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SOLUTIONS MANUAL FOR
by
Thermodynamicsin
Material Science,Second Edition
Robert DeHoff
8165.indd 1 1/24/08 8:58:07 AM
8165.indd 2 1/24/08 8:54:26 AM
SOLUTIONS MANUAL FOR
by
Thermodynamicsin
Material Science,Second Edition
Robert DeHoff
8165.indd 3 1/24/08 8:58:07 AM
CRC PressTaylor & Francis Group6000 Broken Sound Parkway NW, Suite 300Boca Raton, FL 33487-2742
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International Standard Book Number-13: 978-0-8493-8165-2 (Softcover)
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T&F_LOC_C_Master.indd 1 1/24/08 8:50:46 AM8165.indd 4 1/24/08 8:54:27 AM
This Manual is a compilation of solutions to the homework problems presented in thetext:
Thermodynamics in Materials Science, Second Edition, CRC Press, Taylor and Francis Group,
Publishers, ISBN 0-8493-4065-9, (2006).
In preparing this manual the data used in the solutions are consistent with that presentedin the Appendices of the text. The reader should be aware that thermochemical data continues toevolve, so that the numbers may change with time, sometimes significantly. In any real worldapplication in industry or research it is incumbent upon the investigator to seek to obtain thelatest information from appropriate data bases.
Working equations developed in this process use notation that is consistent with that usedin the text. All numerical problems have been worked in MathCadTM, a mathematics softwareprogram, so that every attempt has been made to produce correct answers from the input data andthe strategy devised to solve the problem. All graphical presentations that involve numericalcalculations were also produced in MathCad and copied into this manual. This includes anumber of quantitative surface plots, which are particularly easily generated in this software.
Robert T. DeHoff, July, 2006
Cha
pter
2.
The
Str
uctu
re o
f The
rmod
ynam
ics
1
Cha
pter
2.
Stru
ctur
e of
The
rmod
ynam
ics
2.1.
Cla
ssify
the
follo
win
g th
erm
odyn
amic
syst
ems i
n th
e fiv
eca
tego
ries d
efin
ed in
Sec
tion
2.1:
a. A
solid
bar
of c
oppe
r.b.
A g
lass
of i
ce w
ater
.c.
A y
ttria
stab
ilize
d zi
rcon
ia fu
rnac
e tu
be.
d. A
styr
ofoa
m c
offe
e cu
p.e.
A e
utec
tic a
lloy
turb
ine
blad
e ro
tatin
g at
20,
000
rpm
.
If y
ou fi
nd it
nec
essa
ry to
qua
lify
your
ans
wer
by
defin
ing
the
syst
em m
ore
prec
isel
y, st
ate
your
ass
umpt
ions
.
Ans
wer
to 2
.1.
In e
ach
case
it is
nec
essa
ry to
mak
e so
me
assu
mpt
ions
abo
utth
e ki
nd o
f pro
cess
es th
at m
ay b
e of
inte
rest
in th
e pr
oble
m.
The
sim
ples
t situ
atio
n is
ass
umed
in e
ach
of th
e fo
llow
ing.
a. P
ure
solid
cop
per i
s a u
nary
, hom
ogen
eous
, clo
sed,
non
-re
actin
g ot
herw
ise
sim
ple
syst
em.
b. I
ce w
ater
con
sist
s of t
wo
phas
es, s
olid
and
liqu
id; b
oth
phas
es a
re fi
xed
com
posi
tion.
Thi
s sys
tem
may
be
treat
ed a
s aun
ary,
het
erog
eneo
us, c
lose
d, n
on-r
eact
ing
othe
rwis
e si
mpl
esy
stem
.
c. I
n th
is m
ater
ial s
yste
m th
e yt
tria
(Y2O
3) is
pre
sent
as s
econ
dph
ase
parti
cles
dis
tribu
ted
thro
ugho
ut a
mat
rix o
f ZrO
2. It
may
be tr
eate
d as
a m
ultic
ompo
nent
(bin
ary
if th
e co
mpo
nent
s are
take
n to
be
Y2O
3 and
ZrO
2) he
tero
gene
ous (
two
phas
es),
clos
ed, n
on-r
eact
ing
othe
rwis
e si
mpl
e sy
stem
.
d. S
tyro
foam
is a
pol
ymer
of f
ixed
com
posi
tion.
