# entropy

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```					                          Objectives

• Introduce the thermodynamic property entropy (S) using
the Clausius inequality
• Recognize the fact that the entropy is always increasing for
an isolated system (or a system plus its surroundings)
based on the increase of entropy principle
• Analysis of entopy change of a thermodynamic process
(how to use thermodynamic table, ideal gas relation)
• Property diagrams involving entropy (T-s and h-s
diagrams)
• Entropy balance: entropy change = entropy transfer +
entropy change
Entropy
• Entropy: a thermodynamic property, can be used as a measure of
disorder. The more disorganized a system the higher the entropy.
• Defined using Clausius inequality       Q
       T
 0

• This inequality is valid for all cycles, reversible and irreversible.
• Consider a reversible Carnot cycle
Q         QH          QL                                                                    QL            TL       QL       TL
                             , f r o m C a r n o t e f f ic ic e n y  th  1                        1        ,        
T         TH          TL                                                                    QH            TH       QH       TH

Q                                                                           Q 
T h e re fo re ,          T
 0 f o r a r e v e r s ib le C a r n o t c y c le                       
 T  rev
 0

• Define a thermodynamic property entropy (S), such that
2          2
Q                                                                        Q
dS 
T
, fo r a n y re v e rs ib le p ro c e s s      dS           T
 S 2  S1
rev                                               1          1               rev

T h e c h a n g e o f e n tro p y c a n b e d e fin e d b a s e d o n a re v e rs ib le p ro c e s s
Entropy-2
• Since entropy is a thermodynamic property, it has fixed values at a
fixed thermodynamic states.
2                  1
Q      Q     Q 
T    any                    2                             0
1
T         T  2  T  rev
process
F r o m e n tr o p y d e f in itio n
2                 1
Q                                         Q        Q                    Q 
dS=     ,
 T  rev
    dS  0                    
 T  rev 1  T  rev
               
 T  rev
1        reversible                                                                                            2

process                                   2
Q    Q 
2                 2

T h e re fo re ,        

    
T  1  T  rev
             dS    S 2  S1   S
1                                  1

S                              2
Q 
 S  S 2  S1                   , T h is is v a lid f o r a ll p r o c e s s e s
 T 
1

Q                        Q             Q 
dS               , s in c e d S =         , dS     
T                          T  rev         T  ir r e v

• The entropy change during an irreversible process is greater than the integral of
Q/T during the process. If the process is reversible, then the entropy change is
equal to the integral of Q/T. For the same entropy change, the heat transfer for a
reversible process is less than that of an irreversible. Why?
Entropy Increase Principle
2
Q 
 S  S 2  S1                , d e f in e e n tr o p y g e n e r a tio n S g e n
 T 
1

2                        2
Q                     Q 
 S s y s te m  S 2  S 1             S gen 
 T 
      
 T 
1                        1

w h e r e S g e n  0 . If th e s y s te m is is o la te d a n d " n o " h e a t tr a n s f e r

T h e e n tr o p y w ill s till in c r e a s e o r s ta y th e s a m e b u t n e v e r d e c r e a s e
 S s y s te m  S g e n  0 , e n tr o p y in c r e a s e p r in c ip le

• A process can take place only in the direction that complies with the increase of
entropy principle, that is, Sgen0.

• Entropy is non-conservative since it is always increasing. The entropy of the
universe is continuously increasing, in other words, it is more disorganized and is
approaching chaotic.

• The entropy generation is due to the existence of irreversibilities. Therefore, the
higher the entropy generation the higher the irreversibilities and, accordingly, the
lower the efficiency of a device since a reversible system is the most efficient
system.
Entropy Generation Example
Example: Show that the heat can not transfer from the low-temperature sink to the
high-temperature source based on the increase of entropy principle.
S(source) = 2000/800 = 2.5 (kJ/K)
Source               S(sink) = -2000/500 = -4 (kJ/K)
800 K                Sgen= S(source)+ S(sink) = -1.5(kJ/K) < 0
Q=2000 kJ It is impossible based on the entropy increase principle
Sgen0, therefore, the heat can not transfer from low-temp.
to high-temp. without external work input
Sink
• If the process is reversed, 2000 kJ of heat is transferred
500 K
from the source to the sink, Sgen=1.5 (kJ/K) > 0, and the
process can occur according to the second law
• If the sink temperature is increased to 700 K, how about the entropy generation?
S(source) = -2000/800 = -2.5(kJ/K)
S(sink) = 2000/700 = 2.86 (kJ/K)
Sgen= S(source)+ S(sink) = 0.36 (kJ/K) < 1.5 (kJ/K)
Entropy generation is less than when the sink temperature is 500 K, less
irreversibility. Heat transfer between objects having large temperature difference
generates higher degree of irreversibilities

```
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 views: 1 posted: 12/5/2011 language: English pages: 5