PHYSICS 140A : STATISTICAL PHYSICS
HW ASSIGNMENT #4
(1) The latent heat of vaporization of hexane (C6 H14 ) is ` = 30.8 kJ/mol. The boiling point
at p = 1.00 atm is T ∗ = 68.9◦ C. Assuming that ` is roughly constant over this part of the
vaporization curve, what will be boiling point be at a pressure p = 0.50 atm?
(2) A chemical reaction among σ species may be written symbolically as an equation of the
form
ζ1 A1 + ζ2 A2 + · · · + ζσ Aσ = 0 ,
where Aa is a chemical formula, and ζa is a stoichiometric coefficient. Chemical reactions
are discussed in section §1.13 of the notes.
(a) Show that the dimension of the coexistence space for a system with σ species, ϕ
coexisting phases, in which there are ρ chemical reactions is
dcoex (σ, ϕ, ρ) = 2 + σ − ϕ − ρ .
(b) Consider a chemically reactive system containing solid sulfur S and three gases O2 ,
SO2 , and SO3 . Two possible reactions take place:
S + O2
2 S + 3 O2
−*
)− SO2
−*
)− 2 SO3 .
What is the maximum number of phases of this system that can coexist at any point
in thermodynamic state space?
(3) A small college dormitory contains five different rooms. Each room houses two persons.
Ten students live in the dorm: four physics majors and six chemistry majors.
(a) Suppose the dormitory rules forbid physics and chemistry majors from sharing a room.
How many possible distinct room assignments are there? Note that the rooms are
themselves distinct.
(b) If the rules are relaxed and physics and chemistry majors are allowed to room together,
how many possible distinct room assignments are there?
(c) Generalize to the case of M +N rooms, 2M physics majors, and 2N chemistry majors.
What is the numbers of possible room assignments W1 (M, N ) assuming the rule from
part (a) is enforced? What is the number of possible room assignments W2 (M, N )
assuming the rule is relaxed? Writing M = x · (M + N ), what is the change in
dimensionless entropy ln W2 − ln W1 upon relaxing the rule in the limit where M + N
is large and x is finite?
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