3.1: Volume Exchange
REMEMBER EQUAL DENSITIES
a) NL/ML=NR/(M-ML)
b) the particles are identicle, and there is multiple occupancy, therefore
   OMEGA=(N+M-1)!/((M-1)!*N!)
   entropy = ln[OMEGAL*OMEGAR]
c) DO THIS EXACTLY LIKE LECTURE 6 ACT 2
   find OMEGAL and OMEGAR for each microstate

3.2: Carnot Cycle
a) TC/TH = QC/QH
b) Wby = QH - QC
c) efficiencycarnot = 1 - TC/TH
d) TC/TH = QC/(W+QC)
e) QH = W + QC
f) K = QC / W

3.3: Particles In a Box
N = # of particles
M = # of bins [M=2 because the bins are either left or right]
a) P=1/MN
b) entropy = ln[N!/(N!*0!)] = 0
c) P=[N!/(NL!*NR!)]/MN
d) entropy = ln[N!/(NL!*NR!)]
e) P=[N!/(NL!*NR!)]/MN
f) entropy = ln[N!/(NL!*NR!)]
g) the higher entropy will be more probable

3.4: Carrier Diffusion In a Semiconductor
a) (3/2)*k*T = (1/2)*m*v2
   v = sqrt[3kT/m]
b) t=l/v
   l=tv
c) D=(1/3)*v*l
d) x2=2Dt
   t = x2/2D

3.5: Counting In a Two-State System
a) P=1/2N  ::  N=total trials
b) P=[N!/(NU!ND!)]/2N
c) P(m)=sqrt[2/(N*pi)]*exp[-m2/(2N)]  where m=NU-ND  ... in this case m=0
   P(0)=sqrt[2/(N*pi)]
d) W2/W1 = P1/P2
   P1 = sqrt[2/(N1*pi)]
   P2 = sqrt[2/(N2*pi)]