Chapter 6 Entropy Ppt

5/25/2018 Chapter 6 Entropy Ppt

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Chapter 6ENTROPY

Assoc.Prof.Sommai Priprem, PhD.

Department of Mechanical EngineeringKhon Kaen University

Reference: Sonntag R.E., and an !ylen ".#.,Introduction toThermodynamics: $lassical and Statistical, %rdEd., #ohn !iley & Sons, '(('


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.. 2

Introduction

Last chapter: 2ndLaw apply to CYCLE

This chapter: 2ndLaw apply to PROCESS

stlaw deal with Ener!y and itsConser"ation

2ndlaw deal with Entropy# it is notconser"ed


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.. $

Topics

Ine%uality o& Clausius Entropy Entropy o& pure su'stances Entropy Chan!e durin! Re"ersi'le Process Two I(portant ther(odyna(ic Relations Principle o& Increase o& Entropy Entropy chan!e o& solids and Li%uids

Entropy chan!e o& ideal !ases Isentropic Process o& Ideal )ases Second Law E&&iciency and Isentropic E&&iciency


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.. *

Ine%uality o& CL+,SI,S

Consider a Re"ersi'le -eat En!ineTheory: .L/ 01 .-.L3 4re"

T-and TL3 constant

0 TQ

HeatEngine

Source, TH

Sink, TL

Wrev

QH

QL

0...

0:....

0

=

==

==

=

T

Qcyclereversibleafor

T

Q

T

Q

T

QTherefore

T

Q

T

Q

T

Q

T

QFrom

QQQ

L

L

H

H

L

L

H

H

L

L

H

H

LH

L

L

H

H

T

Q

T

Q

=


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.. 5

Now consider an Irre"ersi'le -eat En!ine which operates 'etween the sa(eT-and TLand recei"es the sa(e .-'ut reects .L7 and produce 4irr

Theory: 4irr 84re" 1 .-.7L3 4irrthere&ore .7L / .L

HeatEngine

Source, TH

Sink, TL

Wirr

QH

QL

)1.6(0....

0...

0:....

0

'

'


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.. 6

ENTROPY: + Property o& a Syste(

C

B

A

1

2

Consider Two Re"ersi'le Cycles +9 and +C

)3.6...(..........

)2.6.........(

............

0;.

0;.

0..

2

112

2

1

2

1

2

1

2

1

2

1

2

1

rev

rev

CB

CA

BA

T

QSS

T

QdSDefined

PROPERTYPATHonnob!saefinalandiniialonde"endsermThis

T

Q

T

Q

T

Q

T

Q

T

QCACycle

T

Q

T

Q

T

QBACycle

T

Qcyclerevfor

=

=

=

+

==

+

==

=


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..

Notes re!ardin! e%n 6;2

Re"ersi'le Process Irre"ersi'le process entropychan!e

entropy chan!e ! statepoint "# 2

Process #"#!! State 2 entropychan!e $ Process Re"ersi'le %$ Irre"ersi'le Process !&Entropy Property


8/56

.. >

The Entropy o& a Pure Su'stance

re&erence "alue : assi!ned s& 4ater s&3 0 at 0;0

oC

Re&ri!erants s&3 0 at *0o

C ?eter(ine "alues the sa(e way as

Other properties1 u# h

See Ta'les @ollier dia!ra(: Ts and hs dia!;


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.. A

@ollier dia!ra(

)*s diagram

h*s diagram


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.. 0

Entropy Chan!e in Re"ersei'le Process

==

===

==

=

3

2

3

232

212

1

2

112

2

112

1

11

)2.6(

TdsQm

#

T

h

T

#Q

mTT

Q

msss

T

QSSe#from

f$

rev

f$

rev

T

s

P

s1

1

s2

s3

2

3

Example: -eatin! sat; li%uid superheated "apor

Process 1-2phase chan!e sat;li% sat;"ap;# T 3constant

Inte!rate and apply st law

% 3 h2h3 h&!

Process 2-3sat; "apor superheated "apor# Tnot constant# need relation 'etween T and . toper&or( inte!ration


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..

System: R*'+.

nitial state: )'- satrated vapor/ state fi0ed. 1inal state: P+2no3n.

Process: Reversi4le and adia4atic.

Model: R*'+ ta4les.

