 
Summary: Physics 408  Exam 1 Name___________________________________________
You are graded on your work, with partial credit where it is deserved.
Please give clear, wellorganized solutions.
heat capacity (at constant volume) for liquid water = 4200 J/kg !K , 0!
C=273 K
1. (a) (13) A kilogram of liquid water is heated from 0!
C to 100!
C . What is its change in entropy? (Note that
the temperature is not constant.)
(b) (12) What is the change in the multiplicity (i.e., the number of allowed microstates)? Give the answer as the
ratio Wfinal /Winitial .
2
2. Imagine an anomalous harmonic oscillator with frequency ! , which has an upper limit N on the number of
quanta that it can accommodate. I.e., the allowed states are n = 0,1,2,...,N with energies !n = nh" , and N
finite. (We are considering only the energy of the quanta, and leaving aside the zeropoint energy.)
(a) (13) Show that the partition function can be summed in the form
Z =
1! e
! N+1( )h"/kT
1! e!h"/kT
