Yunus A. Cengel, Michael A. Boles McGraw-Hill, 2008 ...atayil/Ch7.pdf · Objectives • Apply the...
35
Chapter 7 ENTROPY Thermodynamics: An Engineering Approach, 6 th Edition Yunus A. Cengel, Michael A. Boles McGraw-Hill, 2008 ENTROPY Mehmet Kanoglu Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Transcript of Yunus A. Cengel, Michael A. Boles McGraw-Hill, 2008 ...atayil/Ch7.pdf · Objectives • Apply the...
Ch
ap
ter
7
EN
TR
OP
Y
Th
erm
od
yn
am
ics
: A
n E
ng
ine
eri
ng
Ap
pro
ac
h,
6th
Ed
itio
nY
un
us A
. C
en
gel,
Mic
hael A
. B
ole
s
McG
raw
-Hil
l, 2
008
EN
TR
OP
Y
Meh
met
Kan
og
lu
Co
pyri
gh
t ©
Th
e M
cG
raw
-Hil
l C
om
pa
nie
s, In
c.
Pe
rmis
sio
n r
eq
uir
ed
fo
r re
pro
du
cti
on
or
dis
pla
y.
Ob
jec
tiv
es
•A
pp
ly th
e s
eco
nd
la
w o
f th
erm
od
yn
am
ics t
o p
roce
sse
s.
•D
efin
e a
ne
w p
rop
ert
y c
alle
d entropy t
o q
ua
ntify
th
e s
eco
nd
-
law
effe
cts
.
•E
sta
blis
h th
e increase of entropy principle
.
•C
alc
ula
te th
e e
ntr
op
y c
ha
ng
es t
ha
t ta
ke
pla
ce
du
rin
g
pro
ce
sse
s fo
r p
ure
su
bsta
nce
s, in
co
mp
ressib
le s
ub
sta
nce
s,
an
d id
ea
l g
ase
s.
2
an
d id
ea
l g
ase
s.
•E
xa
min
e a
sp
ecia
l cla
ss o
f id
ea
lize
d p
roce
sse
s, ca
lled
isentropic processes,
an
d d
eve
lop
th
e p
rop
ert
y r
ela
tio
ns f
or
the
se
pro
ce
sse
s.
•D
eri
ve
th
e r
eve
rsib
le s
tea
dy-f
low
wo
rk r
ela
tio
ns.
•D
eve
lop
th
e ise
ntr
op
ic e
ffic
ien
cie
s fo
r va
rio
us s
tea
dy-f
low
de
vic
es.
•In
tro
du
ce
an
d a
pp
ly t
he
en
tro
py b
ala
nce
to
va
rio
us s
yste
ms.
EN
TR
OP
Y
Cla
siu
s
inequalit
y
3
The s
yste
m c
onsid
ere
d in
the d
evelo
pm
ent
of
the
Cla
usiu
s inequalit
y.
The e
qualit
y in t
he C
lausiu
s inequalit
y h
old
s
for
tota
lly o
r ju
st
inte
rnally
revers
ible
cycle
s
and t
he inequalit
y f
or
the irr
evers
ible
ones.
Form
al
definitio
n
of entr
opy
Entr
opy is a
n e
xte
nsiv
e
pro
pert
y o
f a s
yste
m.
The n
et
change
The e
ntr
opy c
hange b
etw
ee
n t
wo
A q
uantity
whose c
yclic
inte
gra
l is
zero
(i.e.,
a
pro
pert
y lik
e v
olu
me)
4
The n
et
change
in v
olu
me (
a
pro
pert
y)
during
a c
ycle
is
alw
ays z
ero
.
The e
ntr
opy c
hange b
etw
ee
n t
wo
specifie
d s
tate
s is t
he s
am
e w
heth
er
the p
rocess is r
evers
ible
or
irre
vers
ible
.
