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Physics 418: Statistical Mechanics I
Prof. S. Teitel stte@pas.rochester.edu ----- Spring 2002

Problem Set 5

Due Tuesday, April 23, in lecture

• Problem 1 [15 points]

Consider a non-interacting ideal gas of non-relativistic bosons (i.e. e(p) = p2/2m) in d dimensions, where d is any number. Show that there is no Bose Einstein condensation for any d less than or equal to two.

• Problem 2 [35 points total]

Consider a gas with hard core inter-particle interactions, i.e.

 u(r) = infinity      0 for rro
(a) Compute the 2nd and 3rd virial coefficients, B2 and B3 for d=1 dimension (hard rods). [7 points]

(b) Do the same for d=2 dimensions (hard disks). [7 points]

(c) Compute the isothermal compressibility, kappaT, in terms of the virial expansion to 2nd order, i.e. through B2 and B3. [7 points]

(d) Compute the specific heat at constant pressure, Cp, in terms of the virial expansion to 2nd order, i.e. through B2 and B3. (Hint: to compute Cp you might wish to use the formula that relates it to CV, kappaT, and the coefficient of thermal expansion alpha.) [7 points]

(e) Using your results in parts (a) and (b), and using Pathria Eqs. (9.3.15) and (9.3.20) to get B2 and B3 for hard spheres in d=3 dimensions, make a table showing how kappaT and Cp-CV vary with dimension d for hard core interactions. Comment on any trends you see. [7 points]

Last update: Monday, August 20, 2007 at 12:10:03 PM.