Homework 1

NOTE: acceptable formats for turning in your homework are as follows:-

(1) handwritten in blue or black ink

(2) handwritten in 2B or darker pencil

(3) typewritten.

NO other types of work will be marked.  (Why?  e.g. light pencils are very hard to read under artificial light; I won't endanger my TA's eyes for the sake of indulging students' colour preferences...  Also, the TA will be marking in red so it would be very unwise to write your answers in red.)

Total marks: 50.

[5 marks] Question 1:  Give a concise definition for the following terms, explaining concisely any symbols you use and giving a brief physics interpretation/example:

(a) Spin Excess

(b) Fundamental Assumption of Thermal Physics

(c) Second Law of Thermodynamics (in statistical form)

(d) Degeneracy/Multiplicity

(e) Configuration

[10 marks] Question 2: KK 2.1  Entropy and Temperature

[10 marks] Question 3: KK 2.3  Quantum harmonic oscillator

[5 marks] Question 4: KK 2.4  Monkeys and Shakespeare

[10 marks] Question 5: KK 2.5  Additivity of entropy for two spin systems

[10 marks] Question 6: . Paramagnetic Systems (part of an old midterm question)

Consider a system S which consists of N nearly independent (and distinguishable) quantum spin elements, each with magnetic moment  m.  . The whole system is in a magnetic field of strength B.  For each spin, three states are possible, as each spin may have component –1, 0, or 1 along the B-field. (Without quantum mechanics, you may think of the spin parallel to the magnetic field, perpendicular to the magnetic field, or antiparallel to the magnetic field.)

[2] (a) What is the total number of possible states of the system?