Analysis:

1irst la3, adia4atic:

'5+6 +7 '8 '3+6 9

'3+6 '*+

Second la3, reversi4le and adia4atic:

s'6 s+

Example 8.1 Consider a cylinder &itted with a piston that containssaturate R2 "apor at 0C; Let this "apor 'e co(pressed in are"ersi'le adia'atic process until the pressure is ;6 @Pa; ?eter(inethe worB per Bilo!ra( o& R2 &or this process;

T

ss1=s

2

1

2

P

P2


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.. 2

Solution

ro( the R2 ta'les#

u3 66;*0 BDB!

s3 s23 0;0* BDB!FP23 ;6 @Pa

There&ore# &ro( the superheat ta'les &or R2#

T23 2;2GC# u23 200;5 BDB!;

w23 uH u2 3 66;*0 200;5 BDB!

3 $*; BDB!


13/56

.. $

Two I(portant Ther(odyna(ics Relations

Consider a internally re"ersi'le CLOSE? syste(1 st Law

. 3 d, J 4

TdS 3 d, JPdK T ds = du + Pdv ;;;;;;;;;


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..

*

Principle o& Increase o& Entropy

)8.6(0

)7.6(0

)6.6(0

11,

11

;

0

0

0

0

0

+=

+=

>

+=

=

$ss!rro!ndinsysem$eneraion

isolae

$ss!rro!ndinsysemne

$ss!rro!ndinsysemne

$ss!rro!ndinsysem

dSdSdSDefined

dS

dSdSdS

Posiiveal%aysTT

henTTSince

TTQ

T

Q

T

QdSdSdS

T

QdS

T

QdS

Surroundings,temperature = T

S!stem,temperature = T

W

Q


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..

5

So(e Re(arBs a'out Entropy

Processes will occur only i& StotalM 0


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..

6


SisolatedM 0

S!en3Stotal3Ssyste(JSsurroundin!sM 0 / 0 Irre"ersi'le process

3 0 Re"ersi'le process

8 0 I(possi'le


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..

S 3


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..

>

E!"#P$E 8.2 Suppose that B! o& saturated water "apor at00GC is condensed to a saturated li%uid at 00GC in a constantpressure process 'y heat trans&er to the surroundin! air# which isat 25GC; 4hat is the net increase in entropy o& the syste( plussurroundin!sQ

Solution

or the syste(# &ro( the stea( ta'les#

Ssyste( 3 (s&!3 6;0*>0 3 6;0*>0 BDF

Concernin! the surroundin!s# we ha"e

. to surroundin!s 3 (h&!3 225;0 3 225 BD

Ssurr 3 .To3 2A>;52A>;5 3 ;500 BDF

Snet 3 Ssyste( JSsurr 3 6;0*>0 J ;500

3 ;5220 BDF

)his increase in entropy is in accordance 3ith the principle of the increase

of entropy, and tells s, as does or e0perience, that this process can ta2e place.


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..

A

Entropy Chan!e o& a Solid or Li%uid

Solid Li%uid

Speci&ic -eat 3 Constant

K "ery s(all hu %

ds 3


20/56

..

20

EXAMPLE 8.3 One kilogra o! li"#i$ %a&er i' (ea&e$ !ro 20)* &o +0)*.

*al#la&e &(e en&ro- (ange, a''#ing on'&an& '-ei!i (ea&, an$ o-are

&(e re'#l& %i&( &(a& !o#n$ %(en #'ing &(e '&ea &a/le'.

System: 4ater;nitial and final states: Fnown;Model: Constant speci&ic heat# "alue at roo( te(perature;

Solutionor constant speci&ic heat#

s2s3 *;>* ln A5> BDB!F

Co(parin! calculation &ro( "alue &ro( ta'le:

s2s3 s&A0C s&20C 3 ;A25 H 0;2A66 3 0;>A5> BDB!F


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..

2

Entropy Chan!e o& an Ideal )as

)12.6...(ln

)11.6...(,

,

)10.6...(ln

)+.6...(,

2

11

212

2

11

212

=

=

===

+=

+=

==+=

P

PR

T

dTCss

P

dPR

T

dTCdsherefore

PRTvanddTCdh$as&deal

vdPdhTdsfrom

Similarly

vvR

TdTCss

v

dvR

T

dTCdsherefore

vRTPanddTCd!$as&deal

Pdvd!Tdsfrom

"o

"o

"o

vo

vo

vo


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..

22

)1.6...(lnln)12.6.(

)13.6...(lnln)10.6.(

1

2

1

212

1

2

1

212

PPR

TTCssE#

v

vR

T

TCssE#

"o

vo

=

+=

; To intr!rate E%n;


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..