A S
pe
cia
l C
as
e:
Inte
rna
lly R
eve
rsib
le
Iso
the
rma
l H
ea
t T
ran
sfe
r P
roc
es
se
s
This
equation is p
art
icula
rly u
sefu
l fo
r dete
rmin
ing
the e
ntr
opy c
hanges o
f th
erm
al energ
y r
eserv
oirs.
TH
E IN
CR
EA
SE
OF
EN
TR
OP
Y P
RIN
CIP
LE
Th
e e
qu
alit
y h
old
s fo
r a
n in
tern
ally
reve
rsib
le p
roce
ss a
nd
th
e in
eq
ua
lity
for
an
irr
eve
rsib
le p
roce
ss.
5
A c
ycle
com
posed o
f a
revers
ible
and a
n
irre
vers
ible
pro
cess.
for
an
irr
eve
rsib
le p
roce
ss.
Som
e e
ntr
opy is generated o
r created d
uring a
n irr
evers
ible
pro
cess,
and t
his
genera
tion is d
ue e
ntire
ly t
o t
he p
resence o
f irre
vers
ibili
ties.
The e
ntr
opy g
enera
tion S
ge
nis
alw
ays a
positive q
uantity
or
zero
.
Can t
he e
ntr
opy o
f a s
yste
m d
uring a
pro
cess d
ecre
ase?
The e
ntr
opy c
hange o
f an isola
ted
6
The e
ntr
opy c
hange o
f an isola
ted
syste
m is t
he s
um
of th
e e
ntr
opy
changes o
f its c
om
ponents
, and is
never
less t
han z
ero
.
A s
yste
m a
nd its
surr
oundin
gs
form
an isola
ted s
yste
m.
The incre
ase
of entr
opy
princip
le
So
me
Re
ma
rks
ab
ou
t E
ntr
op
y
1.
Pro
cesses c
an o
ccur
in a
certain
direction
only
, not
in any
direction. A
pro
cess m
ust
pro
ceed in t
he d
irection t
hat
com
plie
s w
ith
the incre
ase o
f entr
opy p
rincip
le,
that
is,
Sge
n≥
0. A
pro
cess t
hat vio
late
s t
his
princip
le is im
possib
le.
2.
Entr
opy is a
nonconserved property,
and
there
is no s
uch t
hin
g a
s t
he conservation of
entropy principle
. E
ntr
opy is c
onserv
ed
7
The e
ntr
opy c
hange o
f a
syste
m c
an b
e n
egative,
but th
e e
ntr
opy g
enera
tion
cannot.
entropy principle
. E
ntr
opy is c
onserv
ed
during t
he idealiz
ed r
evers
ible
pro
cesses
only
and incre
ases d
uring all
actu
al
pro
cesses.
3.
The p
erf
orm
ance o
f engin
eering s
yste
ms is
degra
ded b
y t
he p
resence o
f irre
vers
ibili
ties,
and entropy generation
is a
measure
of
the
magnitudes o
f th
e irr
evers
ibili
ties d
uring t
hat
pro
cess. It
is a
lso u
sed t
o e
sta
blis
h c
rite
ria
for
the p
erf
orm
ance o
f engin
eering d
evic
es.
EN
TR
OP
Y C
HA
NG
E O
F P
UR
E S
UB
STA
NC
ES
Entr
opy is a
pro
pert
y, a
nd t
hus t
he
valu
e o
f entr
opy o
f a s
yste
m is f
ixed
once t
he s
tate
of
the s
yste
m is f
ixed.
8
The e
ntr
opy o
f a p
ure
substa
nce
is d
ete
rmin
ed f
rom
the t
able
s
(lik
e o
ther
pro
pert
ies).
Schem
atic o
f th
e T-s d
iagra
m f
or
wate
r.
En
tro
py c
ha
ng
e
ISE
NT
RO
PIC
PR
OC
ES
SE
SA
pro
ce
ss d
uri
ng
wh
ich
th
e e
ntr
op
y r
em
ain
s c
on
sta
nt is
ca
lled
an
is
en
tro
pic
pro
ce
ss
.