It m
ay b
eap
prop
riate
to tr
eat i
t as a
una
ry, h
omog
eneo
us, c
lose
d, n
on-
reac
ting
othe
rwis
e si
mpl
e sy
stem
. If
, for
exa
mpl
e, th
e sy
stem
is d
efin
ed to
incl
ude
the
poro
sity
then
add
ition
al (g
aseo
us)
com
pone
nts w
ill b
e pr
esen
t in
thes
e tw
o ph
ases
.
e. A
eut
ectic
syst
em c
onsi
sts o
f alte
rnat
ing
laye
rs o
f tw
oph
ases
, eac
h of
whi
ch is
a so
lid so
lutio
n. T
he p
robl
em a
lso
impo
ses a
cen
trifu
gal f
ield
on
the
rota
ting
part.
Thu
s, th
is is
am
ultic
ompo
nent
, het
erog
eneo
us, c
lose
d, n
on-r
eact
ing
syst
emin
a c
entri
fuga
l fie
ld.
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
- 2.2.
It i
s not
an
over
stat
emen
t to
say
that
with
out s
tate
func
tions
ther
mod
ynam
ics w
ould
be
usel
ess.
Dis
cuss
this
asse
rtion
.
Ans
wer
to 2
.2.
If th
ere
wer
e no
stat
e fu
nctio
ns (l
ike
T, P
, V, c
ompo
sitio
n), i
.e.,
prop
ertie
s tha
t dep
end
only
upo
n th
e cu
rren
t con
ditio
n of
the
syst
em, a
nd n
ot o
n ho
w it
arr
ived
at t
hat c
ondi
tion)
then
the
beha
vior
of a
ll as
pect
s of m
atte
r wou
ld d
epen
d ex
plic
itly
upon
the
hist
ory
of th
e sy
stem
. Th
ere
wou
ld b
e no
var
iabl
es th
at, b
yth
emse
lves
, exp
licitl
y de
scrib
e th
e cu
rren
t con
ditio
n of
any
syst
em.
Thus
, eve
n th
e hi
stor
y ex
perie
nced
by
the
syst
em
2
coul
d no
t be
desc
ribed
in te
rms o
f som
e se
quen
ce o
f cha
nge
ofits
pro
perti
es.
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
-
2.3.
Det
erm
ine
whi
ch o
f the
follo
win
g pr
oper
ties o
f ath
erm
odyn
amic
syst
em a
re e
xten
sive
pro
perti
es a
nd w
hich
are
inte
nsiv
e. a. T
he m
ass d
ensi
ty.
b. T
he m
olar
den
sity
.c.
The
num
ber o
f gra
m a
tom
s of
alu
min
um in
a c
hunk
of a
lum
ina.
d. T
he p
oten
tial e
nerg
y of
the
syst
em in
a g
ravi
tatio
nal
field
.e.
The
mol
ar c
once
ntra
tion
of N
aCl i
n a
salt
solu
tion.
f. T
he h
eat a
bsor
bed
by a
the
gas i
n a
cylin
der w
hen
itis
com
pres
sed.
Ans
wer
to 2
.3.
a. T
he m
ass d
ensi
ty is
the
ratio
of t
he m
ass o
f a sy
stem
to it
svo
lum
e; it
is in
tens
ive.
b. T
he m
olar
den
sity
is th
e ra
tio o
f the
num
ber o
f mol
es to
the
volu
me;
it is
inte
nsiv
e.
c. T
he n
umbe
r of g
ram
ato
ms i
s a p
rope
rty o
f the
syst
em a
s aw
hole
; it i
s an
exte
nsiv
e pr
oper
ty.
d. T
he p
oten
tial e
nerg
y of
the
syst
em is
a p
rope
rty o
f the
syst
em a
s a w
hole
; it i
s thu
s an
exte
nsiv
e pr
oper
ty.
e. T
he m
olar
con
cent
ratio
n is
the
ratio
of n
umbe
r of m
oles
toth
e vo
lum
e if
the
syst
em; i
t is a
n in
tens
ive
prop
erty
.
f. T
he h
eat a
bsor
bed
is a
pro
perty
of t
he sy
stem
as a
who
le; i
tis
an
exte
nsiv
e pr
oper
ty.