2$

E!"#P$E >;* Consider Ea(ple 5;6# in which oy!en is heated&ro( $00 to 500 F; +ssu(e that durin! this process the pressuredropped &ro( 200 to 50 BPa; Calculate the chan!e in entropy perBilo!ra(;

Solution#ethod 1; The (ost accurate answer &or the entropy chan!e# assu(in! ideal!as'eha"ior# would 'e &ro( the ideal!as ta'les# Ta%le ".1&; This result is# usin! E'. (.1(#


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..

2*

#ethod 3; or constantp at3,Ta'le +;2


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..

25

EXAMPLE 8. *al#la&e &(e (ange in en&ro- -er kilogra a' air i'

(ea&e$ !ro 300 &o 600 4 %(ile -re''#re $ro-' !ro 00 &o 300 kPa.

A''#e: 1. *on'&an& '-ei!i (ea&. 2. 5aria/le '-ei!i (ea&.


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..

26

Isentropic Process o& Ideal )ases

(6.17)....................on'&an&

0

0

0)(

1

1

0)(,

)(1

e"n.a'$eal

0

'en&ro-i0,$'-roe'',a$ia/a&ian8or1

,1

!ro

=

=+

=+

=++

=++

+=

=+=+=

=

=

=

=

=

'

v

v

"v

vP

v

"

Pvv

dv'

P

dP

'PdvvdP

PdvvdPPdv

'

PdvvdPPdvR

Cherefore

vdPPdvR

dT

PdvdTCPdvd!Tds

'

'RC

'

RChen

CCRand

C

C'


27/56

..

2

).....(6.1+

...(6.18)..........an$

on'&an&

9:Pe"#a&ionga'i$eal%i&*o/ine

1

2

1

)1(

1

2

1

2

2

1

2

1

1

2

2211

=

=

=

=

====

'''

''

'''

v

v

P

P

T

T

(

(

v

v

P

P

vPvPPv



28/56

..

2>

1

2

1

2

1

2

1

2

r

r

r

r

v

v

v

v

PP

PP

=

=

Ta'le +

&or isentropic process o& ideal !as only

Relati"e Pressure# Pr

Relati"e Kolu(e# "r


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.. 2A

).....(6.21

...(6.20)..........an$

/eoe6.1+


30/56

.. $0

P

E l 8 0 I i'l it i d i


31/56

.. $

Example 8.0In a re"ersi'le process nitro!en is co(pressed in acylinder &ro( 00 BPa# 20GC to 500 BPa; ?urin! the co(pressionprocess the relation 'etween pressure and "olu(e is PK;$ 3constant; Calculate the worB and heat trans&er per Bilo!ra(# andshow this process on P" and T s dia!ra(s;

Syste(: Nitro!en;

Initial state: P# T1 state Bnown;

inal state: P2

Process: Re"ersi'le# polytropic with eponent n 3;$

?ia!ra(: P"# Ts

@odel: Ideal !as# constant speci&ic heat"alue at $00 F;

+nalysis: 9oundary (o"e(ent worB; 43PdKirst law: %3 u2uJw


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.. $2

Solution

polytropic process P"n3c


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.. $$

Second Law E&&iciency

6.2).........(:$e;i,e',on'#e$%ork

6.2).........(:$e;i,e'-ro$#,e$ %ork

)e!!i,ien,A$ia/a&i,(ore!!i,ien,7'en&ro-i,

6.23).........(P#-=ea&

(6.22)..........engine=ea&

-o''i/le)(a>.7$eal;'.A,al:e!!i,ien,la%2n$

ac!al

isenro"ic

isen

isenro"ic

ac!alisen

rev

ac!al

rev

ac!al

%

%%

%

COPCOPCOP

=

=

=

=


34/56

.. $*

"

ss1=s2s s2

P1

2

1

2s

P2"2

"2s

"1

#a#s

$sentropicProcess

%ctua&Process

T

ss1=s2s s2

P1

2

1

2s

P2T2

T2s

T1

$sentropicProcess

%ctua&Process

7'en&ro-i E!!iien o! Compressors

12

12

1212

,

an$:la%1'&

hh

hhherefore

hh%hh%

%

%

%

%

scom"

ass

a

s

ac!al

isenro"ic

isen

=

==

==

w

'ompressor


35/56

.. $5

T

ss1=s2s s2

P2

22s

1

P1

T2

T1

T2s

$sentropicProcess

%ctua&Process

7'en&ro-i E!!iien o! Turbines

12

12

1212

,

,

an$:la%1'&

hh

hhherefore

hh%hh%

%

%

%

%

s

!rbine

ass

s

a

isenro"ic

ac!al!rbisen

=

==

==

wTur(ine

Ea(ple 6> Stea( enters an adia'atic tur'ine steadily at $


36/56

.. $6

Ea(ple 6 > Stea( enters an adia'atic tur'ine steadily at $@Pa and *00C and lea"es at 50 BPa and 00C; i& the power outputo& the tur'ine is 2 @4 and FE and PE are ne!li!i'le# deter(ine


