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Trang 1ENTROPY – 2ND LAW OF THERMODYNAMICS
Trang 2OUTLINE
• Reversible Process vs Irreversible Process
• Quasi-Static vs Quick Process
• Carnot’s theorem
• Clausius’s Integration
• Entropy
• The Principle of Increase of Entropy
• The Change in Entropy of an Ideal Gas
Trang 3REVERSIBLE – IRREVERSIBLE
PROCESS
In a reversible process, the system can be returned to its initial conditions
along the same path on a PV diagram, and every point along this path is an
equilibrium state
A process that does not satisfy these requirements is irreversible
P
V
1
2
reversible
P
V
1
2
reversible
irreversible
Quasi–static process
Quick (sudden) - process
Trang 4QUASI-STATIC vs QUICK PROCES
P
V
1
2
reversible
P
V
1
2
irreversible
Quasi–static process
Quick (sudden) - process
Trang 5Carnot's theorem
Carnot's theorem, developed in 1824 by Nicolas Léonard Sadi Carnot, also
called Carnot's rule, is a principle that specifies limits on the maximum
efficiency any heat engine can obtain
Carnot's theorem states:
• All heat engines between two heat reservoirs are less efficient than
a Carnot heat engine operating between the same reservoirs
• Every Carnot heat engine between a pair of heat reservoirs is equally
efficient, regardless of the working substance employed or the operation details
h
c Carnot
max
T
T 1
e
Trang 6CARNOT ENGINE
0 T
Q T
Q
T
Q T
Q
T
T Q
' Q
T
T 1
Q
' Q 1
e e
c
c h
h
h
h c
c
h
c h
c
h
c h
c carnot
cycle le
irriversib
cycle reversible
0 T
Q
i i
i
cycle le
irriversib
cycle
reversible 0
T
Q
CLAUSIUS’S INTEGRATION
Qj,
Tj
Qi, Ti
V
P
Divide any reversible cycle into a series of thin Carnot cycles, where the isotherms are infinitesimally short:
Two reservoirs,
temperature Th, Tc
Trang 7ENTROPY
P
V
1
2
a
b
Consider a reversible cycle 1a2b1
The Clasius integration has sign “=“
cycle le
irriversib
cycle
reversible 0
T
Q
rever _ 2 b rever
_ 2 a 1
1 2 2
a 1
1 2 2
a 1
1 2 a 1
T
Q T
Q
T
Q T
Q
0 T
Q T
Q
0 T
Q
T
Q dS
T
Q S
rev
reversible _
2 1
Definition: We define a
state variable S that the
change in entropy dS is
equal to this amount of
energy for the reversible
process divided by the
absolute temperature of
the system:
Trang 8ENTROPY (Cont.)
P
V
1
2
a
b
Consider an irreversible cycle
1a2: irreversible
2b1: reversible
The Clasius integration has sign “<“
cycle _
le irriversib
cycle _
reversible 0
T
Q
irr _ 2 a 1
rev 2 1
rev _ 2 b 1
irr _ 2 a 1
rev 1 b 2
irr 2 a 1
rev _ 1 b 2
irrev 2 a 1
irrev _ 1 b 2 a 1
T
Q S
S T
Q
T
Q T
Q
T
Q T
Q
0 T
Q T
Q
0 T
Q
process _
le irreversib
process _
reversible T
Q S
2
Trang 9ENTROPY S
2 _ State
1 _ State
.
rev 1
2
T
Q S
S
Entropy is a state variable
=> the change in entropy during a process depends only on the endpoints
=> the change in entropy is independent of the actual path followed
Consequently, the entropy change for an
irreversible process can be determined by
calculating the entropy change for a
reversible process that connects the same
initial and final states
P
V
1
2
a
b
2 b 1 12
2 a 1 12
12
rev 2 b 1
irrev
2
a
1
T
Q S
T
Q S
S S
S
Trang 10The principle of Increase of Entropy
12
rev 12
T
Q S
0 S
0 S
0 S
For an isolated system dQ=0 =>
process _
reversible
process _
le
irreversib 0
S12
S > 0, for irreversible processes
S = 0, for reversible processes
S < 0, the process is impossible
The entropy of the Universe increases in all real processes
Trang 11The Change in Entropy of an Ideal Gas
1
2 1
2 v
1
2 v
1
2 1
1
2 2 v
1
2 1
2 v
V
V
T
T rev
V
V ln
nR V
V ln
nC P
P ln nC
V
V ln
nR V
P
V P ln nC
V
V ln
nR T
T ln nC
dV V
nR T
nRdT 2
i S
dV V
nR T
nRdT 2
i T
PdV dU
dS
PdV dU
Q
PdV Q
dU
T
Q dS
2 1
2 1
R C R 2
2 i C
R 2
i C
nRT PV
; nRT 2
i U
v p
v
1
2 p
1
2 v
V
V ln
nC P
P ln nC
S
ISOTHERMAL:
Trang 12The Change in Entropy of an Ideal Gas
1
2 p
2
1
p
T
T ln
nC T
dT nC
Isothermal Process
1
2 1
2 12
2
V ln
nR T
V
V ln nRT
T
Q T
dQ
Isovolumetric Process
1
2 v
2
1
v
T
T ln
nC T
dT nC
Isobaric Process
Adiabatic Process S 0 S const Iso_entropy Process
Trang 13Example 22.6 Change in Entropy:
Melting
A solid that has a latent heat of fusion L f melts at a temperature T m
Calculate the change in entropy of this substance when a mass m of the
substance melts
mel f melt
2
1
T
mL T
Q S
Const T
T
T
dQ S