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K. H
eat
an
d T
em
pera
ture
Ch
ap
ter
Ou
tlin
e
1.
Tem
pera
ture
and T
herm
al E
quili
brium
2.
Therm
om
ete
rs a
nd T
em
pera
ture
Scale
s
3.
Therm
al E
xpansio
n
4.
Quantity
of H
eat
�2
01
0 H
erb
ert
B. D
om
ing
o
5.
Calo
rim
etr
yand P
hase C
hanges
K. H
eat
an
d T
em
pera
ture
1. T
em
pe
ratu
re &
Th
erm
al
Eq
uil
ibri
um
•C
on
ce
pt o
f te
mp
era
ture
ro
ote
d in
q
ua
lita
tive
id
ea
s o
f “h
ot”
an
d “
co
ld”
ba
se
d o
n s
en
se
of
tou
ch
.
•M
an
y p
rop
ert
ies o
f m
atte
r w
e c
an
m
ea
su
re d
ep
en
d o
n te
mp
era
ture
.
•T
em
pe
ratu
re is a
lso
re
late
d to
�2
01
0 H
erb
ert
B. D
om
ing
o
•T
em
pe
ratu
re is a
lso
re
late
d to
kin
etic e
ne
rgie
so
f m
ole
cu
les o
f m
ate
ria
l.
•T
o u
se
te
mp
era
ture
as a
me
asu
re
of h
otn
ess a
nd
co
ldn
ess, w
e n
ee
d
to c
on
str
uct
a t
em
pe
ratu
re s
ca
le.
K. H
eat
an
d T
em
pera
ture
1. T
em
pe
ratu
re &
Th
erm
al
Eq
uil
ibri
um
Th
erm
om
ete
r
•F
irst,
se
lect a
ny m
ea
su
rab
le p
rop
ert
y o
f a
syste
m
tha
t va
rie
s w
ith
its
“h
otn
ess”
an
d “
co
ldn
ess”.
•E
xa
mp
les: th
e le
ng
th o
f a
liq
uid
(m
erc
ury
, e
tha
no
l)
in a
tu
be
, p
ressu
re o
f g
as a
nd
th
e e
lectr
ica
l
�2
01
0 H
erb
ert
B. D
om
ing
o
in a
tu
be
, p
ressu
re o
f g
as a
nd
th
e e
lectr
ica
l
resis
tan
ce
of
a
co
nd
uctin
g w
ire
.
•E
ach
of th
e a
bo
ve
ca
n
be
use
d t
o m
ake
a th
erm
om
ete
r.
K. H
eat
an
d T
em
pera
ture
1. T
em
pe
ratu
re &
Th
erm
al
Eq
uil
ibri
um
Th
erm
al E
qu
ilib
riu
m
•W
e u
se
a t
he
rmo
me
ter
to m
ea
su
re t
he
te
mp
era
ture
of a
bo
dy.
•A
t th
e p
oin
t w
he
re t
he
re
ad
ing
on
th
e t
em
pe
ratu
re
rea
ch
es a
ste
ad
y v
alu
e, th
e c
on
ditio
n o
f th
erm
al
�2
01
0 H
erb
ert
B. D
om
ing
o
rea
ch
es a
ste
ad
y v
alu
e, th
e c
on
ditio
n o
f th
erm
al
eq
uili
bri
um
ha
s o
ccu
rre
d.
Insu
lato
r
•A
n in
su
lato
r re
du
ce
sth
e e
xch
an
ge
of
he
at
be
twe
en
tw
o s
yste
ms.
•E
xa
mp
les o
f in
su
lato
rs: w
oo
d,
pla
stic fo
am
, o
r
fib
erg
lass.
K. H
eat
an
d T
em
pera
ture
1. T
em
pe
ratu
re &
Th
erm
al
Eq
uil
ibri
um
Insu
lato
r
•A
n id
ea
l in
su
lato
ris
a m
ate
ria
l th
at
pe
rmits n
o
inte
ractio
n a
t a
ll b
etw
ee
n t
wo
syste
ms, th
us
pre
ve
ntin
g th
erm
al e
qu
ilib
riu
m f
rom
be
ing
re
ach
ed
.
Ze
roth
La
w o
f T
he
rmo
dyn
am
ics
�2
01
0 H
erb
ert
B. D
om
ing
o
Ze
roth
La
w o
f T
he
rmo
dyn
am
ics
•It
is a
n im
po
rta
nt
pro
pe
rty
of th
erm
al e
qu
ilib
riu
m
•C
on
sid
er
thre
e s
yste
ms:
A,
Ba
nd
C.
K. H
eat
an
d T
em
pera
ture
1. T
em
pe
ratu
re &
Th
erm
al
Eq
uil
ibri
um
Ze
roth
La
w o
f T
he
rmo
dyn
am
ics
•S
yste
m A
an
d B
initia
lly s
ep
ara
ted
by id
ea
l
insu
latin
g w
all,
bu
t w
e le
t C
inte
ract w
ith
Aa
nd
B.
•T
he
id
ea
l in
su
latin
g w
all
is th
en
pla
ce
d b
etw
ee
n C
an
d A
an
d B
an
d a
co
nd
uctin
g w
all
is p
lace
d
�2
01
0 H
erb
ert
B. D
om
ing
o
an
d A
an
d B
an
d a
co
nd
uctin
g w
all
is p
lace
d
be
twe
en
Aa
nd
Bto
le
t th
em
in
tera
ct.
•E
xp
eri
me
nt
sh
ow
s t
ha
t n
oth
ing
ha
pp
en
s!
•T
ha
t is
, th
ere
is n
o a
dd
itio
na
l ch
an
ge
s t
o A
an
d B
.
•C
on
clu
sio
n:
If C
is in
itia
lly in
th
erm
al e
qu
ilib
riu
m
with
bo
th A
an
d B
, th
en
Aa
nd
Ba
re a
lso
in
th
erm
al
eq
uili
bri
um
with
ea
ch
oth
er.
K. H
eat
an
d T
em
pera
ture
1. T
em
pe
ratu
re &
Th
erm
al
Eq
uil
ibri
um
Ze
roth
La
w o
f T
he
rmo
dyn
am
ics
•S
up
po
se
we
re
pla
ce
Cw
ith
a t
he
rmo
me
ter
an
d is in
co
nta
ct w
ith
Aa
nd
B.
•W
he
n th
erm
om
ete
r re
ach
es a
sta
ble
va
lue
, b
oth
A
an
d B
ha
s t
he
sa
me
te
mp
era
ture
.
�2
01
0 H
erb
ert
B. D
om
ing
o
an
d B
ha
s t
he
sa
me
te
mp
era
ture
.
•C
on
clu
sio
n:
Tw
o s
yste
ms a
re in
th
erm
al
eq
uili
bri
um
if a
nd
on
ly if th
ey h
ave
th
e s
am
e
tem
pe
ratu
re.