All
of th
e pr
oper
ties i
dent
ified
as i
nten
sive
als
o sh
are
the
char
acte
ristic
that
they
may
be
defin
ed a
t a p
oint
with
in th
esy
stem
, and
inde
ed m
ay v
ary
from
poi
nt to
poi
nt.
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
-
2.4.
Why
is h
eat a
pro
cess
var
iabl
e?
Ans
wer
to 2
.4.
Hea
t is f
unda
men
tally
a fl
ow o
f ene
rgy.
Hea
t is
trans
ferr
ed b
etw
een
two
syst
ems,
or b
etw
een
parts
of t
he sa
me
syst
em;
this
rear
rang
emen
t of t
he d
istri
butio
n of
ene
rgy
isne
cess
arily
acc
ompa
nied
by
chan
ges i
n at
leas
t som
e of
the
prop
ertie
s of t
he sy
stem
s inv
olve
d. S
uch
a ch
ange
is b
yde
finiti
on a
pro
cess
.
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
---
2.5.
Writ
e th
e to
tal d
iffer
entia
l of t
he fu
nctio
n
a. I
dent
ify th
e co
effic
ient
s of t
he th
ree
diff
eren
tials
in
3
this
exp
ress
ion
as a
ppro
pria
te p
artia
l der
ivat
ives
.b.
Sho
w th
at th
ree
Max
wel
l rel
atio
ns h
old
amon
g th
ese
coef
ficie
nts
Ans
wer
to 2
.5.
a.W
rite
the
tota
l diff
eren
tial o
f the
func
tion
z:
b.
Eval
uate
the
cros
s der
ivat
ives
:
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
-
4
2.6.
Des
crib
e w
hat t
he n
otio
n of
equ
ilibr
ium
mea
ns to
you
. Li
st a
s man
y at
tribu
tes a
s you
can
thin
k of
that
wou
ld b
eex
hibi
ted
by a
syst
em th
at h
as c
ome
to e
quili
briu
m.
Why
do
you
thin
k th
ese
char
acte
ristic
s of a
syst
em in
equ
ilibr
ium
are
impo
rtant
in th
erm
odyn
amic
s?
Ans
wer
to 2
.6.
Attr
ibut
es o
f equ
ilibr
ium
:
1. A
stat
e of
rest
: st
ate
of th
e sy
stem
doe
s not
cha
nge
with
tim
e.
2. A
stab
le st
ate:
if t
he st
ate
is d
ispl
aced
from
the
equi
libriu
m st
ate,
it w
ill re
turn
to it
.
3. A
stat
e of
inte
rnal
uni
form
ity;
(in th
e ab
senc
e of
exte
rnal
fiel
ds) g
radi
ents
of i
nten
sive
pro
perti
es v
anis
h.
The
equi
libriu
m st
ate
is th
e fin
al st
ate
of e
very
pro
cess
. Th
epr
imar
y go
al o
f the
rmod
ynam
ics i
s the
pre
dict
ion
of th
epr
oper
ties o
f the
fina
l equ
ilibr
ium
stat
e fo
r any
giv
en in
itial
cond
ition
of a
ny sy
stem
. "H
ow fa
r the
syst
em is
" fr
om th
eeq
uilib
rium
stat
e is
a m
easu
re o
f the
driv
ing
forc
e fo
r pro
cess
esch
angi
ng th
e sy
stem
tow
ard
equi
libriu
m, a
nd c
ontro
ls th
e ra
teof
app
roac
h to
the
final
stat
e of
rest
.
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
-
Cha
pter
3. T
he L
aws o
f The
rmod
ynam
ics
5
Cha
pter
3. T
he L
aws o
f The
rmod
ynam
ics
3.1.
The
law
s of t
herm
odyn
amic
s are
"pe
rvas
ive"
. Ex
plai
n in
deta
il th
e m
eani
ng o
f thi
s im
porta
nt st
atem
ent.
