## 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.

**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 p_{1}^{2}/2m +
p_{2}^{2}/2m = U constrains these 6 components to the
surface of a 6-dimensional hypersphere.

**What is the surface area of a 4-dimensional hypersphere? **
For radius r: ``area'' = 2 (pi)^{2} r^{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 U^{f N/2}. This checks for the
monatomic ideal gas, where f=3 and the multiplicity goes as U^{3N/2}.

**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 1/2^{N}, so the probability is reduced by the same factor.

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

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