11. The ground state energy of a free Fermi gas comprising N particles in a box of volume V in terms of the Fermi energy Ep is Part N 1 ET A) NEF B) NEF NEF D) NEP E) 2 N Ef= Ite na un N 2 2n=N Ef = 1/₂ n= cv MON P No 24
11. The ground state energy of a free Fermi gas comprising N particles in a box of volume V in terms of the Fermi energy Ep is Part N 1 ET A) NEF B) NEF NEF D) NEP E) 2 N Ef= Ite na un N 2 2n=N Ef = 1/₂ n= cv MON P No 24
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Transcribed Image Text:n=1
11. The ground state energy of a free Fermi gas comprising N particles in a box of volume V in terms of
Part = N
the Fermi energy Ep is
NORT
A) NEF
B) NEF
A) PR
B) P₁ = e
C) P₁₁ = e
D) Pn=f
NEF
D) NEF
E) 2 N
12. For a given macrostate of a system, let P be the probability that the system is in the microstate
14 >. The corresponding Gibbs entropy is given by S-k En PinPn. We can obtain the familiar
Boltzmann entropy S = k In from the given Gibbs entropy if the probability distribution is, (♫ is
the number of accessible microstates),
=
hw
WEE
=
Ef-
nt & hun)
1
A) E
B) E2
2 N
~/M
D) E
E) Independent of energy E
+
2
E) P₁ = 2²
=
13.For a system with linear dispersion E(k)= hvk, in three dimensions, the density of states at energy
E depends on energy as
+ 1 h mk + / buk
2n=N
M/M.
rim
Ef = 1/1/₂
n = q
S = -x En Pulupn.
S = Kenn
-* & Plukk
€ (K) = hvk
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