Ans
wer
to 3
.1.
"Per
vasi
ve"
mea
ns th
at th
e la
ws a
pply
a. I
n ev
ery
syst
emb.
At e
very
inst
ant i
n tim
ec.
In
ever
y vo
lum
e el
emen
t
in w
hich
cha
nge
is o
ccur
ring.
Thi
s cha
ract
eris
tic e
mph
asiz
esth
e ge
nera
lity,
and
thus
the
pow
er, o
f the
law
s of
ther
mod
ynam
ics.
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
--
3.2.
Lis
t the
kin
ds o
f ene
rgy
conv
ersi
ons i
nvol
ved
inpr
opel
ling
an a
utom
obile
.
Ans
wer
to 3
.2.
Elec
trica
l ene
rgy
(the
spar
k) c
ombi
nes w
ith c
hem
ical
ene
rgy
(in th
e fu
el) t
o pr
oduc
e he
at a
nd m
echa
nica
l wor
k th
at d
rives
the
pist
ons i
n th
e en
gine
blo
ck; t
he m
echa
nica
l wor
k is
then
trans
mitt
ed th
roug
h th
e cr
anks
haft
and
trans
mis
sion
to th
e ax
lean
d th
e di
ffer
entia
l tha
t ulti
mat
ely
turn
s the
whe
els.
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
3.3.
Lis
t the
kin
ds o
f ene
rgy
conv
ersi
ons i
nvol
ved
in o
pera
ting
a ha
nd c
alcu
lato
r.
Ans
wer
to 3
.3.
Che
mic
al e
nerg
y st
ored
in a
bat
tery
is c
onve
rted
to e
lect
rical
ener
gy th
at fl
ows t
hrou
gh th
e co
nnec
tors
and
inte
grat
edci
rcui
ts a
long
pat
hs d
eter
min
ed b
y m
echa
nica
l inp
ut th
roug
hth
e ke
ypad
. D
epen
ding
upo
n th
e na
ture
of t
he d
ispl
ay, t
hepa
ttern
of o
utpu
t ele
ctric
al e
nerg
y m
ay b
e us
ed to
alte
r the
stru
ctur
e of
mol
ecul
es in
a li
quid
cry
stal
or c
onve
rt to
ligh
ten
ergy
in a
n LE
D a
rray
.
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
-
3.4.
Lis
t the
kin
ds o
f ene
rgy
conv
ersi
ons i
nvol
ved
in u
sing
your
arm
and
han
d to
turn
the
page
in th
is te
xt.
Ans
wer
to 3
.4.
Cha
pter
3. T
he L
aws o
f The
rmod
ynam
ics
6
Stor
ed c
hem
ical
ene
rgy
deriv
ed fr
om fo
od p
rodu
cts a
ndox
ygen
is c
onve
rted
to e
lect
rical
ene
rgy
whi
ch g
ener
ates
patte
rns i
n th
e br
ain
that
are
tran
smitt
ed th
roug
h th
e ne
ural
netw
ork
to m
uscl
es in
the
arm
and
han
d. T
hese
sign
als i
nduc
ech
emic
al a
nd e
lect
rical
cha
nges
in th
e re
quire
d m
uscl
esca
usin
g th
em to
con
tract
app
ropr
iate
ly;
this
con
tract
ion
isco
nver
ted
to th
e m
echa
nica
l wor
k in
volv
ed in
the
mot
ion
of th
ear
m a
nd h
and
as th
ey m
ove
thei
r wei
ght a
nd th
at o
f the
pap
erin
a g
ravi
tatio
nal f
ield
.
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
---
3.5.
Sup
pose
the
conv
entio
n w
ere
adop
ted
that
def
ines
W a
ndW
' in
the
first
law
of t
herm
odyn
amic
s to
be th
e "w
ork
done
by
the
syst
em o
n th
e su
rrou
ndin
gs".
a. W
rite
the
first
law
with
this
alte
rnat
e co
nven
tion.
b. W
hy d
o th
e si
gns c
hang
e?
Ans
wer
to 3
.5.
a. b.