K. H
eat
an
d T
em
pera
ture
2. T
he
rmo
me
ters
an
d T
em
pe
ratu
re S
ca
les
Ce
lsiu
s te
mp
era
ture
sca
le/L
iqu
id-i
n-t
ub
e
the
rmo
me
ter
•T
o m
ake
th
e liq
uid
-in
-tu
be
de
vic
e in
to a
use
ful
the
rmo
me
ter,
we
ne
ed
to
ma
rk a
sca
le o
n t
he
tu
be
wa
ll w
ith
nu
mb
ers
on
it.
•T
he
nu
mb
ers
are
arb
itra
ry a
nd
ma
ny n
um
be
r
�2
01
0 H
erb
ert
B. D
om
ing
o
•T
he
nu
mb
ers
are
arb
itra
ry a
nd
ma
ny n
um
be
r sch
em
es w
ere
use
d in
th
e p
ast.
•S
up
po
se
we
la
be
l th
e t
he
rmo
me
ter’
s liq
uid
le
ve
l a
t th
e f
ree
zin
g t
em
pe
ratu
re o
f p
ure
wa
ter
“ze
ro”
an
d th
e le
ve
l a
t b
oili
ng
te
mp
era
ture
“1
00
”, a
nd
d
ivid
e th
e d
ista
nce
be
twe
en
th
e t
wo
pts
in
to 1
00
e
qu
al in
terv
als
ca
lled
de
gre
es.
K. H
eat
an
d T
em
pera
ture
2. T
he
rmo
me
ters
an
d T
em
pe
ratu
re S
ca
les
Ce
lsiu
s te
mp
era
ture
sca
le/L
iqu
id-i
n-t
ub
e
the
rmo
me
ter
•W
e g
et a
Ce
lsiu
s t
em
pe
ratu
re s
ca
le (
form
erl
y
ca
lled
th
e c
en
tig
rad
e s
ca
le in
En
glis
h-s
pe
akin
g
co
un
trie
s).
�2
01
0 H
erb
ert
B. D
om
ing
o
•C
els
ius te
mp
era
ture
fo
r a
sta
te c
old
er
tha
n
fre
ezin
g w
ate
r is
a n
eg
ative
nu
mb
er.
K. H
eat
an
d T
em
pera
ture
2. T
he
rmo
me
ters
an
d T
em
pe
ratu
re S
ca
les
Bim
eta
llic s
trip
th
erm
om
ete
r
•A
no
the
r co
mm
on
th
erm
om
ete
r
use
s a
bim
eta
llic s
trip
, m
ad
e b
y
bo
nd
ing
tw
o d
iffe
ren
t m
eta
ls
tog
eth
er.
�2
01
0 H
erb
ert
B. D
om
ing
o
•W
he
n te
mp
era
ture
of co
mp
osite
str
ip in
cre
ase
s, o
ne
me
tal e
xp
an
ds
mo
re t
ha
n t
he
oth
er
an
d t
he
str
ip
be
nd
s.
•A
s s
ho
wn
th
e p
oin
ter
rota
tes in
resp
on
se
to
te
mp
era
ture
ch
an
ge
s.
K. H
eat
an
d T
em
pera
ture
2. T
he
rmo
me
ters
an
d T
em
pe
ratu
re S
ca
les
Re
sis
tan
ce
th
erm
om
ete
r
•T
he
ch
an
gin
g e
lectr
ica
l re
sis
tan
ce
of a
co
il o
f fin
e
wir
e, a
ca
rbo
n c
ylin
de
r, o
r a
ge
rma
niu
m c
rysta
l is
m
ea
su
red
.
•S
ince
re
sis
tan
ce
ca
n b
e m
ea
su
red
ve
ry p
recis
ely
, re
sis
tan
ce
th
erm
om
ete
rs a
re m
ore
pre
cis
e th
an
�2
01
0 H
erb
ert
B. D
om
ing
o
resis
tan
ce
th
erm
om
ete
rs a
re m
ore
pre
cis
e th
an
o
the
r ty
pe
s o
f th
erm
om
ete
rs.
K. H
eat
an
d T
em
pera
ture
2. T
he
rmo
me
ters
an
d T
em
pe
ratu
re S
ca
les
Th
erm
op
ile
•A
n e
ar
the
rmo
me
ter
is a
typ
e o
f d
evic
e c
alle
d a
the
rmo
pile
.
•It
me
asu
res t
he
am
ou
nt
of in
fra
red
ra
dia
tio
n
em
itte
d b
y t
he
ea
rdru
m,
wh
ich
in
dic
ate
s th
e
�2
01
0 H
erb
ert
B. D
om
ing
o
em
itte
d b
y t
he
ea
rdru
m,
wh
ich
in
dic
ate
s th
e
ea
rdru
m’s
te
mp
era
ture
.
•A
dva
nta
ge
of
this
te
ch
niq
ue
is it
do
es n
ot
req
uir
e
a p
hysic
al co
nta
ct o
f th
e t
he
rmo
me
ter
with
th
e
ea
rdru
m.
K. H
eat
an
d T
em
pera
ture
2. T
he
rmo
me
ters
an
d T
em
pe
ratu
re S
ca
les
Fa
hre
nh
eit t
em
pe
ratu
re s
ca
le
•T
his
te
mp
era
ture
sca
le is u
se
d in
da
ily life
in
th
e
Un
ite
d S
tate
s.
•T
he
fre
ezin
g t
em
pe
ratu
re o
f w
ate
r is
32
°F.
•T
he
bo
ilin
g t
em
pe
ratu
re o
f w
ate
r is
21
2°F
.
�2
01
0 H
erb
ert
B. D
om
ing
o
•T
he
bo
ilin
g t
em
pe
ratu
re o
f w
ate
r is
21
2°F
.
•B
oth
are
me
asu
red
at
sta
nd
ard
atm
osp
he
ric
pre
ssu
re.
•T
he
re a
re 1
80
de
gre
es b
etw
ee
n f
ree
zin
g a
nd
bo
ilin
g, co
mp
are
d t
o C
els
ius s
ca
le (
10
0 d
eg
ree
s).
K. H
eat
an
d T
em
pera
ture
17
.2 T
he
rmo
me
ters
an
d T
em
pe
ratu
re S
ca
les
Co
nve
rsio
n b
etw
ee
n F
ah
ren
he
it/C
els
ius t
em
pe
ratu
re
sca
les
•T
o c
on
ve
rt f
rom
Ce
lsiu
s t
o F
ah
ren
he
it
)1(3
259
°+
=C
FT
T
�2
01
0 H
erb
ert
B. D
om
ing
o
•T
o c
on
ve
rt f
rom
Fa
hre
nh
eit t
o C
els
ius
5
)2(
)3
2(
95°
−=
FC
TT
K. H
eat
an
d T
em
pera
ture
2. T
he
rmo
me
ters
an
d T
em
pe
ratu
re S
ca
les
Te
mp
era
ture
in
terv
al
•It
is im
po
rta
nt
to d
iffe
ren
tia
te b
etw
ee
n a
n a
ctu
al
tem
pe
ratu
re a
nd
a t
em
pe
ratu
re in
terv
al.
