Prof. Raghuveer Parthasarathy
University of Oregon; Spring 2008
Physics 353 – Statistical Mechanics
Study Guide: Solutions to Suggested Problems
1. Barometric pressure.
I’ll call the height h, to avoid too many “z”s.
Consider “layers” of atmosphere, each with some concentration ()nh . Diffusive equilibrium means
that the chemical potential of all layers is the same; ()h
μ
= constant. The chemical potential has an
“internal” and “external” part, where the external chemical potential is any relevant potential energy:
int ext
μ
μμ
=+. Here, ()
ln
int
Qint
nh
nZ
μτ
⎛
=
⎞
⎜⎟
⎜⎟
⎝⎠
(given) and ext mgh
μ
=
(gravitational potential). Calling
the concentration at height zero 0
n, wee see that () (0)h
μ
μ
=
implies:
0
()
ln ln 0
Qint Qint
n
nh mgh
nnZZ
ττ
⎛⎞ ⎛⎞
+= +
⎜⎟ ⎜⎟
⎜⎟ ⎜⎟
⎝⎠ ⎝⎠
. Therefore
() ()
0
ln ( ) ln
mgh
nh n
τ
=− + , and
()
0
() exp /nh n mgh
τ
=− .
2. Fermion chemical potential.
