Statistical Mechanics - Physics at Oregon State University

66 CHAPTER 3. VARIABLE NUMBER OF PARTICLES
A system can be in one of four states. These are
(1) No particles, zero energy
(2) One particle, energy ɛ1
(3) One particle, energy ɛ2
(4) Two particles, energy ɛ1 + ɛ2 + I
where ɛ2 > ɛ1 > 0 and I < 0. This sign of I is unusual. The temperature
is T and the chemical potential is µ. This is a very simple model, and in order
to make this realistic we should really consider many of these systems together.
That is not asked in this question, though.
(A) Calculate the grand partition function
(B) Calculate N(T, µ)
(C) Calculate
∂N
∂T µ and show that this can be negative. What does that
mean?