Thermodynamics I Chapter 6 Entropy

Transcription

1 hermodynamics I hater 6 Entroy Mohsin Mohd ies Fakulti Keuruteraan Mekanikal, Uniersiti eknologi Malaysia

2 Entroy (Motiation) he referred direction imlied by the nd Law can be better understood and quantified by the concet of entroy. Entroy quantifies the nd Law and imoses the direction of rocesses. Here we will study entroy and how rocesses will roceed only in the direction of increasing entroy.

3 lausius Inequality H H H E re W E irre W irre L L,irre L onsider two heat engines between the same temeratures

4 onsider of the whole cycle (a) E re 0 0 re L L H H L L H H L L H H re

5 (b) E irre L,irre L,irre > L L Δ

6 ombined to be: 0 if reersible < 0 if irreersible > 0 imossible

7 ENOPY B A 0 B B A B A re Does not deend on ath; thermodynamic roerty! Let's call this roerty entroy, [kj/k] re d

8 Entroy, extensie roerty [kj/k] ecific entroy, s intensie roerty [kj/kg.k] d re We hae actually defined entroy change From statistical thermodynamics, entroy ~ measure of molecular disorder Work is an ordered form of energy (High quality) No entroy transfer along with work transfer Heat is a disordered form of energy (Low quality) Entroy is transferred along with heat transfer Entroy zero for ure crystal at 0 K hird Law of hermodynamics Entroy with a 0 K reference is called absolute entroy

9 -ds elations o find the relationshi between δ and so that the integration of δ/ can be erformed - From the st Law (neglecting KE & PE) W U δ re δwre du d dv du d du dv ds du d δ δw (a) re re d dv

10 - From the definition of enthaly h dh du u du dh d d d d From (a) ds du d dh d d d ds dh d (b)

11 -ds elations ds du d ds dh d & ds ds du dh d d an be used for of any rocess (re. & irre.) an be used for oen & closed system

12 Entroy hange of Pure ubstances an be obtained from ds elations in conunction with other thermodynamic relations For hase substances like water and -34a, use roerty tables For ideal gas, from ds relations ds ds ds s du s d d d d d s du d Assume constant & integrate

13 s s s d d ds d d ds d dh ds Another relation, d dh Assume constant & integrate

14 s s s s s s Both equations gie the same result hoose according to aailable data.. Entroy change

15 Isentroic Processes, 0 For ideal gases, with constant & 0 k k s k k

16 k k k k s 0 Another one k k k

17 ombined to become k k k Isentroic rocess for ideal gas, constant,

18 Work for Oen ystems eersible boundary work for closed systems w B d Oen system reersible work, from st Law (single inlet/outlet) δq re δw re dh d δw dh d re dh d ( ke) d( e) ( ke) d( e) neglecting ke & e, & rearrange; δq δq re ds df d re ds dh d δw w re re d d eersible work for oen system

19 Increase in Entroy Princile For reersible rocesses, entroy of unierse (system surrounding) doesn't change, it is ust transferred (along with heat transfer) In real rocesses, irreersibilities cause entroy of unierse to increase Heat reseroirs don't hae irreersibility o simlify analysis, assume irreersibilities to exist only inside the system under study. Inside the system, entroy transfer and generation occur. irre re Irreersible cycle since one of the rocesses is irreersible From lausius Inequality;

20 earrange < > δ δ irre irre Generalize for all rocesses δ δ gen when re > when irre < imossible gen entroy generated 0 when re. > 0 when irre. < 0 imossible

21 Entroy Generation for losed ystem b gen hange of system entroy ransfer of entroy ( where is transferred, usually at boundary Entroy generation

22 gen is the measure of irreersibilities inoled during rocess gen Δtotal,unierse Δ surrounding Δ system 0 surrounding or system may decrease (-e), but total (surrounding system) must be > 0 Entroy of unierse always increases (Entroy increase rincile) No such thing as entroy conseration rincile For a rocess to occur, gen > 0

23 Entroy Generation for losed ystem gen n gen b gen b For multile heat transfers at different temeratures

24 Entroy Generation for losed ystem d dt d n n gen gen In rate form In differential form gen - deends on the rocess (friction, etc.) - not a roerty

25 Entroy Generation for Oen ystems Aart from heat, mass flows also carry entroy along with them V m out s out m in s in V V in in ms in out ms out gen gen

26 Entroy Generation for Oen ystems V m in s in d dt V msin ms out gen in ate of change of system entroy ate of entroy transfer ate of entroy generation

27 teady Flow Process gen o o i i gen o o i i V V out in V m s m s m s m s dt d dt d m m dt dm 0 0 0

28 m m s s s s m gen i o gen o i ) ( 0 single inlet/outlet; teady Flow Process

29 eersible adiabatic rocess isentroic rocess Isentroic is not necessarily reersible adiabatic eersible rocess gen 0 Produces W max onsumes W min

30 IENOPI EFFIIENIE OF EADY-FLOW DEVIE Also known as Adiabatic Efficiency or nd Law Efficiency he isentroic rocess inoles no irreersibilities and seres as the ideal rocess for adiabatic deices. Isentroic Efficiency of urbines he h-s diagram for the actual and isentroic rocesses of an adiabatic turbine. 30

31 Isentroic Efficiencies of omressors and Pums When kinetic and otential energies are negligible omressors are sometimes intentionally cooled to minimize the work inut. he h-s diagram of the actual and isentroic rocesses of an adiabatic comressor. 3

32 Isentroic Efficiency of Nozzles If the inlet elocity of the fluid is small relatie to the exit elocity, the energy balance is hen, he h-s diagram of the actual and isentroic rocesses of an adiabatic nozzle. A substance leaes actual nozzles at a higher temerature (thus a lower elocity) as a result of friction. 3