volume of V f . Calculate the temperature of the gas after expansion if V f is sufficiently large for the classical limit to apply. (12 pts) By what factor of expansion does the gas need to undergo so that its temperature will settle into a constant final value? (12 pts) 2. (30 pts) A container is divided into two equal parts by a partition containing a small hole of diameter D . Helium gas in the two parts is held at temperature T 1 = 100 K and T 2 = 400 K respectively through heating of the walls. a) How does the diameter D determine the physical processes which bring the system into a steady state? State the working principles behind each case you consider. (10 pts) b) What is the ratio of the mean free paths 1 / 2 between the two parts when D 1 , 2 and the system has reached a steady state? (10 pts) c) What is the ratio...

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