9
During a
n inte
rnally
revers
ible
, adia
batic
(isentr
opic
) pro
cess,
the
entr
opy r
em
ain
s c
onsta
nt.
The isentr
opic
pro
cess a
ppears
as a
vertical lin
e s
egm
ent
on a
T-s d
iagra
m.
PR
OP
ER
TY
DIA
GR
AM
S IN
VO
LV
ING
EN
TR
OP
Y
On a
T-S
dia
gra
m,
the
are
a u
nder
the
pro
cess c
urv
e
repre
sents
the
heat tr
ansfe
r fo
r
inte
rnally
revers
ible
10
revers
ible
pro
cesses.
For
adia
batic s
teady-f
low
devic
es,
the v
ert
ical dis
tance
∆h o
n a
n h-s d
iagra
m is a
measure
of
work
, and t
he
horizonta
l dis
tance ∆s is a
measure
of
irre
vers
ibili
ties.
Mo
llie
r d
iag
ram
:T
he h-s
dia
gra
m
WH
AT
IS
EN
TR
OP
Y?
A p
ure
cry
sta
lline s
ubsta
nce a
t absolu
te z
ero
Boltzm
ann
rela
tion
11
The level of
mole
cula
r
dis
ord
er
(entr
opy)
of
a
substa
nce incre
ases a
s
it m
elts o
r evapora
tes.
A p
ure
cry
sta
lline s
ubsta
nce a
t absolu
te z
ero
tem
pera
ture
is in p
erf
ect
ord
er,
and its
entr
opy is
zero
(th
e t
hir
d law
of
therm
od
yn
am
ics).
Dis
org
aniz
ed e
nerg
y d
oes n
ot
cre
ate
much
usefu
l effect,
no m
att
er
how
larg
e it is
.
The p
addle
-whee
l w
ork
done o
n a
gas incre
ases t
he
level of
dis
ord
er
(entr
opy)
of th
e g
as,
and t
hus e
nerg
y
is d
egra
ded d
uring t
his
pro
cess.
12
In the a
bsence o
f
fric
tion, ra
isin
g a
weig
ht
by a
rota
ting
shaft
does n
ot
cre
ate
any d
isord
er
(entr
opy),
and t
hus
energ
y is n
ot
degra
ded d
uring t
his
pro
cess.
is d
egra
ded d
uring t
his
pro
cess.
During a
heat
transfe
r pro
cess,
the
net entr
opy
incre
ases.
(The
incre
ase in t
he
entr
opy o
f th
e c
old
body m
ore
than
offsets
the d
ecre
ase
in the e
ntr
opy o
f
the h
ot
body.
)
TH
E T ds R
EL
AT
ION
S
the first T ds, or Gibbsequation
13
The T ds r
ela
tions a
re v
alid
for
both
revers
ible
and irr
evers
ible
pro
cesses a
nd f
or
both
clo
sed
and o
pen s
yste
ms.
the s
econd T ds equation
Diffe
rential changes
in e
ntr
opy in t
erm
s
of oth
er
pro
pert
ies
EN
TR
OP
Y C
HA
NG
E O
F L
IQU
IDS
AN
D S
OL
IDS
Sin
ce
f
or
liquid
s a
nd s
olid
s
Liq
uid
sand s
olid
scan b
e
appro
xim
ate
d a
s
incompressible substances
sin
ce t
heir s
pecific
volu
mes
rem
ain
nearly c
onsta
nt
during a
pro
cess.
14
For
and isentr
opic
pro
cess o
f an incom
pre
ssib
le s
ubsta
nce
TH
E E
NT
RO
PY
CH
AN
GE
OF
ID
EA
L G
AS
ES
Fro
m the f
irst T ds
rela
tion
Fro
m the s
econd T ds
rela
tion
15
A b
roadcast
from
channel IG
.
