Microsoft PowerPoint - PchemIII-4.pptIII. Equilibrium statistical mechanics III. Equilibrium statistical mechanics II. Statistical thermodynamics II. Statistical thermodynamics
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IIIIII--1. Entropy1. Entropy
Equilibrium state 1
Equilibrium state 2
Review PChem-I Path1
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T q
exact differential
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Consider an isolated system: the energy remains constant, so any spontaneous process must be due to an increase in entropy. Unlike energy, entropy is not conserved; it increases whenever a spontaneous process takes place. The entropy of an isolated system will continue to increase until the system is in equilibrium.
dS > 0 (irreversible process) dS = 0 (reversible process)
dU = 0
0ln SkS B
max21 21
,,, wnnnw Nnnn
M M
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nnnw
21
,,, 21
N indistinguishable particles in cubic box, number of state with energy < E
Example: use
Example: Example: Free expansion and mixtureFree expansion and mixture MMN
Nw !/
! max
1!/ !
11
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Suppose that system is in microstate k with nk molecules
kknkkkk nPPPPP k 1,,2,1,
P k k
V h
Derive directly from
T T
z V
z V
NV V T
NPNPNP P T
VP T U
NPNTNVNP T V
All state functions (definition may be different from text book)
But we concern about only change of state functions, it will be same
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IIIIII--4. Calculation of internal energy 4. Calculation of internal energy
V B T

-123 JK10380.1 Bk
molJhvNUvib /12983 20
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V TNk
P B
IIIIII--5. Partition function of Van 5. Partition function of Van derder Waals equation*Waals equation*
fNbV h