With
this
con
vent
ion
W is
def
ined
to b
e po
sitiv
e w
hen
it is
trans
mitt
ed fr
om th
e sy
stem
to th
e su
rrou
ndin
gs;
thus
if W
ispo
sitiv
e, th
e in
tern
al e
nerg
y of
the
syst
em d
ecre
ases
.
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
--
3.6.
Giv
e fiv
e ex
ampl
es o
f the
ope
ratio
n of
the
seco
nd la
w o
fth
erm
odyn
amic
s in
your
dai
ly e
xper
ienc
e; t
hey
mus
t be
diff
eren
t fro
m th
ose
give
n in
the
text
.
Ans
wer
to 3
.6.
1. T
he m
orni
ng c
offe
e co
ols w
ith ti
me.
2. S
ugar
dis
solv
es in
hot
cof
fee.
3. L
eft t
o its
elf,
a pe
ndul
um w
ill sl
ow to
a st
op.
4. O
rgan
ism
s die
.5.
An
expa
ndin
g ga
s coo
ls.
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
---
3.7.
Bio
logi
cal s
yste
ms,
- org
anel
les,
cells
, org
ans,
plan
ts a
ndan
imal
s,- a
re h
ighl
y or
dere
d, y
et fo
rm sp
onta
neou
sly.
Doe
s the
form
atio
n an
d gr
owth
of b
iolo
gica
l sys
tem
s vio
late
the
seco
ndla
w o
f the
rmod
ynam
ics?
Exp
lain
you
r ans
wer
.
Ans
wer
to 3
.7.
No,
it d
oes n
ot v
iola
te th
e se
cond
law
of t
herm
odyn
amic
s. Th
eir f
orm
atio
n an
d gr
owth
are
acc
ompa
nied
by
chan
ges i
nth
eir s
urro
undi
ngs s
uch
that
the
tota
l cha
nge
in e
ntro
py o
f the
biol
ogic
al sy
stem
plu
s its
surr
ound
ings
is p
ositi
ve.
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
3.8.
"Ir
reve
rsib
le"
is a
n aw
kwar
d ad
ject
ive.
Why
is th
is te
rmso
app
ropr
iate
in it
s app
licat
ion
to th
e de
scrip
tion
of p
roce
sses
Cha
pter
3. T
he L
aws o
f The
rmod
ynam
ics
7
in th
erm
odyn
amic
s? S
ugge
st tw
o or
thre
e al
tern
ate
wor
ds o
rph
rase
s tha
t mig
ht b
e us
ed to
repl
ace
"irr
ever
sibl
e" in
thes
eco
ntex
ts.
Ans
wer
to 3
.8.
Irre
vers
ible
mea
ns:
"Inc
apab
le o
f bei
ng re
vers
ed"
"The
reve
rse
proc
ess c
anno
t hap
pen"
"Per
man
ent c
hang
e pr
oces
s""I
rret
raca
ble"
The
wor
d is
app
ropr
iate
bec
ause
all
real
pro
cess
es a
reac
com
pani
ed b
y pe
rman
ent c
hang
e in
the
univ
erse
. By
defin
ition
, the
se p
erm
anen
t cha
nges
can
not b
e un
done
by
reve
rsin
g th
e in
fluen
ces d
rivin
g th
e pr
oces
s.
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
3.9.
Con
trast
the
rela
tive
mag
nitu
des o
f the
ent
ropy
tran
sfer
vers
us e
ntro
py p
rodu
ctio
n in
the
follo
win
g pr
oces
ses:
a. A
ther
mal
ly in
sula
ted
cont
aine
r has
two
com
partm
ents
of e
qual
size
. In
itial
ly o
ne si
de is
fille
dw
ith a
gas
and
the
othe
r is e
vacu
ated
. A
val
ve is
open
ed a
nd th
e ga
s exp
ands
to fi
ll bo
th c
ompa
rtmen
ts.
b. A
gas
con
tain
ed in
a st
eel c
ylin
der i
s slo
wly
expa
nded
to tw
ice
its v
olum
e.