Co
ns
tan
t S
pe
cif
ic H
ea
ts (
Ap
pro
xim
ate
An
aly
sis
)
Entr
opy c
hange o
f an ideal gas o
n a
16
Under
the c
onsta
nt-
specific
-
heat assum
ption,
the s
pecific
heat is
assum
ed t
o b
e c
onsta
nt
at som
e a
vera
ge v
alu
e.
Entr
opy c
hange o
f an ideal gas o
n a
unit–m
ole
basis
Va
ria
ble
Sp
ec
ific
He
ats
(E
xa
ct
An
aly
sis
)
We c
hoose a
bsolu
te z
ero
as t
he r
efe
rence
tem
pera
ture
and d
efine a
function s
°as
17
The e
ntr
opy o
f an
ideal gas d
epends o
n
both
T a
nd P
. T
he
function s r
epre
sents
only
the t
em
pera
ture
-
dependent
part
of
entr
opy.
On a
unit–m
ole
basis
On a
unit–m
ass b
asis
Ise
ntr
op
ic P
roc
es
se
s o
f Id
ea
l G
as
es
Co
ns
tan
t S
pe
cif
ic H
ea
ts (
Ap
pro
xim
ate
An
aly
sis
)
Sett
ing this
eq.
equal to
zero
, w
e g
et
18
The isentr
opic
rela
tions o
f id
eal
gases a
re v
alid
for
the isentr
opic
pro
cesses o
f id
eal gases o
nly
.
Isen
tro
pic
Pro
cesses o
f Id
eal G
ases
Va
ria
ble
Sp
ec
ific
He
ats
(E
xa
ct
An
aly
sis
)
Re
lati
ve
Pre
ss
ure
an
d R
ela
tive
Sp
ec
ific
Vo
lum
e
exp(s
°/R
) is
the r
ela
tive
pre
ssure
Pr.
The u
se o
f Prdata
for
calc
ula
ting t
he
final te
mpera
ture
during a
n isentr
opic
pro
cess.
19
T/Pris
the r
ela
tive
specific
volu
me vr.
pro
cess.
The u
se o
f vrdata
for
calc
ula
ting t
he f
inal
tem
pera
ture
during a
n
isentr
opic
pro
cess
RE
VE
RS
IBL
E S
TE
AD
Y-F
LO
W W
OR
K
Wh
en
kin
etic a
nd
po
ten
tia
l e
ne
rgie
s
20
Revers
ible
work
rela
tions f
or
ste
ady-f
low
and c
losed
syste
ms.
are
ne
glig
ible
The larg
er
the
specific
volu
me,
the
gre
ate
r th
e
work
pro
duced (
or
consum
ed)
by
a s
teady-f
low
devic
e.
For
the s
teady f
low
of
a liq
uid
thro
ugh a
devic
e t
hat
involv
es n
o w
ork
inte
ractions
(such a
s a
pip
e s
ection),
the w
ork
term
is
zero
(B
ern
oulli
equation):
Pro
of
tha
t S
tea
dy-F
low
De
vic
es
De
live
r th
e M
os
t a
nd
Co
ns
um
e
the
Le
as
t W
ork
wh
en
th
e P
roc
es
s Is
Re
ve
rsib
le
Actu
al
Revers
ible
Takin
g h
eat
input
and w
ork
outp
ut
positiv
e:
21
A r
evers
ible
turb
ine d
eliv
ers
more
work
than a
n irr
evers
ible
one if
both
opera
te b
etw
een t
he s
am
e
end s
tate
s.
Work
-pro
ducin
g d
evic
es s
uch a
s
turb
ines d
eliv
er
more
work
, and w
ork
-
consum
ing d
evic
es s
uch a
s p
um
ps
and c
om
pre
ssors
require less w
ork
when t
hey o
pera
te r
evers
ibly
.
