Physics 224   Fall 1998

		Phenomenology 		due 11:00 am Thursday Nov. 5

PROBLEM SET 5

Oct. 30 Colloquium: ``On the Geometry of 'Time Travel' in Godel's Universe''
Professor David Malament, University of Chicago
3 pm, 101 Rowland Hall (formerly PS I)

1.

What will your final report be on? To find possible topics, look at Eisberg and Resnick, The New Physics, or Scientific American.

2.

In the transition $^{10}H_{3/2}\;-\;^{10}G_{1/2}$, how many lines will appear in the Zeeman pattern? Explain your reasoning by listing the allowed transitions.

3.

Eisberg and Resnick problem 12.22(a).

4.

How does the transition temperature T_C depend on the number of particles N if E=pc for Bose condensation? (Hint:You don't have to evaluate any integrals. Just try scaling, i.e., make the variables in the integral dimensionless. Your answer should be of the form $T_C\sim N^{\alpha}$. Find $\alpha$.)

5.

In the Weiss (mean-field) theory of ferromagnetism the Gibbs free energy ( G=E(M)-HM-TS, where H is the externally applied magnetic field, M is the magnetization, E is the internal energy, and S is the entropy) has the form

G=G_o(T)+a(T)M²+b(T)M⁴+O(M⁶)-MH (1)

where G_o(T) is independent of M, and where the coefficient b(T) is a slowly varying function of T but a(T) is of the form a_o(T-T_C), T_C being the critical temperature in Weiss theory. Assume that T is close to T_C and that M is small. Using the fact that in thermal equilibrium M will take the value which minimizes G, find (a) the equilibrium value of Mfor H=0, for T>T_C and T<T_C; (b) the form of M at T_C as a function of H; (c) the zero-field differential susceptibility $\chi=(\partial M/\partial H)_{T,H=0}$for T>T_C and T<T_C; and (d) the discontinuity in the specific heat at constant H ( $C_H=-T(\partial^2G/\partial T^2)_H$) at the point T=T_C and H=0. In other words find the difference between the limits of C_H(T,H=0) as $T\rightarrow T_C$ from above and from below.