PHYS 317 Reading Assignment #7

Read section 2.5 and answer the following questions by email, hardcopy, or web form before class Monday, September 15.

  1. For a 2 particle system, what is the dimension of the momentum space hypersphere?

    6. Since each particle has 3 momentum components, 2 particles have 6 momentum components, and a fixed value of p12/2m + p22/2m = U constrains these 6 components to the surface of a 6-dimensional hypersphere.

  2. What is the surface area of a 4-dimensional hypersphere?

    For radius r: ``area'' = 2 (pi)2 r3

  3. For a system of N particles where all of its energy is contained in quadratic degrees of freedom (f per particle), the multiplicity is proportional to U raised to what power?

    Multiplicity is proportional to Uf N/2. This checks for the monatomic ideal gas, where f=3 and the multiplicity goes as U3N/2.

  4. What is the probability of finding all N particles of a gas on the left half of a container?

    The multiplicity with all the particles on the left half is reduced by a factor of 1/2N, so the probability is reduced by the same factor.

  5. Was there anything you had particular difficulty with in this reading? Is so, describe briefly.

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