Physics 224   Fall 2000

		Discoveries and Inventions of Modern Physics 		due 11:00 am Tuesday Oct. 10

PROBLEM SET 2

Oct. 5 Colloquium: ``Imaging the Early Universe: First Results from BOOMERANG''
Professor Andrew Lange, Caltech
3:30 pm, 101 Rowland Hall

1.

Consider a nonrelativistic free particle in a cubic container of edge length L and volume V=L³.

(a)

Each quantum state s of this particle has a corresponding kinetic energy $\varepsilon_{s}$ which depends on V. What is $\varepsilon_{s}(V)$?

(b)

Find the contribution to the gas pressure $p_{s}=-(\partial \varepsilon_{s}/\partial V)$ of a particle in this state in terms of $\varepsilon_{s}$ and V.

(c)

Use this result to show that the mean pressure <p> of any ideal gas of particles is always related to its mean total kinetic energy <E>by $<p>=\frac{2}{3}<E>/V$.

2.

Eisberg and Resnick: 1.16

3.

Eisberg and Resnick: 11.3 (Note that in terms of the notation used in class $\varepsilon_F=\mu$.)

4.

Eisberg and Resnick: 11.5 (Note that in terms of the notation used in class $\alpha=-\beta\mu$.)

5.

Plot the blackbody distribution spectrum $\rho_{T}(\eta)$versus $\eta=\hbar\omega/kT$ at T=3 K.

6.

Eisberg and Resnick: 1.19 (Hint: Use the result of the previous problem and the result stated in problem 1.18.)

7.

Eisberg and Resnick: 1.12