The second law of thermodynamics states that: 1) Entropy of an isolated system always increases during a spontaneous process. 2) It is impossible for heat to flow from a cooler body to a hotter body without any work being done. 3) The entropy of the universe increases in any spontaneous process.

1. Second law of Thermodynamics
•A gas expands to fill the available volume.
•A hot body cools to the temperature of its
surroundings.
•A chemical reaction runs in one direction rather
than another.
The direction of change that does not require work
to be done to bring the change about is called
spontaneous direction of change.
Internal energy lets us access whether a change is
permissible. Only those changes occurs for which the
internal enegy of an isolated system remains constant.

2. Is it perhaps the internal energy that tends toward
minimum for a spontaneous process?
System
Surroundings
dU<0
dU>0
Perfect gas expands spontaneously into vaccum. dU=0

3. No process is possible in which the sole
result is the absorption of heat from a
reservoir and its complete conversion into
work.

4. A ball bouncing on the floor
A ball resting on the warm surface.

5. Entropy is measure of randomness/ chaosness.
Total entropy of the system and its surroundings
increases in the course of a spontaneous change.

6. Thermodynamic definition of entropy.
surr
rev
surr
surr
sys
rev
sys
sys
surr
sys
Total
rev
T
dq
dS
T
dq
dS
dS
dS
dS
T
dq
dS
,
,
0
0
change,
s
spontaneou
a
For







7. surr
surr
surr
rev
surr
surr
surr
rev
surr
irr
surr
rev
surr
surr
surr
surr
rev
surr
surr
T
dq
T
dq
dS
dq
dq
dq
dU
dU
dU
dq
T
dq
dS
irr
su rr








,
,
,
,
,
,
function.
state
a
is
U
Since
olume.
constant v
of
reservoir
of
consists
g
Surroundin
Since

8. T
V
A
B
C
0
l
n
l
n
l
n
l
n
,
0
;
0
process
i
c
(C)Adi
abat
l
n
,
0
process
V)
(Const.
Isochori
c
(B)
l
n
:
process
Isotherm
al
(A)
1
2
1
2
1
2
2
1
1
2
2
1
1
2
1
2




































T
T
C
V
V
R
T
dq
T
dq
T
dq
V
V
R
T
T
C
V
V
T
T
Also
T
dq
dq
T
T
C
T
dT
C
T
dq
dT
C
dU
dq
w
V
V
R
T
dq
V
dV
RT
pdV
dw
dq
V
C
B
A
V
C
R
C
C
V
V
B
V
A
A
A
V
T1,V1,p1 T1,V2,p2
T2,V2,p3

9. T
V
A
B
C
0
l
n
)
(
l
n
l
n
l
n
l
n
Al
so,
l
n
process
c
(C)Isobari
l
n
,
0
process
V)
(Const.
Isochori
c
(B)
l
n
:
process
Isotherm
al
(A)
2
1
1
2
2
1
1
2
1
2
1
2
1
2
2
1
1
2
1
2























 








T
T
C
C
T
T
R
T
dq
T
T
C
T
T
C
V
V
R
T
dq
T
dq
T
dq
T
T
V
V
T
T
C
T
dH
T
dq
T
T
C
T
dT
C
T
dq
dT
C
dU
dq
w
V
V
R
T
dq
V
dV
RT
pdV
dw
dq
V
p
P
V
C
B
A
P
C
V
V
B
V
A
A
A
T2,V2,p1
T1,V1,p1 T1,V2,p2

10. 0
l
n
l
n
gi
ves
(i
i
)
and
(i
)
of
ti
on
Mul
ti
pl
i
ca
(i
i
)
4
process
For
(i
)
2
Process
For
l
n
l
n










 
 
D
C
B
A
rev
C
D
B
A
C
c
C
h
D
B
C
c
C
h
C
A
C
c
D
C
h
A
C
h
B
C
c
C
D
C
B
A
rev
V
V
nR
V
V
nR
T
dq
V
V
V
V
T
T
V
V
T
T
V
V
T
V
T
V
T
V
T
V
V
V
nR
V
V
nR
T
dq

11. A
B
C
D
P
V
Constant P
Adiabatic
Isothermal
Consta
nt
V

12. Clausius inequality theorm
0
process
reversible
a
for
change
Entropy
change.
s
spontaneou
a
of
course
in the
increases
system
isolated
an
of
entropy
The
0
0
isolated,
is
system
the
If
0















surr
sys
surr
sys
surr
sys
sys
sys
surr
sys
surr
sys
dS
dS
dS
dS
dq
dq
dS
dq
T
dq
dS
dS
dS
dS
dS

13. dp
T
V
dT
T
C
dp
T
V
dT
T
H
T
dS
V
T
V
T
p
H
dp
V
p
H
T
dT
T
H
T
T
dq
dp
V
p
H
dT
T
H
dq
Vdp
dp
p
H
dT
T
H
dq
Vdp
dH
pdV
Vdp
pdV
dH
dw
pV
H
d
dw
dU
dq
P
p
P
P
P
T
T
P
T
P
T
P












































































































