Ans
wer
to 3
.9.
a. I
n th
e th
erm
ally
insu
late
d ca
se th
ere
is n
o en
tropy
tran
sfer
; th
e to
tal e
ntro
py c
hang
e in
this
cas
e is
ent
ropy
pro
duct
ion.
b. S
low
exp
ansi
on m
inim
izes
dis
sipa
tion
effe
cts,
and
thus
isac
com
pani
ed b
y a
smal
l pro
duct
ion
of e
ntro
py;
mos
t of t
heen
tropy
cha
nge
in th
is c
ase
is e
ntro
py tr
ansf
er.
3.10
. C
onsi
der a
n is
olat
ed sy
stem
(no
heat
, mat
ter o
r wor
km
ay b
e ex
chan
ged
with
the
surr
ound
ings
) con
sist
ing
of th
ree
inte
rnal
com
partm
ents
A, B
and
C, o
f equ
al v
olum
es.
The
com
partm
ents
are
sepa
rate
d by
par
titio
ns; e
ach
parti
tion
has a
valv
e w
hich
may
be
open
ed re
mot
ely.
Ini
tially
the
cent
ral
volu
me
B is
fille
d w
ith a
gas
at 2
98K
(25o C
) and
the
oute
r tw
oar
e ev
acua
ted.
Con
side
r the
follo
win
g tw
o pr
oces
ses:
a. T
he v
alve
to th
e A
side
is o
pene
d, th
e ga
s exp
ands
free
ly in
to th
e co
mpa
rtmen
t A, a
nd th
e sy
stem
com
es to
equi
libriu
m.
Then
the
valv
e to
the
C si
de is
ope
ned,
and
the
syst
em a
gain
com
es to
equ
ilibr
ium
.b.
Bot
h va
lves
are
ope
ned
sim
ulta
neou
sly,
the
gas
expa
nds f
reel
y in
to b
oth
com
partm
ents
, and
the
syst
emco
mes
to it
s equ
ilibr
ium
.
Whi
ch o
f the
se p
roce
sses
pro
duce
s mor
e en
tropy
?
Ans
wer
to 3
.10.
The
initi
al st
ates
are
the
sam
e fo
r the
se p
roce
sses
; th
e fin
alst
ates
are
als
o th
e sa
me.
Sin
ce e
ntro
py is
a st
ate
func
tion,
the
entro
py c
hang
e fo
r bot
h pr
oces
ses m
ust b
e th
e sa
me.
Cha
pter
3. T
he L
aws o
f The
rmod
ynam
ics
8
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
---
3.11
. It w
ill b
e sh
own
in c
hapt
er 4
that
the
chan
ge in
ent
ropy
)S
asso
ciat
ed w
ith p
roce
ss a
in p
robl
em 3
.6 is
4.6
0 (J
/mol
-K),
and
that
the
initi
al a
nd fi
nal s
tate
s will
be
at th
e sa
me
tem
pera
ture
. A
pplic
atio
n of
equ
atio
n (3
.10)
sugg
ests
that
the
heat
abs
orbe
d by
the
syst
em d
urin
g th
is p
roce
ss is
Yet
the
desc
riptio
n of
the
syst
em sa
ys it
is is
olat
ed fr
om it
ssu
rrou
ndin
gs so
that
Q =
0.
Expl
ain
this
app
aren
tco
ntra
dict
ion.
Ans
wer
to 3
.11.
Equa
tion
(3.1
0) a
pplie
s onl
y to
reve
rsib
le p
roce
sses
. It
ther
efor
e do
es n
ot a
pply
to th
e pr
oces
ses d
escr
ibed
in P
robl
em3.
10.
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
3.12
. Giv
e th
ree
exam
ples
of p
roce
sses
that
are
impo
rtant
inm
ater
ials
scie
nce
that
are
ther
mod
ynam
ical
ly "
irrev
ersi
ble"
. Sp
ecul
ate
brie
fly a
bout
the
natu
re o
f the
dis
sipa
tions
in th
ese
proc
esse
s tha
t con
tribu
te to
the
prod
uctio
n of
ent
ropy
.
