 #1
Clara Chung
 304
 14
 Homework Statement:

Attached below
Please tell me whether my a,b,c,d,e parts are right and teach me how to solve f and g
 Relevant Equations:
 Attached below
Equations that might be helpful:
Attempt:
a) (N_max)!/(n!*(N_maxn)!) i.e. N_max C n
b) Total Z = sum n=0 to N_max [(N_max C n) e^(buN)] = (1+e^(bu))^N_max
Individual Z = 1+e^(bu*1) = (1+e^(bu))
so individual Z^N_max = total Z
c) Now, I use Z to represent the total Z,
By equation 6.14, N = KT d(InZ)/du = kTN_max b/(1+e^bu)= N_max / (1+e^bu) (because b=1/kT)
After some manipulation, bu=In(N/ (N_maxN))
d) N decreases, so bu increases, so bu decreases.
e) using the grand potential. S=uN/T + k/T*lnZ = uN/T + kNln(1+e^bu)=uN/T+kNln(1+N/(N_maxN)) = uN/T+kNln(N_max/(N_maxN))
when N tends to zero it becomes 0, when N tends to N_max it becomes infinity (which I think is a bit strange), when N tends to N_max/2, it tends to N_max(kln2u/2T).
f) I try to write down the grand partition function but I don't know how to model it and not sure if it is helpful... Can someone tell me what to do...?