1
state
of
equation
amic
thermodyn
From
1
1
)
(
amics,
thermodyn
of
law
first
From

14. dV
T
p
T
dT
C
dV
T
p
dT
T
U
T
dS
p
V
U
T
p
T
dV
p
V
U
T
dT
T
U
T
T
dq
dV
p
V
U
dT
T
U
dq
pdV
dV
V
U
dT
T
U
dq
dw
dU
dq
V
V
V
V
T
V
T
V
T
V
T
V


























































































































1
state
of
equation
amic
thermodyn
From
1
1
amics,
thermodyn
of
law
first
From

15. Entropy changes in a Reversible process
 
1
1
,
,
85
:
Rule
s
Trouton'
0
P)
(T,
vapour
P)
(T,
liquid
process.
reversible
a
always
is
change
Phase
:
change
Phase
(a)




























mol
JK
T
H
S
S
S
T
H
S
T
dH
T
dq
T
dq
dS
T
H
S
T
dH
T
dq
T
dq
dS
b
vap
surr
sys
Total
surr
sys
rev
surr
surr
sys
p
sys
rev
sys

16. Heating or Cooling process
i
f
p
sys
p
sys
P
p
sys
i
f
V
sys
V
sys
V
V
sys
T
T
C
S
dT
T
C
dS
dp
T
V
dT
T
C
dS
T
T
C
S
T
dT
C
dS
dV
T
p
T
dT
C
dS
ln
Pressure,
const.
At
Also,
ln
olume,
constant v
At
.
reversibly
out
carried
be
can
cooling
and
Heating



























17. i
f
V
sys
V
sys
T
T
C
S
T
dT
C
dS
ln




19. Isothermal process for an ideal gas
T
V
V
p
T
w
T
dq
T
dq
dS
T
w
V
V
nR
T
dq
dS
V
V
nR
S
V
V
nR
S
dV
V
nR
dS
dV
T
p
dS
dV
T
p
T
dT
C
dS
ext
sys
surr
surr
rev
rev
sys
surr
sys
sys
V
sys
V
V
sys
)
(
ln
process,
le
irreversib
an
For
ln
ln
e,
Temperatur
constant
At
:
process
Reversible
1
2
1
2
1
2
1
2




































20. rev
f
irrev
f
m
V
sys
i
irrev
f
m
V
i
rev
f
m
V
sys
i
irrev
f
m
V
i
f
sys
sys
rev
sys
sys
sys
rev
sys
sys
surr
sys
sys
surr
T
T
C
S
T
T
C
T
T
C
S
T
T
C
V
V
R
S
T
dq
T
dq
dS
T
dq
T
dq
dS
S
dq
T
dq
dS
,
,
,
,
,
,
,
,
,
,
,
l
n
l
n
l
n
l
n
l
n
gas,
i
deal
an
For
:
process
l
e
Irreversi
b
(b)
0
:
process
Reversi
bl
e
(a)
0
0
process,
adi
abati
c
an
i
n
Si
nce,



















Adiabatic Processes for an ideal gas

21. Entropy changes in irreversible Processes
To obtain the change in entropy in an irreversible
process we have to calculate S along a reversible
path between the initial state and the final state.
Freezing of water below its freezing point
H2O( l , -10 °C) H2O( s , -10 °C)
H2O( l , 0°C) H2O( s , 0 °C)
Irrev
273
263
263
273
ln ice
crys
liq C
T
H
C
S 





22. Absolute entropy of a substance
)
(
)
(
)
(
)
0
(
)
(
0











T
T
p
b
v
T
T
p
f
f
T p
b
b
f
f
T
dT
g
C
T
H
T
dT
l
C
T
H
T
dT
s
C
S
T
S
Third law of thermodynamics:
The entropy of each pure element or substance in a
perfectly crystalline form is zero at absolute zero.

23. energy.
free
helmholtz
called
is
A
0
)
(
0
)
(
)
(
T
and
V
constant
At
0
or
0
0
0
work
additional
no
olume,
constant v
At
0
0
,
,
,
,





















T
V
T
V
V
S
V
U
v
sys
surr
sys
surr
sys
A
d
TS
U
d
TS
d
dU
TdS
dU
dU
dS
TdS
dU
TdS
dq
TdS
dq
T
dq
dS
dS
dS
dS
dS
Spontaneous process

24. energy.
free
s
Gibb'
called
is
G
0
)
(
0
)
(
)
(
T
and
P
constant
At
0
or
0
0
0
work
additional
no
pressure,
constant
At
0
0
,
,
,
,





















T
V
T
P
p
S
p
H
p
sys
surr
sys
surr
sys
G
d
TS
H
d
TS
d
dH
TdS
dH
dH
dS
TdS
dH
TdS
dq
TdS
dq
T
dq
dS
dS
dS
dS
dS