•A
ctu
al te
mp
era
ture
of
20
°C is s
tate
d a
s 2
0°C
(tw
en
ty d
eg
ree
s C
els
ius).
�2
01
0 H
erb
ert
B. D
om
ing
o
(tw
en
ty d
eg
ree
s C
els
ius).
•A
te
mp
era
ture
in
terv
al o
f 2
0°is
20
C°(t
we
nty
Ce
lsiu
s d
eg
ree
s).
K. H
eat
an
d T
em
pera
ture
2. T
he
rmo
me
ters
an
d T
em
pe
ratu
re S
ca
les
Ke
lvin
te
mp
era
ture
sca
le
•It
wa
s n
am
ed
aft
er
Bri
tish
ph
ysic
ist L
ord
Ke
lvin
.
•T
he
un
its (
K)
are
th
e s
am
e s
ize
as t
ho
se
on
th
e
Ce
lsiu
s s
ca
le, b
ut
ze
ro is s
hifte
d s
o t
ha
t
0 K
= −
27
3.1
5°C
an
d 2
73
.15
K =
0°C
�2
01
0 H
erb
ert
B. D
om
ing
o
0 K
= −
27
3.1
5°C
an
d 2
73
.15
K =
0°C
)3(
15
.2
73
+=
CK
TT
K. H
eat
an
d T
em
pera
ture
2. T
he
rmo
me
ters
an
d T
em
pe
ratu
re S
ca
les
•In
SI
no
me
ncla
ture
, “d
eg
ree
” is
no
t u
se
d w
ith
Ke
lvin
sca
le.
•2
93
K is r
ea
d a
s “
29
3 k
elv
ins”,
no
t “d
eg
ree
s
Ke
lvin
.
•W
e c
ap
ita
lize
Ke
lvin
wh
en
it re
fers
to
th
e
�2
01
0 H
erb
ert
B. D
om
ing
o
•W
e c
ap
ita
lize
Ke
lvin
wh
en
it re
fers
to
th
e
tem
pe
ratu
re s
ca
le.
•H
ow
eve
r, t
he
un
it o
f
tem
pe
ratu
re is th
e
ke
lvin
, w
hic
h is n
ot
ca
pita
lize
d.
K. H
eat
an
d T
em
pera
ture
Ex
am
ple
1. T
em
pe
ratu
re C
on
ve
rsio
n
Wh
at a
re t
he
eq
uiv
ale
nt
Ce
lsiu
s a
nd
Ke
lvin
tem
pe
ratu
res o
f 5
0.0
°F?
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
Ex
am
ple
1. (S
OL
N)
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
Te
mp
era
ture
Co
nv
ers
ion
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
2. T
he
rmo
me
ters
an
d T
em
pe
ratu
re S
ca
les
Re
latio
nsh
ip b
etw
ee
n d
iffe
ren
t sca
les
�2
01
0 H
erb
ert
B. D
om
ing
o
Eqn 1
7.5
K. H
eat
an
d T
em
pera
ture
2. T
he
rmo
me
ters
an
d T
em
pe
ratu
re S
ca
les
Ab
so
lute
te
mp
era
ture
sca
le
•T
he
Ke
lvin
te
mp
era
ture
sca
le is c
alle
d a
n
ab
so
lute
te
mp
era
ture
sca
le.
•It
s z
ero
po
int
(T=
0 K
= 2
73
.15
°C)
is c
alle
d a
n
ab
so
lute
ze
ro.
�2
01
0 H
erb
ert
B. D
om
ing
o
ab
so
lute
ze
ro.
K. H
eat
an
d T
em
pera
ture
3. T
he
rma
l E
xp
an
sio
n
•M
ost m
ate
ria
ls e
xp
an
d w
he
n t
he
ir te
mp
era
ture
incre
ase
s.
•E
xa
mp
les o
f th
erm
al e
xp
an
sio
n:
–e
xp
an
din
g liq
uid
in
a liq
uid
-in
-tu
be
the
rmo
me
ter,
�2
01
0 H
erb
ert
B. D
om
ing
o
the
rmo
me
ter,
–b
en
din
g b
ime
talli
c s
trip
s,
–lo
ose
nin
g a
me
tal ja
r lid
by r
un
nin
g h
ot
wa
ter
ove
r it.
K. H
eat
an
d T
em
pera
ture
3. T
he
rma
l E
xp
an
sio
n
Lin
ea
r E
xp
an
sio
n
•A
ro
d o
f m
ate
ria
l h
as a
le
ng
th L
0a
t so
me
in
itia
l
tem
pe
ratu
re T
0.
•W
he
n te
mp
era
ture
ch
an
ge
s b
y �
T,
len
gth
ch
an
ge
s b
y �
L
�2
01
0 H
erb
ert
B. D
om
ing
o
ch
an
ge
s b
y �
L
•E
xp
eri
me
nts
sh
ow
th
at if �
Tis
no
t to
o la
rge
(le
ss
tha
n 1
00
°C o
r so
), �
Lis
dir
ectly p
rop
ort
ion
al to
�T
.
•If
tw
o r
od
s m
ad
e o
f sa
me
ma
teri
al h
ave
sa
me
tem
pe
ratu
re c
ha
ng
e,
bu
t o
ne
is tw
ice
as lo
ng
,
the
n c
ha
ng
e in
its
le
ng
th is a
lso
twic
e a
s g
rea
t.
K. H
eat
an
d T
em
pera
ture
3. T
he
rma
l E
xp
an
sio
n
Lin
ea
r E
xp
an
sio
n
•T
he
refo
re, �
Lm
ust a
lso
be
pro
po
rtio
na
l to
L0.
•In
tro
du
ce
a p
rop
ort
ion
alit
y c
on
sta
nt
α(v
ari
es
acco
rdin
g to
typ
e o
f m
ate
ria
ls),
we
ge
t )4(
TL
L∆
=∆
α
�2
01
0 H
erb
ert
B. D
om
ing
o
)4(
0T
LL
∆=
∆α
()
)5(
10
00
0T
LT
LL
LL
L∆
+=
∆+
=∆
+=
αα
•If
a b
od
y h
as le
ng
th L
0a
t te
mp
era
ture
T0, th
en
its le
ng
th L
at te
mp
era
ture
T=
T0
+ �
Tis
K. H
eat
an
d T
em
pera
ture
3. T
he
rma
l E
xp
an
sio
n
Lin
ea
r E
xp
an
sio
n
•T
he
co
nsta
nt
αw
hic
h d
escri
be
s th
e t
he
rma
l
exp
an
sio
n p
rop
ert
ies o
f a
pa
rtic
ula
r m
ate
ria
l is
ca
lled
th
e c
oe
ffic
ien
t o
f lin
ea
r e
xp
an
sio
n.
