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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posted:12/5/2011
language:English
pages:5