nhiệt động học, nguyên lý ETROPY, định lý 2 NDHs

ENTROPY –
LAW OF
THERMODYNAMICS
ND
2


OUTLINE
• 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


REVERSIBLE – 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

P
1

1

Quasi–static
process

irreversible Quick (sudden) process
2

2
irreversible

reversible

V

V


QUASI-STATIC vs QUICK PROCES

P

P
1

Quasi–static
process

1

Quick (sudden) process

2

2
irreversible

reversible

V

V


Carnot'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.

Tc
emax  eCarnot  1 
Th


CARNOT ENGINE
Two reservoirs,

temperature Th, Tc

e  ecarnot
Q'
T
1 c  1 c
Qh
Th
Q'
T
 c  c
Qh
Th
Qc
Q
 h
Tc
Th
Qh Qc

0
Th
Tc

CLAUSIUS’S INEGALITY
Qj,
Tj

P

Divide any reversible cycle into a
series of thin Carnot cycles, where
the isothermal processes are
infinitesimally short:

Qi, Ti
V
  reversiblecycle
Qi

0
 T   irriversiblecycle
i
i




  reversiblecycle
 0
T
  irriversible cycle

Q




ENTROPY

  reversiblecycle
 0
T
  irriversible cycle

Q

Consider a reversible cycle 1a2b1
The Clausius integration has sign “=“

P
1

Q



a
2
b

1a 2b1



1a 2

V
Definition: We define a
state variable S that the

change in the entropy dS
is equal to the heat
received in a reversible
process divided by the
absolute temperature of
the system



1a 2

T

Q
T

Q
T



0





Q
T

2b1

 

Q

2b1

Q

1a 2 _ rever

T



S 

0

T





1b 2 _ rever.

Q

12 _ reversible

dS 

Qrev.
T

T

Q
T


ENTROPY (Cont.)
Consider an irreversible cycle
1a2: irreversible
2b1: reversible
The Clausius integration has sign “<“
P
1
a
2
b
V

S 



12

Q   reversible_ process


T   irreversible _ process

Q   reversible_ cycle
 T  0  irreversible _ cycle

Q
0

T
1a 2b1 _ irrev.
Q
Q
 T   T 0
1a 2irrev.
2b1 _ rev.
Q
Q
 T   T
1a 2irr.
2b1rev.
Q
Q
 T  T
1a 2 _ irr.
1b2 _ rev.
Q

 T  S
1 2rev.
Q
S  
T
1a 2 _ irr.


ENTROPY S
• Entropy S is a state variable

S  S2  S1 

State_ 2



State_1
P

1
a
2
b
V

S1a 2irrev.  S1b2rev.  S12
Q
S12  
T

1a 2
S12 

Q
 T
1b2

Qrev.
T

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.


The principle of Increase of Entropy
Qrev
S12  
T
12

S may be >0; <0 or =0

 irreversible _ process
For an isolated system dQ=0 => S12  0
 reversible_ process
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.


The Change in Entropy of an Ideal Gas
dS 

Qrev

T
dU  Q  PdV
Q  dU  PdV
dU  PdV i nRdT nR
dS 


dV
T
2 T
V
T2
V
i nRdT 2 nR
S  


dV
T1 2 T
V1 V
T2
V
 nR ln 2
T1
V1
PV
V
 nCv ln 2 2  nR ln 2
P1V1
V1
P
V
V
 nCv ln 2  nCv ln 2  nR ln 2
P1
V1
V1

 nCv ln

P2
V2
S  nCv ln  nCp ln
P1
V1

i
U  nRT; PV  nRT
2
i
Cv  R
2
i2
Cp 
R  Cv  R
2


The Change in Entropy of an Ideal Gas
Isothermal Process

2

dQ Q12


T
1 T

S  

V2
V1

T

 nR ln

V2
V1

2

nCvdT
T2
S  
 nCv ln
T
T1
1

Isovolumetric Process

2 nC dT
p

S  

Isobaric Process

1

Adiabatic Process

nRTln

S  0

T

 nCp ln

S  const

T2
T1
Iso_entropy Process


Example 22.6 Change in Entropy: Melting
A solid that has a latent heat of fusion Lf melts at a
temperature Tm.
Calculate the change in entropy of this substance when a
mass m of the substance melts.

2

dQ
S  
1 T
T  Tmelt  Const
Q mLf
S  
T Tmel

Entropy trao đổi, entropy tạo ra
Độ biến thiên entropy của hệ

Entropy trao đổi
Q: nhiệt mà hệ nhận
Tnguon nhiet: Nhiệt độ của nguồn nhiệt
Entropy tạo ra

S  Straodoi  Stao _ ra
2
Q
S  
T
1
Q
Straodoi 
Tnguon _ nhiet
Stao _ ra  S  Straodoi

Stạo ra =0: quá trình Thuận nghịch
Stạo ra >0: quá trình Không Thuận nghịch