 
Summary: Physics 408  Exam 3 Name___________________________________________
You are graded on your work, with partial credit where it is deserved.
Please give clear, wellorganized, understandable solutions.
h = 6.63!10"34
J s [Planck's constant] k = 1.38 !10"23
J/K [Boltzmann constant]
c = 3.00 !108
m/s [speed of light] G = 6.67 !10"11 N m2
kg2 [gravitational constant]
mn = 1.67 !10"27
kg [mass of neutron] M! = 1.99 !1030
kg [solar mass, i.e. mass of Sun]
The variables have their usual meanings: E = energy, S = entropy, V = volume, N = number of particles,
T = temperature, P = pressure, µ = chemical potential, B = applied magnetic field, CV = heat capacity at
constant volume, F = Helmholtz free energy, k = Boltzmann constant. Also, !!! represents an average.
1. The Gibbs free energy G is defined by G = E !TS + PV .
(a) (5) Using the standard expression for d E , obtain dG in terms of dT , dP , and dN .
(b) (5) Then obtain S , V , and µ as partial derivatives of G .
Now specialize to a system, at fixed temperature and pressure, for which
G T,P,N( )= !NkT ln z , z =