•It
s u
nits a
re K
-1o
r (°
C)-
1.
�2
01
0 H
erb
ert
B. D
om
ing
o
•It
s u
nits a
re K
or
(°C
).
•T
hu
s L
co
uld
be
th
e t
hic
kn
ess o
f a
ro
d,
sid
e le
ng
th
of a
sq
ua
re s
he
et,
or
the
dia
me
ter
of a
ho
le.
K. H
eat
an
d T
em
pera
ture
3. T
he
rma
l E
xp
an
sio
n
•If
a s
olid
ob
ject
ha
s a
ho
le in
it,
wh
at
ha
pp
en
s
to th
e s
ize
of
it w
he
n t
he
te
mp
era
ture
of
the
ob
ject in
cre
ase
s?
•C
om
mo
n m
isco
nce
ptio
n is th
at th
e m
ate
ria
l
will
exp
an
d in
to t
he
ho
le.
�2
01
0 H
erb
ert
B. D
om
ing
o
•T
he
fa
ct is
th
e h
ole
exp
an
ds a
lon
g w
ith
th
e
ob
ject.
•E
ve
ry lin
ea
r d
ime
nsio
n
of a
n o
bje
ct
ch
an
ge
s in
the
sa
me
wa
y w
he
n
tem
pe
ratu
re c
ha
ng
es.
K. H
eat
an
d T
em
pera
ture
Su
rfa
ce
Ex
pa
ns
ion
Do H
ole
s E
xpand o
r C
ontr
act
When t
he T
em
pera
ture
Incre
ases?
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
3. T
he
rma
l E
xp
an
sio
n
Lin
ea
r E
xp
an
sio
n
•N
ote
th
e d
ire
ct p
rop
ort
ion
alit
y e
xp
resse
d in
Eq
n4
.
•It
is a
pp
roxim
ate
ly c
orr
ect o
nly
fo
r su
ffic
ien
tly s
ma
ll
tem
pe
ratu
re c
ha
ng
es.
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
3. T
he
rma
l E
xp
an
sio
n
Vo
lum
e E
xp
an
sio
n
•T
he
co
nsta
nt
βch
ara
cte
rize
s t
he
vo
lum
e
exp
an
sio
n p
rop
ert
ies o
f a
pa
rtic
ula
r m
ate
ria
l.
•It
is c
alle
d t
he
co
eff
icie
nt o
f vo
lum
e e
xp
an
sio
n
•It
s u
nits a
re K
-1o
r (°
C)-
1.
�2
01
0 H
erb
ert
B. D
om
ing
o
•It
s u
nits a
re K
-1o
r (°
C)-
1.
K. H
eat
an
d T
em
pera
ture
3. T
he
rma
l E
xp
an
sio
n
Vo
lum
e E
xp
an
sio
n
•In
cre
asin
g te
mp
era
ture
usu
ally
ca
use
s a
n in
cre
ase
in v
olu
me
fo
r b
oth
so
lid a
nd
liq
uid
ma
teri
als
.
•E
xp
eri
me
nts
sh
ow
th
at if te
mp
era
ture
ch
an
ge
�T
is
no
t to
o g
rea
t (l
ess th
an
10
0°C
), t
he
in
cre
ase
in
�2
01
0 H
erb
ert
B. D
om
ing
o
no
t to
o g
rea
t (l
ess th
an
10
0°C
), t
he
in
cre
ase
in
vo
lum
e �
Vis
ap
pro
xim
ate
ly p
rop
ort
ion
al to
bo
th
tem
pe
ratu
re c
ha
ng
e �
Ta
nd
in
itia
l vo
lum
e V
0;
)6(
0T
VV
∆=
∆β
K. H
eat
an
d T
em
pera
ture
�2
01
0 H
erb
ert
B. D
om
ing
o
This
gap in t
he r
oadw
ay o
f a b
ridge is
calle
d a
n e
xpansio
n join
t; it
allo
ws t
he
bridge t
o e
xpand a
nd c
ontr
act.
K. H
eat
an
d T
em
pera
ture
Ex
am
ple
2.
Le
ng
th c
ha
ng
e d
ue
to
te
mp
era
ture
ch
an
ge
I
A s
urv
eyo
r u
se
s a
ste
el m
ea
su
rin
g t
ap
e t
ha
t is
exa
ctly 5
0.0
00
m lo
ng
at a
te
mp
era
ture
of 2
0°C
.
Wh
at is
its
le
ng
th o
n a
ho
t su
mm
er
da
y w
he
n t
he
tem
pe
ratu
re is 3
5 °
C.
�2
01
0 H
erb
ert
B. D
om
ing
o
15
K1
02.
1−
−×
=st
eel
α
K. H
eat
an
d T
em
pera
ture
Ex
am
ple
2.
(SO
LN
)
Te
mp
era
ture
ch
an
ge
is �
T=
T−
T0
= 1
5C
°, s
o th
e
ch
an
ge
in
le
ng
th �
La
nd
th
e f
ina
l le
ng
th L
= L
0+
�L
are
()(
)()
mm
0.9
m1
00.
9
K1
5m
50
K1
02.
13
15
0
=×
=
×=
∆=
∆−
−−
TL
Lα
�2
01
0 H
erb
ert
B. D
om
ing
o
Th
us th
e le
ng
th a
t 3
5°C
is 5
0.0
09
m.
m0
09
.5
0m
00
9.
0m
00
0.
50
mm
0.9
m1
00.
9
0=
+=
+=
=×
=
LL
L
K. H
eat
an
d T
em
pera
ture
Ex
am
ple
3.
Le
ng
th C
ha
ng
e D
ue
to
Te
mp
era
ture
Ch
an
ge
II
In e
xa
mp
le 2
, th
e s
urv
eyo
r u
se
s th
e m
ea
su
rin
g t
ap
e
to m
ea
su
re a
dis
tan
ce
wh
en
th
e te
mp
era
ture
is 3
5°C
;
the
va
lue
th
at sh
e r
ea
ds o
ff th
e t
ap
e is 3
5.7
94
m.
Wh
at is
th
e a
ctu
al d
ista
nce
? A
ssu
me
th
at th
e t
ap
e is
ca
libra
ted
fo
r u
se
at
20
°C.
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
Ex
am
ple
3. L
en
gth
Ch
an
ge
Du
e t
o T
em
pe
ratu
re C
ha
ng
e II
Th
e r
atio
L/L
0is
(5
0.0
09
m)/
(50
.00
0 m
), s
o t
he
tru
e
dis
tan
ce
is
()
mm
mm800
.35
794
.35
000
.50
009
.50
=
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
Exam
ple
4. V
olu
me c
han
ge d
ue t
o t
em
pera
ture
ch
an
ge
A g
lass fla
sk w
ith
vo
lum
e 2
00
cm
3is
fill
ed
to
th
e b
rim
with
me
rcu
ry a
t 2
0°C
. H
ow
mu
ch
me
rcu
ry o
ve
rflo
ws
wh
en
th
e t
em
pe
ratu
re o
f th
e s
yste
m is r
ais
ed
to
10
0°C
? T
he
co
eff
icie
nt o
f lin
ea
r e
xp
an
sio
n o
f th
e
gla
ss is 0
.40
×1
0-5
K-1
.