37/56

.. $

Solution

+ssu(e Ideal !as : P" 3 RT

Isentropic process : P"B3 constant

B 3 CpC"

Ea(ple 6A +ir is co(pressed 'y an adia'atic co(pressor &ro(00 BPa and 2C and to a pressur o& >00 BPa at a stead rate o& 0;2B!s; I& the the adia'atic e&&iciency o& the co(pressor is >0V#deter(ine


38/56

Su((ary


39/56

.. $A

Ine%uality o& CL+,SI,S

Consider a Re"ersi'le -eat En!ineTheory: .L/ 01 .-.L3 4re"

T-and TL3 constant

0 TQ

HeatEngine

Source, TH

Sink, TL

Wrev

QH

QL

0...

0:....

0

=

==

==

=

T

Qcyclereversibleafor

T

Q

T

Q

T

QTherefore

T

Q

T

Q

T

Q

T

QFrom

QQQ

L

L

H

H

L

L

H

H

L

L

H

H

LH

L

L

H

H

T

Q

T

Q

=


40/56

.. *0

Now consider an Irre"ersi'le -eat En!ine which operates 'etween the sa(eT-and TLand recei"es the sa(e .-'ut reects .L7 and produce 4irr

Theory: 4irr 84re" 1 .-.7L3 4irrthere&ore .7L / .L

HeatEngine

Source, TH

Sink, TL

Wirr

QH

QL

)1.6(0....

0...

0:....

0

'

'


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.. *

ENTROPY: + Property o& a Syste(

C

B

A

1

2

Consider Two Re"ersi'le Cycles +9 and +C

)3.6...(..........

)2.6.........(

............

0;.

0;.

0..

2

112

2

1

2

1

2

1

2

1

2

1

2

1

rev

rev

CB

CA

BA

T

QSS

T

QdSDefined

PROPERTYPATHonnob!saefinalandiniialonde"endsermThis

T

Q

T

Q

T

Q

T

Q

T

QCACycle

T

Q

T

Q

T

QBACycle

T

Qcyclerevfor

=

=

=

+

==

+

==

=


42/56


43/56

.. *$


)8.6(0

)7.6(0

)6.6(0

11,

11

;

0

0

0

0

0

+=

+=

>

+=

=

$ss!rro!ndinsysem$eneraion

isolae

$ss!rro!ndinsysemne

$ss!rro!ndinsysemne

$ss!rro!ndinsysem

dSdSdSDefined

dS

dSdSdS

Posiiveal%aysTT

henTTSince

TTQ

T

Q

T

QdSdSdS

T

QdS

T

QdS

Surroundings,temperature = T

S!stem,temperature = T

W

Q


44/56

.. **

Entropy Chan!e o& a Solid or Li%uid

Solid Li%uid

Speci&ic -eat 3 Constant

K "ery s(all hu %

ds 3


45/56

.. *5

Entropy Chan!e o& an Ideal )as

)12.6...(ln

)11.6...(,

,

)10.6...(ln

)+.6...(,

2

11

212

2

11

212

=

=

===

+=

+=

==+=

P

PR

T

dTCss

P

dPR

T

dTCdsherefore

PRTvanddTCdh$as&deal

vdPdhTdsfrom

Similarly

vvR

TdTCss

v

dvR

T

dTCdsherefore

vRTPanddTCd!$as&deal

Pdvd!Tdsfrom

"o

"o

"o

vo

vo

vo


46/56

.. *6

).....(6.1+

...(6.18)..........an$

on'&an&

9:Pe"#a&ionga'i$eal%i&*o/ine

1

2

1

)1(

1

2

1

2

2

1

2

1

1

2

2211

=

=

=

=

====

'''

''

