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)]