12. For a given macrostate of a system, let P, be the probability that the system is in the microstate >. The corresponding Gibbs entropy is given by 5-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), A) P₁₂ = PR E = 1/₂hw NEF ==WEE B) P₁ = e-a C) P₁ = e D) P₁ = 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 -* (en (k) E(K) = hvk + 1 h nk + 1 huk A) E B) E2 C) E D) E E) Independent of energy E of an ideal بدارية بمرايت ~/M + + S = -K EnPnlupn. S = klnn rim is confined to half of a boy s 12 lukk moved and Joule (free)

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12. For a given macrostate of a system, let Pn be the probability that the system is in the microstate
n>. The corresponding Gibbs entropy is given by 5-k En PnInPn. 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),
Pn
-
A) E
B) E2
B) P₁ = e-a
C) P₁ = e
D) P₁ = f
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
-
€ =
E = 1/₂₂hw
WEE
A) 3R In2
B) 2R
C) R In2
D) R In
E) R In2
3
بدارية بمارين
2
*
S = -x En Pulun.
S = Kenn
+ ²/1/2 € (K) = hvk
C) E
D) E-
E) Independent of energy E
14. A mole of an ideal gas is confined to half of a box. If the partition is removed and Joule (free)
expansion of the gas is allowed, the change in entropy is
B
2호
plus
w
-* & fluf
D
+ 1 h nk ± !
huk
S =
The state and it has energy E= -NkTin (), where Vo
Transcribed Image Text:12. For a given macrostate of a system, let Pn be the probability that the system is in the microstate n>. The corresponding Gibbs entropy is given by 5-k En PnInPn. 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), Pn - A) E B) E2 B) P₁ = e-a C) P₁ = e D) P₁ = f 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 - € = E = 1/₂₂hw WEE A) 3R In2 B) 2R C) R In2 D) R In E) R In2 3 بدارية بمارين 2 * S = -x En Pulun. S = Kenn + ²/1/2 € (K) = hvk C) E D) E- E) Independent of energy E 14. A mole of an ideal gas is confined to half of a box. If the partition is removed and Joule (free) expansion of the gas is allowed, the change in entropy is B 2호 plus w -* & fluf D + 1 h nk ± ! huk S = The state and it has energy E= -NkTin (), where Vo
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