Ans
wer
3.1
2
a. H
eat f
low
is c
ruci
al in
man
y in
dust
rial r
efin
ing
oper
atio
ns in
whi
ch c
hem
ical
reac
tions
pro
duce
larg
e qu
antit
ies o
f hea
t. T
hedi
sper
sion
of h
eat t
hrou
gh th
e sy
stem
and
surr
ound
ings
is a
diss
ipat
ion
that
can
not b
e re
cove
red.
b. M
ost m
icro
stru
ctur
al c
hang
es in
mat
eria
ls in
volv
e a
redi
strib
utio
n of
the
chem
ical
com
pone
nts c
alle
d di
ffus
ion.
Li
ke h
eat f
low
, the
rear
rang
emen
t of t
he sp
atia
l dis
tribu
tion
ofth
e at
oms t
hrou
gh th
e sy
stem
is a
dis
sipa
tion
that
can
not b
ere
cove
red.
c. I
ons i
mpl
ante
d in
the
fabr
icat
ion
of d
opan
t lay
ers i
n th
infil
ms i
n in
tegr
ated
circ
uits
are
not
rem
oved
by
sim
ply
reve
rsin
g th
e el
ectri
cal f
ield
. R
emov
al o
f the
ions
cou
ld o
nly
be a
ccom
plis
hed
by e
vapo
ratin
g th
e w
hole
film
and
rede
posi
ting
it.
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
---
3.13
. The
not
ion
of a
"re
vers
ible
" pr
oces
s is a
fict
ion
in th
e re
alw
orld
. W
hat m
akes
this
con
cept
, whi
ch a
t firs
t gla
nce
wou
ldap
pear
to b
e on
ly o
f aca
dem
ic in
tere
st, s
o us
eful
in a
pply
ing
ther
mod
ynam
ics t
o re
al w
orld
"irr
ever
sibl
e" p
roce
sses
?
Ans
wer
to 3
.13.
If th
e pr
oper
ty c
hang
es th
at a
re o
f int
eres
t in
a re
al ir
reve
rsib
lepr
oces
s are
stat
e fu
nctio
ns, t
hen
thei
r cha
nges
will
be
the
sam
efo
r eve
ry p
roce
ss th
at c
onne
cts t
he in
itial
and
fina
l sta
tes o
f the
proc
ess.
In p
artic
ular
, the
se c
hang
es w
ill b
e th
e sa
me
as fo
rso
me
reve
rsib
le p
roce
ss th
at ta
kes t
he sy
stem
bet
wee
n th
ese
Cha
pter
3. T
he L
aws o
f The
rmod
ynam
ics
9
two
stat
es.
Cal
cula
tion
of c
hang
es fo
r a re
vers
ible
pro
cess
isve
ry m
uch
sim
pler
than
for i
rrev
ersi
ble
proc
esse
s bec
ause
inte
rnal
inte
nsiv
e pr
oper
ties l
ike
tem
pera
ture
and
pre
ssur
e ar
eun
iform
in th
e sy
stem
dur
ing
the
chan
ge. T
hus c
alcu
latio
ns o
fch
ange
s in
stat
e fu
nctio
ns fo
r irr
ever
sibl
e pr
oces
ses a
re m
ade
acce
ssib
le th
roug
h th
e us
eful
fict
ion
of th
e re
vers
ible
proc
esse
s.
In a
dditi
on,
for r
ever
sibl
e pr
oces
ses g
ener
al re
latio
nshi
ps a
reav
aila
ble
for c
ompu
ting
W a
nd Q
from
stat
e fu
nctio
nin
form
atio
n by
inte
grat
ing
alon
g th
e si
mpl
est p
ath
that
con
nect
s the
initi
al a
nd fi
nal s
tate
s.Th
ese
resu
lts m
ay b
e us
ed to
est
imat
e pr
oper
ties o
f rea
lev
olvi
ng sy
stem
s tha
t are
car
ried
out s
low
ly, n
ear e
quili
briu
m.
They
als
o pr
ovid
e es
timat
es o
f the
max
im h
eat a
bsor
bed
orw
ork
that
cou
ld b
e do
ne o
n th
e sy
stem
.