'''

v

v

P

P

T

T

(

(

v

v

P

P

vPvPPv



47/56

.. *

).....(6.21

...(6.20)..........an$

/eoe6.1+


48/56

.. *>

Second Law E&&iciency

6.2).........(:$e;i,e',on'#e$%ork

6.2).........(:$e;i,e'-ro$#,e$ %ork

)e!!i,ien,A$ia/a&i,(ore!!i,ien,7'en&ro-i,

6.23).........(P#-=ea&

(6.22)..........engine=ea&

-o''i/le)(a>.7$eal;'.A,al:e!!i,ien,la%2n$

ac!al

isenro"ic

isen

isenro"ic

ac!alisen

rev

ac!al

rev

ac!al

%

%%

%

COP

COPCOP

=

=

=

=


49/56

So(e Selected Pro'le(s


50/56

. . 0

>; Consider a Carnotcycle heat en!ine with water as the worBin!&luid; The heat trans&er to the worBin! &luid taBes place at $00GC1 durin! thisprocess the water chan!es &ro( saturated li%uid to saturated "apor; -eat isreected &ro( the worBin! &luid at *0GC; * +n insulated cylinder &itted with a &rictionless piston contains


51/56

. . 1

>;* +n insulated cylinder &itted with a &rictionless piston contains0; B! o& water at 00GC# A0 percent %uality; The piston is (o"ed#co(pressin! the water until it reaches a pressure o& ;2 @Pa; -ow (uchworB is re%uired in this processQ

>;5 + cylinder containin! R22 at 0GC# 00 BPa# has an initial"olu(e o& 20 L; + piston co(presses the R22 in a re"ersi'le#isother(al process until it reaches the saturated "apor point; Calculatethe re%uired worB and heat trans&er needed to acco(plish this chan!e o&state;

>;6 One Bilo!ra( o& water at $00GC epands a!ainst a piston ina cylinder unril is reaches a('ient pressure# 00 BPa# at which point thewater has a %uality o& A0 percent; It (ay 'e assu(ed that theepansion is re"ersi'le and adia'atic;;> + ri!id# insulated "essel contains superheated "apor stea(t > @P $5O C + l th l i d ll i t t


52/56

. . 2

at ;> @Pa# $5OoC ; + "al"e on the "essel is opened# allowin! stea( toescape; It (ay 'e assu(ed that at any instant the stea( re(ainin!inside the "essel has under!one a re"ersi'le# adiWa'atic epansion;?eter(ine the &raction o& stea( that has escaped when the stea(re(ainin! inside the "essel reaches the saturated "apor line;

>;A +n insulated cylinder &itted with a &rictionless piston contains0; B! o& superheated "apor stea(; The stea( epands to a('ientpressure# 00 BPa# at which point the te(perature o& the stea( insidethe cylinder is 50GC; The stea( does 50 BD o& worB a!ainst the pistondurin! this epansion; 4hat were the initial pressure and te(peratureQ

>;2 4e wish to cool a !i"en %uantity o& (aterial rapidly to ate(perature o& lOGC; The process re%uires a heat reection o& 2000 BD;One possi'ility is to i((erse the (aterial in a (iture o& ice and water#allowin! heat trans&er &ro( the (aterial to the ice# which (elts the ice;+nother possi'ility is to cool the (aterial 'y e"aporatin! RW22 at 20GC;The heat trans&er to the R22 chan!es it &ro( a saturated li%uid to a

saturated "apor; + third possi'ility is to e"aporate li%uid nitro!en at0;$BPa pressure;


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. . 3

605 Nitro!en !as is co(pressed &ro( >0 BPa and2GC to *>0 BPa 'y a OB4 co(pressor; ?eter(ine the (ass&low rate o& nitro!en throu!h the co(pressor# assu(in! the

co(pression process to 'e =a> isentropic;


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. .

60A Stea( enters an adia'atic tur'ine at > @Pa and 500GC witha (ass &low rate o& $ B!s and lea"es at $0 BPa; The adia'atic e&&iciencyo& the tur'ine is 0;A0; Ne!lectin! the Binetic ener!y chan!e o& the stea(#deter(ine 0 (sand lea"es at 50 BPa# 00GC# and *0 (s; I& the power output o& thetur'ine is 5 @4# deter(ine 0 percent# deter(ine


55/56

. .

6* +ir enters an adia'atic co(pressor at 00 BPa and GC at arate o& ;2 ($s# and it eits at 25GC; The co(pressor has anadia'atic e&&iciency o& >* percent; Ne!lectin! the chan!es in Binetic

and potential ener!ies# deter(ine 0 (so I& the

adia'atic e&&iciency o& the co(pressor is >5 percent# deter(ine


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End of Chapter 6

Documents

Chapter 6 Entropy Ppt