�2
01
0 H
erb
ert
B. D
om
ing
o
βm
ercu
ry=
18
×1
0-5
K-1
K. H
eat
an
d T
em
pera
ture
Ex
am
ple
4.
(SO
LN
)
Incre
ase
in
vo
lum
e o
f g
lass f
lask
()(
) ()
3
31
5
0
20
10
02
00
10
2.1
CC
cm
K
=
°−
°×
=
∆=
∆
−−
TV
Vg
lass
gla
ssβ
()
15
11
10
2.1
10
40
.0
33
−−
−−
×=
×=
=K
Kg
lass
gla
ssα
β
�2
01
0 H
erb
ert
B. D
om
ing
o
Incre
ase
in
vo
lum
e o
f m
erc
ury
is
31
9.
0cm
=
()(
) ()
3
31
5
0
9.2
20
10
02
00
10
18
cm
CC
cm
K
=
°−
°×
=
∆=
∆
−−
TV
Vm
ercu
rym
ercu
ryβ
K. H
eat
an
d T
em
pera
ture
Ex
am
ple
4.
(SO
LN
)
Vo
lum
e o
f m
erc
ury
th
at o
ve
rflo
ws
33
37.
21
9.
09.
2cm
cm
cm
=−
=∆
−∆
gla
ssm
ercu
ryV
V
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
3. T
he
rma
l E
xp
an
sio
n
Th
erm
al e
xp
an
sio
n o
f w
ate
r
•W
ate
r in
th
e t
em
pe
ratu
re r
an
ge
of
0°C
to
4°C
,
de
cre
ase
s in
vo
lum
e w
ith
in
cre
asin
g t
em
pe
ratu
re.
•In
th
e a
bo
ve
ra
ng
e,
its c
oe
ffic
ien
t o
f vo
lum
e
exp
an
sio
n is n
eg
ative
.
�2
01
0 H
erb
ert
B. D
om
ing
o
exp
an
sio
n is n
eg
ative
.
•A
bo
ve
4°C
, w
ate
r e
xp
an
ds w
he
n h
ea
ted
, h
en
ce
wa
ter
ha
s its
gre
ate
st
de
nsity a
t 4°C
.
•W
ate
r a
lso
exp
an
ds w
he
n it fr
ee
ze
s.
•T
his
an
om
alo
us b
eh
avio
r o
f w
ate
r h
as a
n
imp
ort
an
t e
ffe
ct o
n p
lan
t a
nd
wa
ter
life
in
la
ke
s,
pa
rtic
ula
rly d
uri
ng
win
ter.
K. H
eat
an
d T
em
pera
ture
4. Q
ua
nti
ty o
f H
ea
t
Qu
an
tity
of
he
at
•E
ne
rgy tra
nsfe
r ta
ke
s p
lace
so
lely
be
ca
use
of a
tem
pe
ratu
re d
iffe
ren
ce
ca
lled
he
at
flo
w o
r h
ea
t
tra
nsfe
r.
•E
ne
rgy tra
nsfe
rre
d in
th
is w
ay is c
alle
d h
ea
t.
�2
01
0 H
erb
ert
B. D
om
ing
o
•E
ne
rgy tra
nsfe
rre
d in
th
is w
ay is c
alle
d h
ea
t.
•S
ir J
am
es J
ou
le
dis
co
ve
red
th
at
tem
pe
ratu
re r
ise
is
dir
ectly p
rop
ort
ion
al
to th
e a
mo
un
t o
f
wo
rk d
on
e.
K. H
eat
an
d T
em
pera
ture
Cats
, such a
s t
his
Bengal
tiger,
oft
en p
ant
to g
et
rid o
f
excess h
eat.
(P
hoto
Dis
c
�2
01
0 H
erb
ert
B. D
om
ing
o
Blu
e/P
hoto
Dis
c,
Inc./
Gett
y
Images)
K. H
eat
an
d T
em
pera
ture
4. Q
ua
nti
ty o
f H
ea
t
•K
ee
p c
lea
rly in
min
d t
he
dis
tin
ctio
n b
etw
ee
n
tem
pe
ratu
re a
nd
he
at.
•T
em
pe
ratu
re d
ep
en
ds o
f th
e p
hysic
al sta
te o
f a
ma
teri
al a
nd
is a
qu
an
tita
tive
de
scri
ptio
n o
f its h
otn
ess o
r co
ldn
ess.
•H
ea
t a
lwa
ys r
efe
r to
en
erg
y in
tra
nsit fro
m o
ne
b
od
y o
r syste
m to
an
oth
er
be
ca
use
of a
�2
01
0 H
erb
ert
B. D
om
ing
obo
dy o
r syste
m to
an
oth
er
be
ca
use
of a
te
mp
era
ture
diffe
ren
ce
, n
eve
r to
th
e a
mo
un
t o
f e
ne
rgy c
on
tain
ed
with
in a
pa
rtic
ula
r syste
m.
•W
e c
ha
ng
e t
he
te
mp
era
ture
of a
bo
dy b
y
ad
din
g h
ea
t to
it o
r re
mo
vin
g h
ea
t a
wa
y f
rom
it.
K. H
eat
an
d T
em
pera
ture
4. Q
ua
nti
ty o
f H
ea
t
Qu
an
tity
of
he
at
•W
e d
efin
e a
un
it o
f q
ua
ntity
of h
ea
t b
ase
d o
n
tem
pe
ratu
re c
ha
ng
es o
f so
me
sp
ecific
ma
teri
al.
•T
he
ca
lori
e is d
efin
ed
as th
e a
mo
un
t o
f h
ea
t
req
uir
ed
to
ra
ise
th
e t
em
pe
ratu
re o
f o
ne
gra
m o
f
�2
01
0 H
erb
ert
B. D
om
ing
o
req
uir
ed
to
ra
ise
th
e t
em
pe
ratu
re o
f o
ne
gra
m o
f
wa
ter
by o
ne
C°.
•C
orr
esp
on
din
g u
nit o
f h
ea
t u
sin
g F
ah
ren
he
it
de
gre
es a
nd
Im
pe
ria
l u
nits is th
e B
ritish
th
erm
al
un
it (
Btu
).
•O
ne
Btu
is th
e q
ua
ntity
of h
ea
t re
qu
ire
d t
o r
ais
e th
e
tem
pe
ratu
re o
f o
ne
po
un
d o
f w
ate
r b
y o
ne
F°.
