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361 Lec 10Thur 13sep12
?8000/400=20
8000/400=20
‐12000/400= ‐30
‐8000/400= ‐20
20 30 10
0
20‐30=‐10No Way!!
0
1
The 3rd Law of ThermodynamicsIn 1867, Ludwig Boltzmann earned his PhD for research on the kinetic theory of gases. Later, he began to see th t t ld b l t d t di d d hthat entropy could be related to disorder, and he published the famous equation for absolute entropy
S = kBlnN where N is the number of microstates(the number of possible arrangements of the positions and(the number of possible arrangements of the positions and velocities of the collection of molecules in the system—a truly enormous number ), and
kB = Boltzmann’s constant (= R/6x1023) so has units ofJ K‐1 molecule‐1J K 1 molecule 1This, however, was well ahead of its time, and he died a discouraged man in 1906, just as the world of physics was waking up to the idea of atoms and molecules. 2
3
As 0 Kelvin is approached, all systems are in the zero point energy level. If the lowest energy level is only 1 microstate :
S = kBln 1 = 0, i.e.,
The entropy of a perfect crystal at 0 K = 0.(this is one form of the 3rd Law)
b l tThis means there is a basis for having absolute values for entropy, (unlike energy)
4
Table A.5Appendix
715
361 Lec 11Fri 16sep11
page 715
For ions in solution the S0 values are relative to H+(aq)
5
222 TTT d∫∫∫ ≈==Δ2
1
2
1
2
1
)(TTT
rev
TdTCslowlydone
TCdT
Tdq
S111
This is heat capacity times the sum of fractional differences in T t ti t T1 d di t T2differences in T starting at T1 and ending at T2 and that is ??
6
2T
1
2lnTTCS ≅Δ over a small enough temperature range that C is effectively constant
1Phase transitions at the transition temperature (e.g., melting point,
i blboiling point, ) are reverisble, so:
mp
fusionfusion T
HS
Δ=Δ
boiling
vapvap T
HS
Δ=Δ
7
boiling
Absolute (Third Law) Entropy at any temperature T
solidCHsolidCTT mptran
∫∫Δ )2()1( dT
TsolidC
TH
dTTsolidCTS
T
P
trans
transitionP
trans
∫∫ +Δ
++=)2()1(0)(
0
dTTgasC
TH
dTTliquidC
TH T P
il
vapT
Pfusionbp
∫∫ +Δ
++Δ
+)()(
TTTTTequilTmp bpmp∫∫
8
Solid-->solidtransition
boiling
transition
melting point
boiling point
9
boiling
melting point
boiling point
point
10
11
Table A.5Appendix
715
361 Lec 11Fri 16sep11
page 715
For ions in solution the S0 values are relative to H+(aq)
12
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