Chemistry 163B
S of the UNIVERSE
and
Deriving Thermodynamic Relationships
Challenged Penmanship
Notes
1
goals
1. ΔSuniverse > 0
2. Maxwell-Euler Relationships
3. ΔSΦ= ΔHΦ / TΦ (Φ is phase transtion)
2
2nd Law of Thermodynamics in terms of entropy
• S is a STATE FUNCTION
• xS
dqrev
T
rev
dqirrev
T
irrev
3
Suniverse  0
today
system
S surroundings
S universe
0
disorder increases
4
the entropy of the UNIVERSE increases
dS
dq
T
S system
S system
dqsurr
S system
dqsys
T
S surr
dqsurr
T
S surr
dqsys
T
dqsurr
T
dqsys
dqsys
T
T
? dqsys
S surr
0
Ssystem + Ssurroundings= S??= SUNIVERSE  0
5
towards a universal PEA SOUP
Plotkin's Entropy
Clark’s Entropy # 2 Acrylic 30 x 24
http://www.donnabellas.com/abstract/science/plotkinentropy.htm
http://www.williamgclark.com/entropy.jpg
S>0
UNIVERSE
PEA
SOUP
6
BUT ALAS:
Ssystem < 0 (order) if Ssurroundigns > 0 (disorder)
Ssurroundings > 0
Ssystem < 0
7
Raff’s Sammy
Pext
0
Pint
nR(300 K )
20 L
VAC
Pint
nR(300 K )
40 L
w=0
q=0
ΔU=0
ΔT=0
Poor
Sam
?
Smarty
Leigh
ΔS=R ln 2
(isothermal reversible)
8
trepanation, the mind and the brain
P. Treveris, 1525, England
H. Bosch, 1480, Dutch
Peru, ~ 1000AD, pre-Incan
trepanation and the second law
d qREVERSIBLE
Oouch,d Iqshould
T have been
T
Poor Chem163B
I’ll fix that !
a music major
!!
student thought
dq
T
d qREVERSIBLE
T
remember
•
•
reversible
final
•
dqreversible
T
initial
irreversible
final
dq
T
initial
•
•
•
11
tools for evaluating thermodynamic relationships: starting relationships
definitions:
U
H
A
G
 internal energy
 U + PV
 U TS
 H TS
relationships from 1st and 2nd Laws:
[no change of material (dni=0) and, only PV work (dwother=0)]
_
_
dqV
nCV dT
dq P
dU
dq dw
dq PdV
dS
dqrev
T
nC P dT
dq Tds
12
differential relationships
U
H
A
G
 internal energy
dU
 U + PV
 U TS
 H TS
dU
dS
TdS
PdV
dq dw dq PdV
dqrev
dq TdS
T
U ( S ,V )
TdS PdV
dH
dU
PdV VdP
dH
TdS VdP
H (S, P)
TdS PdV
dA dU TdS
dA
SdT
SdT
PdV
A(T ,V )
TdS VdP
dG
dG
dH TdS
SdT
SdT VdP
G (T , P )
13
example of Maxwell-Euler ( dG=-S dT +V dP )
dG
S
dT
V
dP
1st and 2nd Laws
G (T , P ) :
G
T
dG
G
T
so:
what
about:
thus:
P
P
G
P
S
P
G
T
S
P
=
P
T
T
G
P
dT
T
V
T
G
P
P
dP
math, total differential
T
V
T
T
P
Maxwell-Euler Relationship
from dG
14
Euler-Maxwell relationships (handout #4 Math Comments)
d
d
x, y
x, y
x
dx
y
y
M
dx
y
N
x
y
M
y
x
x
dy
x
dy
x
N
x
y
x
y
y
15
Euler-Maxwell relationships
dU TdS PdV
dH TdS VdP
dA
dG
SdT PdV
SdT VdP
T
V
T
P
S
V
S
V
S
P
S
P
S
S
P
S
V
S
T
T
P
P
T
T
T
V
P
T
V
T
V
V
P
V
T
P
16
entropy variations with T and P
_
_
S
T
CV
T
V
_
_
S
T
CP
T
P
_
S
P
T
_
V
V
T
_
_
S
P
V
T
T
P
17
finite changes from derivatives: isothermal volume change
S
T
dS (T ,V )
isothermal
S
V
dS
V
dT
T
V1
V2
V1
V2
SV1
[
V2
S
V
V1
dS
V2
V
V2
V1
SV1
dV
dS
V2
T
general for no work other;
no change of composition
P
T
dV
V2 ,Tconst
dV
0
V2
SV1
S
V
dT
nR
dV
V
V1
SV1
P
T
V2
dV
T
V1
V
ideal
P
T
V
V
nR ln 2
V1
V2
dV
for
dV
qrev
T
P
T
V
gas :
nR
V
rev
18
calculating entropy (see summary on review handout)







19
S for equilibrium phase transition
for phase transition
(e.g.)
at equilibrium conditions
H2O()  H2O (g, 1atm, 373K)
or H2O()  H2O (s, 1atm, 273K)
H
S
HW6 #35
P
qreversible
H
P
P
T
S for H2O()  H2O (s, 1atm, 263K)
20
End of Lecture
21