K. H
eat
an
d T
em
pera
ture
4. Q
ua
nti
ty o
f H
ea
t
Qu
an
tity
of
he
at
•T
hu
s,
1 c
al =
4.1
86
J
1 k
ca
l =
41
86
J
1 B
tu =
25
2 c
al =
10
55
J
•T
he
ca
lori
e is n
ot
a f
un
da
me
nta
l S
I u
nit, in
ste
ad
�2
01
0 H
erb
ert
B. D
om
ing
o
•T
he
ca
lori
e is n
ot
a f
un
da
me
nta
l S
I u
nit, in
ste
ad
jou
le is u
se
d a
s th
e b
asic
un
it o
f e
ne
rgy in
all
form
s, in
clu
din
g h
ea
t.
K. H
eat
an
d T
em
pera
ture
4. Q
ua
nti
ty o
f H
ea
t
Sp
ecific
he
at
•Q
is u
se
d t
o r
ep
rese
nt
qu
an
tity
of
he
at.
•Q
ua
ntity
of
he
at
req
uir
ed
to
in
cre
ase
te
mp
era
ture
of a
ma
ss m
of
ce
rta
in m
ate
ria
l fr
om
T1
to T
2is
fou
nd
to
be
ap
pro
xim
ate
ly p
rop
ort
ion
al to
�2
01
0 H
erb
ert
B. D
om
ing
o
fou
nd
to
be
ap
pro
xim
ate
ly p
rop
ort
ion
al to
tem
pe
ratu
re c
ha
ng
e �
T=
T2
−T
1. It
is a
lso
pro
po
rtio
na
l to
ma
ss m
of th
e m
ate
ria
l. T
hu
s,
we
ha
ve
!
"#$
%&
"#c
as t
he
sp
ecific
he
at
of th
e m
ate
ria
l.
)7(
Tm
cQ
∆=
K. H
eat
an
d T
em
pera
ture
4. Q
ua
nti
ty o
f H
ea
t
•H
ea
t is
alw
ays e
ne
rgy in
tra
nsit a
s a
re
su
lt o
f
tem
pe
ratu
re d
iffe
ren
ce
.
•T
he
re is n
o s
uch
th
ing
as “
the
am
ou
nt
of h
ea
t
in a
bo
dy”.
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
4. Q
ua
nti
ty o
f H
ea
t
Sp
ecific
he
at
•T
he
sp
ecific
he
at
of
a m
ate
ria
l a
lwa
ys d
ep
en
ds o
n
the
in
itia
l te
mp
era
ture
an
d t
he
te
mp
era
ture
in
terv
al.
•S
pe
cific
he
at
of w
ate
r is
ap
pro
xim
ate
ly
41
90
J/k
g·K
�2
01
0 H
erb
ert
B. D
om
ing
o
41
90
J/k
g·K
1 c
al/g
·C°
1 B
tu/lb
·F°
K. H
eat
an
d T
em
pera
ture
Ex
am
ple
5.
Fe
ed
a c
old
, s
tarv
e a
fe
ve
r
Du
rin
g a
bo
ut
with
flu
, a
n 8
0-k
g m
an
ra
n a
fe
ve
r o
f
39
.0°C
(1
02
.2°F
) in
ste
ad
of th
e n
orm
al b
od
y
tem
pe
ratu
re o
f 3
7.0
°C (
98
.6°F
). A
ssu
min
g t
ha
t th
e
hu
ma
n b
od
y is m
ostly w
ate
r, h
ow
mu
ch
he
at
is
req
uir
ed
to
ra
ise
his
te
mp
era
ture
by th
at a
mo
un
t?
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
Ex
am
ple
5.
(SO
LN
) ()(
)()
JK
KJ/k
gkg
51
07.
60.
24
19
08
0×
=⋅
=∆
=T
mc
Q
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
Ex
am
ple
6.
Ov
erh
ea
tin
g e
lec
tro
nic
s
Yo
u a
re d
esig
nin
g a
n e
lectr
on
ic c
ircu
it e
lem
en
t m
ad
e
of 2
3 m
g o
f sili
co
n.
Th
e e
lectr
ic c
urr
en
t th
rou
gh
it
ad
ds e
ne
rgy a
t th
e r
ate
of 7
.4 ×
10
-3J/s
. If
yo
ur
de
sig
n d
oe
sn
’t a
llow
an
y h
ea
t tr
an
sfe
r o
ut o
f th
e
ele
me
nt,
at
wh
at
rate
do
es its
te
mp
era
ture
in
cre
ase
?
Sp
ecific
he
at
of sili
co
n is 7
05
J/k
g⋅K
.
�2
01
0 H
erb
ert
B. D
om
ing
o
Sp
ecific
he
at
of sili
co
n is 7
05
J/k
g⋅K
.
K. H
eat
an
d T
em
pera
ture
Ex
am
ple
6.
(SO
LN
)
In o
ne
se
co
nd
, Q
= (
7.4
×1
0-3
J/s
)(1
s)
= 7
.4 ×
10
-3J.
Fro
m Q
= m
c�T
,'"
&(")%
'*)"
#+,%$-"#.$#/
$"#0
"+/$1#.0
() (
)K
KJ/k
gkg
J4
6.
07
05
10
23
10
4.7 6
3
=⋅
×
×=
=∆
−
−
mc
QT
�2
01
0 H
erb
ert
B. D
om
ing
o
() (
)K
J/k
gkg
70
51
02
3⋅
×m
c
K. H
eat
an
d T
em
pera
ture
4. Q
ua
nti
ty o
f H
ea
t
•T
he
te
rm “
he
at
ca
pa
city”
is u
nfo
rtu
na
te
be
ca
use
it g
ive
s t
he
err
on
eo
us im
pre
ssio
n
tha
t a
bo
dy c
on
tain
s a
ce
rta
in a
mo
un
t o
f h
ea
t.
•R
em
em
be
r th
e h
ea
t is
en
erg
y in
tra
nsit to
or
fro
m a
bo
dy,
no
t th
e e
ne
rgy r
esid
ing
in
th
e
�2
01
0 H
erb
ert
B. D
om
ing
obo
dy.
K. H
eat
an
d T
em
pera
ture
5. C
alo
rim
etr
ya
nd
Ph
as
e C
ha
ng
es
•C
alo
rim
etr
ym
ea
ns “
me
asu
rin
g h
ea
t”.
Ph
ase
ch
an
ge
s
•T
he
te
rm p
ha
se
is u
se
d t
o d
escri
be
a s
pe
cific
sta
te
of m
att
er,
su
ch
as s
olid
, liq
uid
or
ga
s.