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
---
3.14
. The
com
bine
d st
atem
ent o
f the
firs
t and
seco
nd la
ws o
fth
erm
odyn
amic
s, eq
uatio
n (3
.15)
, ev
alua
tes t
he h
eat a
bsor
bed
and
mec
hani
cal w
ork
done
on
a sy
stem
with
rela
tions
hips
that
are
only
val
id fo
r rev
ersi
ble
proc
esse
s. S
ince
reve
rsib
lepr
oces
ses d
o no
t occ
ur in
the
real
wor
ld, h
ow is
it p
ossi
ble
for
the
com
bine
d st
atem
ent t
o pl
ay a
n im
porta
nt ro
le in
the
anal
ysis
of p
ract
ical
"irr
ever
sibl
e" p
roce
sses
enc
ount
ered
inna
ture
and
in te
chno
logy
?
Ans
wer
to 3
.14.
The
com
bine
d st
atem
ent i
s use
d to
eva
luat
e dU
, whi
ch is
ast
ate
func
tion.
Thu
s, th
e co
mbi
ned
stat
emen
t may
be
used
toca
lcul
ate
the
chan
ge in
inte
rnal
ene
rgy
for a
ny ir
reve
rsib
lepr
oces
s bec
ause
)U
is th
e sa
me
as fo
r a re
vers
ible
pro
cess
join
ing
the
sam
e in
itial
and
fina
l sta
tes.
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
---
3.15
. D
escr
ibe
the
kind
s of e
xper
imen
tal o
bser
vatio
ns th
atha
ve b
een
invo
ked
to su
ppor
t the
hyp
othe
sis t
hat t
he e
ntro
py o
fal
l sub
stan
ces i
s the
sam
e at
abs
olut
e ze
ro.
Ans
wer
to 3
.15.
Entro
py c
hang
es a
ssoc
iate
d w
ith h
eatin
g or
coo
ling
the
pure
elem
ents
and
com
poun
ds m
ay b
e co
mpu
ted
from
hea
t cap
acity
mea
sure
men
ts a
s a fu
nctio
n of
tem
pera
ture
for t
hese
subs
tanc
es.
Entro
py c
hang
es fo
r rea
ctio
ns b
etw
een
thes
esu
bsta
nces
may
be
eval
uate
d fr
om h
eats
of r
eact
ion
orm
easu
rem
ents
equ
ilibr
ium
com
posi
tions
.
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
----
3.16
. U
se th
e fo
llow
ing
valu
es o
f abs
olut
e en
tropi
es o
fel
emen
ts a
nd c
ompo
unds
at 2
98K
to c
ompu
te th
e st
anda
rden
tropy
cha
nges
ass
ocia
ted
with
as m
any
chem
ical
reac
tions
as
you
can
gene
rate
from
this
list
.
Cha
pter
3. T
he L
aws o
f The
rmod
ynam
ics
10
Al
2
8.3
CO
197.
9
C(g
r)
5.
69C
O2
213.
64
Si
1
8.83
Al 2O
3 5
1.1
O2
20
5.03
SiC
16.
54
SiO
2
41.
5
Ans
wer
to 3
.16.
For a
ny re
actio
n of
the
form
whe
re l,
m, r
, s,..
. are
stoi
chio
met
ric c
oeff
icie
nts f
or th
eco
mpo
nent
s L, M
, R, S
,...,
the
corr
espo
ndin
g ch
ange
in e
ntro
pyfo
r the
tran
sfor
mat
ion
from
pur
e re
acta
nts t
o pu
re p
rodu
cts a
t29
8 K
(the
"st
anda
rd e
ntro
py c
hang
e") i
s giv
en b
y
The
follo
win
g lis
t of r
eact
ions
can
be
gene
rate
d am
ong
thes
eco
mpo
nent
s is n
ot e
xhau
stiv
e.
REA
CTI
ON
)So (J
/mol
K)
Form
atio
n R
eact
ions
:
Line
ar C
ombi
natio
ns:
A la
rge
num
ber o
f lin
ear c
ombi
natio
ns o
f the
form
atio
nre
actio
ns m
ay b
e co
nstru
cted
, inc
ludi
ng, e
.g.,