Problem 2 [35 points total]
Consider a gas with hard core inter-particle interactions, i.e.
(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]