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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