•T
he
co
mp
ou
nd
H2O
exis
ts in
th
e s
olid
ph
ase
as
ice
, liq
uid
ph
ase
as w
ate
r, a
nd
ga
se
ou
s p
ha
se
as
�2
01
0 H
erb
ert
B. D
om
ing
o
ice
, liq
uid
ph
ase
as w
ate
r, a
nd
ga
se
ou
s p
ha
se
as
ste
am
(a
lso
kn
ow
n a
s s
tate
s o
f m
att
er)
.
•A
tra
nsitio
n fro
m o
ne
ph
ase
to
an
oth
er
is c
alle
d
ph
ase
ch
an
ge
or
ph
ase
tra
nsitio
n.
•A
ph
ase
ch
an
ge
ta
ke
s p
lace
at a
de
fin
ite
te
mp
era
ture
, a
cco
mp
an
ied
by a
bso
rptio
n/e
mis
sio
n
of h
ea
t a
nd
a c
ha
ng
e in
vo
lum
e a
nd
de
nsity.
K. H
eat
an
d T
em
pera
ture
5. C
alo
rim
etr
ya
nd
Ph
as
e C
ha
ng
es
Ph
ase
ch
an
ge
s
•T
o c
ha
ng
e 1
kg
of ic
e a
t 0°C
to
1 k
g o
f liq
uid
wa
ter
at
0°C
at
no
rma
l a
tmo
sp
he
ric p
ressu
re r
eq
uir
es
3.3
4 ×
10
5J o
f h
ea
t.
•H
ea
t re
qu
ire
d p
er
un
it m
ass is c
alle
d t
he
he
at
of
�2
01
0 H
erb
ert
B. D
om
ing
o
•H
ea
t re
qu
ire
d p
er
un
it m
ass is c
alle
d t
he
he
at
of
fusio
n (
or
late
nt h
ea
t o
f fu
sio
n),
de
no
ted
by L
f.
•F
or
wa
ter
at n
orm
al a
tmo
sp
he
ric p
ressu
re,
the
he
at o
f fu
sio
n is L
f=
3.3
4 ×
10
5J =
79
.6 c
al/g
=
14
3 B
tu/lb
•G
en
era
lly,
Q =
mL
f
•N
ote
th
at th
e a
bo
ve
pro
ce
ss is r
eve
rsib
le.
K. H
eat
an
d T
em
pera
ture
5. C
alo
rim
etr
ya
nd
Ph
as
e C
ha
ng
es
Ph
ase
ch
an
ge
s
•W
e n
ee
d t
o r
em
ove
he
at
to fre
eze
liq
uid
wa
ter
to
ice
at
0°C
, th
e m
ag
nitu
de
is th
e s
am
e e
xce
pt
tha
t Q
is n
eg
ative
be
ca
use
he
at
is r
em
ove
d.
•T
o c
ove
r b
oth
po
ssib
ilitie
s a
nd
oth
er
kin
ds o
f p
ha
se
�2
01
0 H
erb
ert
B. D
om
ing
o
•T
o c
ove
r b
oth
po
ssib
ilitie
s a
nd
oth
er
kin
ds o
f p
ha
se
ch
an
ge
s, w
e w
rite
•H
ea
t o
f fu
sio
n is d
iffe
ren
t fo
r d
iffe
ren
t m
ate
ria
ls a
nd
als
o v
ari
es s
om
ew
ha
t w
ith
pre
ssu
re.
)8(
mL
Q±
=
K. H
eat
an
d T
em
pera
ture
5. C
alo
rim
etr
ya
nd
Ph
as
e C
ha
ng
es
Ph
ase
eq
uili
bri
um
•F
or
a g
ive
n m
ate
ria
l a
t a
ny g
ive
n p
ressu
re,
the
fr
ee
zin
g te
mp
era
ture
is th
e s
am
e a
s t
he
me
ltin
g
tem
pe
ratu
re.
•T
he
co
nd
itio
n w
he
re liq
uid
an
d s
olid
ph
ase
s c
an
co
exis
t is
ca
lled
ph
ase
eq
uili
bri
um
.
�2
01
0 H
erb
ert
B. D
om
ing
o
co
exis
t is
ca
lled
ph
ase
eq
uili
bri
um
.
He
at o
f va
po
riza
tio
n
•T
he
pre
vio
us p
ha
se
ch
an
ge
ca
n a
lso
be
ap
plie
d t
o
bo
ilin
g o
r e
va
po
ratio
n,
a tra
nsitio
n b
etw
ee
n t
he
liq
uid
an
d g
ase
ou
s p
ha
se
s.
•T
he
he
at n
ee
de
d is c
alle
d t
he
he
at
of va
po
riza
tio
n,
Lv
= 2
.25
6 ×
10
6J/k
g =
53
9 c
al/g
= 9
70
Btu
/lb
K. H
eat
an
d T
em
pera
ture
5. C
alo
rim
etr
ya
nd
Ph
as
e C
ha
ng
es
He
at o
f va
po
riza
tio
n
•L
ike
me
ltin
g,
bo
ilin
g is a
re
ve
rsib
le t
ran
sitio
n.
•W
he
n h
ea
t is
re
mo
ve
d f
rom
a g
as a
t b
oili
ng
tem
pe
ratu
re,
the
ga
s r
etu
rns t
o th
e liq
uid
ph
ase
,
tha
t is
, it c
on
de
nse
s.
�2
01
0 H
erb
ert
B. D
om
ing
o
tha
t is
, it c
on
de
nse
s.
•L
va
nd
bo
ilin
g t
em
pe
ratu
re o
f a
ma
teri
al d
ep
en
d o
n
pre
ssu
re.
•T
he
gra
ph
sh
ow
s h
ow
te
mp
era
ture
va
rie
s w
he
n w
e
ad
d h
ea
t co
ntin
uo
usly
to
a s
pe
cim
en
of
ice
with
initia
l te
mp
era
ture
be
low
0°C
, w
he
n it
rea
ch
es
me
ltin
g b
oili
ng
po
ints
.
K. H
eat
an
d T
em
pera
ture
5. C
alo
rim
etr
ya
nd
Ph
as
e C
ha
ng
es
Heat of vaporization
�2
01
0 H
erb
ert
B. D
om
ing
o
Fig
17.1
8
K. H
eat
an
d T
em
pera
ture
5. C
alo
rim
etr
ya
nd
Ph
as
e C
ha
ng
es
Heat of vaporization
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
5. C
alo
rim
etr
ya
nd
Ph
as
e C
ha
ng
es
Su
blim
atio
n
•S
om
e s
ub
sta
nce
s c
an
so
me
tim
es c
ha
ng
e d
ire
ctly
fro
m s
olid
to
th
e g
ase
ou
s p
ha
se
, a
pro
ce
ss w
e
ca
lled
su
blim
atio
n.
•T
he
co
rre
sp
on
din
g h
ea
t n
ee
de
d is t
he
he
at
of
�2
01
0 H
erb
ert
B. D
om
ing
o
•T
he
co
rre
sp
on
din
g h
ea
t n
ee
de
d is t
he
he
at
of
su
blim
atio
n,
Ls.