MIN
IMIZ
ING
TH
E C
OM
PR
ES
SO
R W
OR
K
Isentr
opic
(Pvk=
consta
nt)
:
Poly
tropic
(Pvn
= c
onsta
nt)
:
Wh
en
kin
etic a
nd
po
ten
tia
l e
ne
rgie
s
are
ne
glig
ible
22
Isoth
erm
al (Pv =
consta
nt)
:P
-v d
iagra
ms o
f is
entr
opic
,
poly
tropic
, and isoth
erm
al
com
pre
ssio
n p
rocesses b
etw
een
the s
am
e p
ressure
lim
its.
The a
dia
batic c
om
pre
ssio
n (Pvk=
consta
nt)
requires t
he m
axim
um
work
and t
he
isoth
erm
al com
pre
ssio
n (T =
consta
nt)
requires t
he m
inim
um
.W
hy?
Mu
ltis
tag
e C
om
pre
ss
ion
wit
h I
nte
rco
oli
ng
The g
as is c
om
pre
ssed
in s
tages a
nd c
oole
d
betw
een e
ach s
tage b
y
passin
g it
thro
ugh a
heat exchanger
calle
d
anintercooler. P
-v a
nd T-s
dia
gra
ms f
or
a t
wo-
sta
ge s
teady-f
low
23
sta
ge s
teady-f
low
com
pre
ssio
n
pro
cess.
To minimize compression work during two-stage
compression, the pressure ratio across each
stage of the compressor must be the same.
ISE
NT
RO
PIC
EF
FIC
IEN
CIE
S O
F
ST
EA
DY
-FL
OW
DE
VIC
ES
The isentr
opic
pro
cess involv
es n
o
irre
vers
ibili
ties a
nd s
erv
es a
s t
he ideal
pro
cess f
or
ad
iab
ati
c d
evic
es.
Isen
tro
pic
Eff
icie
ncy
24
The h-s d
iagra
m f
or
the a
ctu
al and
isentr
opic
pro
cesses o
f an
adia
batic t
urb
ine.
Eff
icie
ncy
of
Tu
rbin
es
Ise
ntr
op
ic E
ffic
ien
cie
s o
f C
om
pre
ss
ors
an
d P
um
ps
The h-s d
iagra
m
Isoth
erm
al
For
a
pum
p
Wh
en
kin
etic a
nd
po
ten
tia
l e
ne
rgie
s
are
ne
glig
ible
25
The h-s d
iagra
m
of th
e a
ctu
al and
isentr
opic
pro
cesses o
f an
adia
batic
com
pre
ssor.
Com
pre
ssors
are
som
etim
es
inte
ntionally
coole
d t
o
min
imiz
e t
he
work
input.
Isoth
erm
al
effic
iency
Can y
ou u
se isentr
opic
effic
iency f
or
a
non-a
dia
batic c
om
pre
ssor?
Can y
ou u
se isoth
erm
al effic
iency f
or
an a
dia
batic c
om
pre
ssor?
Ise
ntr
op
ic E
ffic
ien
cy
of
No
zzle
s
The h-s d
iagra
m
of th
e a
ctu
al and
isentr
opic
If the inle
t velo
city o
f th
e
fluid
is s
mall
rela
tive t
o
the e
xit v
elo
city,
the
energ
y b
ala
nce is
26
isentr
opic
pro
cesses o
f an
adia
batic n
ozzle
.
Then,
A s
ubsta
nce leaves
actu
al nozzle
s a
t a
hig
her
tem
pera
ture
(thus a
low
er
velo
city)
as a
result o
f fr
iction.
EN
TR
OP
Y B
AL
AN
CE
En
tro
py C
han
ge o
f a
Syste
m,
∆S
sys
tem
27
Energ
y a
nd e
ntr
opy
bala
nces f
or
a s
yste
m.
When the p
ropert
ies o
f th
e
syste
m a
re n
ot
uniform
Me
ch
an
ism
s o
f E
ntr
op
y T
ran
sfe
r, S
ina
nd
So
ut
1 H
eat
Tra
nsfe
rE
ntr
opy t
ransfe
r by h
eat
transfe
r:
En
tro
py t
ran
sfe
r b
y w
ork
:
28
Heat tr
ansfe
r is
alw
ays
accom
panie
d b
y e
ntr
opy t
ransfe
r
in the a
mount
of Q/T
, w
here
T is
the b
oundary
tem
pera
ture
.