Su
pe
rco
ole
d
•V
ery
pu
re w
ate
r ca
n b
e c
oo
led
to
se
ve
ral d
eg
ree
s
be
low
th
e f
ree
zin
g t
em
pe
ratu
re w
ith
ou
t fr
ee
zin
g,
this
sta
te is d
escri
be
d a
s s
up
erc
oo
led
.
K. H
eat
an
d T
em
pera
ture
5. C
alo
rim
etr
ya
nd
Ph
as
e C
ha
ng
es
Su
pe
rco
ole
d
•V
ery
pu
re w
ate
r ca
n b
e c
oo
led
to
se
ve
ral d
eg
ree
s
be
low
th
e f
ree
zin
g t
em
pe
ratu
re w
ith
ou
t fr
ee
zin
g.
•T
his
sta
te is d
escri
be
d a
s s
up
erc
oo
led
an
d t
he
pri
ncip
le is a
pp
lied
in
“se
ed
ing
” clo
ud
s.
�2
01
0 H
erb
ert
B. D
om
ing
o
pri
ncip
le is a
pp
lied
in
“se
ed
ing
” clo
ud
s.
Su
pe
rhe
ate
d
•S
imila
rly, a
liq
uid
ca
n a
lso
be
su
pe
rhe
ate
d a
bo
ve
its n
orm
al b
oili
ng
te
mp
era
ture
.
K. H
eat
an
d T
em
pera
ture
5. C
alo
rim
etr
ya
nd
Ph
as
e C
ha
ng
es
Eva
po
rative
co
olin
g
•T
em
pe
ratu
re c
on
tro
l m
ech
an
ism
of
ma
ny a
nim
als
ma
ke
s u
se
of h
ea
t o
f va
po
riza
tio
n t
o r
em
ove
he
at
fro
m th
e b
od
y.
•B
y r
em
ovin
g w
ate
r fr
om
th
e t
on
gu
e (
pa
ntin
g)
or
�2
01
0 H
erb
ert
B. D
om
ing
o
•B
y r
em
ovin
g w
ate
r fr
om
th
e t
on
gu
e (
pa
ntin
g)
or
fro
m th
e s
kin
(sw
ea
tin
g)
by v
ap
ori
zin
g w
ate
r, a
n
op
tim
um
bo
dy t
em
pe
ratu
re c
an
be
ma
inta
ine
d.
•It
is a
lso
use
d t
o c
oo
l b
uild
ing
s in
ho
t, d
ry c
lima
tes
an
d to
re
cir
cu
late
“u
se
d”
ste
am
in
co
al-
fire
d o
r
nu
cle
ar-
po
we
red
ele
ctr
ic-g
en
era
tin
g p
lan
ts.
K. H
eat
an
d T
em
pera
ture
5. C
alo
rim
etr
ya
nd
Ph
as
e C
ha
ng
es
He
at o
f co
mb
ustio
n
•C
he
mic
al re
actio
ns (
e.g
., c
om
bu
stio
n)
tha
t a
re
sim
ilar
to p
ha
se
ch
an
ge
as t
he
y in
vo
lve
de
fin
ite
qu
an
titie
s o
f h
ea
t.
He
at ca
lcu
latio
ns
�2
01
0 H
erb
ert
B. D
om
ing
o
He
at ca
lcu
latio
ns
•L
aw
of
ca
lori
me
try:
Wh
en
he
at
flo
w o
ccu
rs
be
twe
en
tw
o b
od
ies t
ha
t a
re iso
late
d fro
m t
he
ir
su
rro
un
din
gs, a
mo
un
t o
f h
ea
t lo
st b
y o
ne
bo
dy
mu
st e
qu
al th
e a
mo
un
t g
ain
ed
by t
he
oth
er.
•In
oth
er
wo
rds,
the
co
nse
rva
tio
n o
f e
ne
rgy.
K. H
eat
an
d T
em
pera
ture
�2
01
0 H
erb
ert
B. D
om
ing
o
This
hig
hly
magnifie
d im
age s
how
s a
fabric t
hat
has b
een c
oate
d
with m
icro
scopic
balls
of heat-
resis
tant
pla
stic. T
he b
alls
conta
in a
substa
nce k
now
n a
s a
“phase-c
hange m
ate
rial,”
the m
eltin
g a
nd
freezin
g o
f w
hic
h a
bsorb
s a
nd r
ele
ases h
eat.
Such f
abrics
auto
matically
adju
st
in r
eaction t
o y
our
body h
eat
to h
elp
main
tain
a
consta
nt te
mpera
ture
next
to y
our
skin
. (C
ourt
esy O
utlast
Technolo
gie
s,
Bould
er,
CO
)
K. H
eat
an
d T
em
pera
ture
Exam
ple
7. T
em
pera
ture
ch
an
ge w
ith
no
ph
ase c
han
ge
A 0
.05
0 k
g m
eta
l b
olt is h
ea
ted
to
an
un
kn
ow
n in
itia
l
tem
pe
ratu
re.
It is t
he
n d
rop
pe
d in
to a
be
ake
r
co
nta
inin
g 0
.15
kg
of w
ate
r w
ith
an
in
itia
l
tem
pe
ratu
re o
f 2
1.0
°C
. T
he
bo
lt a
nd
th
e w
ate
r th
en
rea
ch
a f
ina
l te
mp
era
ture
of 2
5.0
°C.
If th
e m
eta
l h
as
�2
01
0 H
erb
ert
B. D
om
ing
o
a s
pe
cific
he
at ca
pa
city o
f 8
99
J/k
g-C
°, f
ind
the
in
itia
l te
mp
era
ture
of th
e m
eta
l.
K. H
eat
an
d T
em
pera
ture
Ex
am
ple
7. (S
OL
N)
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
Ex
am
ple
7. (S
OL
N)
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
Ex
am
ple
7. (S
OL
N)
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
Ca
lori
me
try
(no
ph
as
e c
ha
ng
e)
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
Ex
am
ple
8. C
ha
ng
es
in
bo
th t
em
pe
ratu
re a
nd
ph
as
e
Ho
w m
uch
en
erg
y is r
em
ove
d w
he
n 1
0.0
g o
f w
ate
r is
co
ole
d f
rom
ste
am
at 1
33
.0°C
to
liq
uid
at 5
3.0
°C?
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
Ex
am
ple
8.
Ch
an
ge
s in
bo
th t
em
pe
ratu
re a
nd
ph
as
e
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
Ex
am
ple
8. (S
OL
N)
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
Ex
am
ple
8. (S
OL
N)
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
Ex
am
ple
8. (S
OL
N)
�2
01
0 H
erb
ert
B. D
om
ing
o
K. H
eat
an
d T
em
pera
ture
Ca
lori
me
try
(wit
h p
os
sib
le p
ha
se
ch
an
ge
)
�2
01
0 H
erb
ert
B. D
om
ing
o
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