No e
ntr
opy a
ccom
panie
s w
ork
as it
cro
sses
the s
yste
m b
oundary
. B
ut
entr
opy m
ay b
e
genera
ted w
ithin
the s
yste
m a
s w
ork
is
dis
sip
ate
d into
a less u
sefu
l fo
rm o
f energ
y.
2 M
ass F
low
Entr
opy t
ransfe
r by m
ass:
Ma
ss c
on
tain
s e
ntr
op
y a
s w
ell
as
en
erg
y, a
nd
th
us m
ass flo
w in
to o
r
When the p
ropert
ies o
f th
e m
ass
change d
uring t
he p
rocess
Mech
an
ism
s o
f E
ntr
op
y T
ran
sfe
r, S
inan
d S
ou
t
29
en
erg
y, a
nd
th
us m
ass flo
w in
to o
r
ou
t o
f syste
m is a
lwa
ys
acco
mp
an
ied
by e
ne
rgy a
nd
en
tro
py tra
nsfe
r.
En
tro
py G
en
era
tio
n, S
ge
nE
ntr
opy g
enera
tion
outs
ide s
yste
m
boundaries c
an b
e
accounte
d f
or
by
writing a
n e
ntr
opy
bala
nce o
n a
n
exte
nded s
yste
m t
hat
inclu
des t
he s
yste
m
and its
im
media
te
surr
oundin
gs.
30
Mechanis
ms o
f entr
opy t
ransfe
r fo
r a
genera
l syste
m.
Clo
se
d S
ys
tem
s
31
Co
ntr
ol
Vo
lum
es
32
The e
ntr
opy o
f a
substa
nce a
lwa
ys
incre
ases (
or
rem
ain
s c
onsta
nt
in
the c
ase o
f a
revers
ible
pro
cess)
as it
flow
s t
hro
ugh a
sin
gle
-str
eam
,
adia
batic,
ste
ady-
flow
devic
e.
The e
ntr
opy o
f a c
ontr
ol
volu
me c
hanges a
s a
result o
f m
ass f
low
as w
ell
as h
eat
transfe
r.
Entropy balance for heat
transfer through a wall
EX
AM
PL
ES
33
Entropy balance for
a throttling process
En
tro
py g
en
era
tio
n a
sso
cia
ted
wit
h a
heat
tran
sfe
r p
rocess
34
Gra
phic
al re
pre
senta
tion o
f entr
opy g
enera
tion d
uring
a h
eat
transfe
r pro
cess
thro
ugh a
fin
ite t
em
pera
ture
diffe
rence.
Su
mm
ary
•E
ntr
op
y
•T
he
In
cre
ase
of
en
tro
py p
rin
cip
le
•S
om
e r
em
ark
s a
bo
ut
en
tro
py
•E
ntr
op
y c
ha
ng
e o
f p
ure
su
bsta
nce
s
•Is
en
tro
pic
pro
ce
sse
s
•P
rop
ert
y d
iag
ram
s in
vo
lvin
g e
ntr
op
y
•W
ha
t is
en
tro
py?
35
•W
ha
t is
en
tro
py?
•T
he
T ds r
ela
tio
ns
•E
ntr
op
y c
ha
ng
e o
f liq
uid
s a
nd
so
lids
•T
he
en
tro
py c
ha
ng
e o
f id
ea
l g
ase
s
•R
eve
rsib
le s
tea
dy-f
low
wo
rk
•M
inim
izin
g t
he
co
mp
resso
r w
ork
•Is
en
tro
pic
eff
icie
ncie
s o
f ste
ad
y-f
low
de
vic
es
•E
ntr
op
y b
ala
nce
