define
work
chapter
three
notes
3
. 1
and
Heat
Work
classically.
thermodynamically ?
classically Force
thermodynamics
work
of
derive
at
They
PV
work
concept
subtle
more
:
types
distance
X
:
broader
,
range processes
work
mechanical
fax
surface
ada
EdQ
electrical
can
note?
we "beat" this ?
derive
PV
work
comes
gravitational mgdh
up
lot !
a
we
consider
in
gas
derive
to
P
, V,T
can
g
Pext =
PLVzT
-
W =
system
same
,
but
-
w=
*
-
Pext
w=
w
have
two eawor
signify
?
e
W =
have
two
under
if
giveagraphicare
these
system
still ,
enables
-
1st law
thermodynamics .
,
Pins Pext
when
Pin = Pext
gas expands
If reached
W =
-
PAU
Pin-Pext
32
First Law
1st
law
method
for this
gas expands
and
Pext
by
=
Pin-ap
o
SY PindV -SRTa
=
-w =
-
nRT(()
=
-
work ?
expansion
is
work
,
maximize
can
reversible
a
nRTin))
work
done
by
making e is
process
,
process
us
to
would
o
p
infinite
take
calculate
two
time
p
/
diff T
energy fn .; path-dependent
Thermodynamics
thermodynamics :
energy
cannot
SEuniv =
SV =
q
can
never
really
done
be
Pi , Vi
.
/
state
of
-
wmax
PV
bodies
+
d
&P
=
=
////IPV
a
sand
(barely)
SYSPin-aP((aV) Su Pinar-a
expansion
coud. ,
comparison
transfer
not
define
as
will stop
Pin > Pext
V
.
note :
can
by dp
stop the expansion
always infinitesimally close to >
reversible
heat
mg(sh)
SPexd
I constant
-
=
grains of
removed ,
maximum
we Pext
true
graphical
heat.
-
(substitute)
bKWorkinexpansiondone against Pext
caveat ?
=
=
(like
expressions
nRTin() represents
-
why ?
I
why? Key
we
now
we
Sam
when dm
ra
wai t ...
principles
my Pext A
-
PextA(Ah)
m =
m-dm
now
thermodynamic
"beat" this ? (Wa Pext & V
we
consider :
wai t ...
-mg(d)
- fd = ma(d) =
w =
-:
.....
define
key
piston
M
M
S
what
it
use
now.
:
PdU
expansion
.
constant P
be
created/destroyed
+
is
function !
state
dq
+
Etot
=
k
in most
=
o
-path-dep
=
W
~
BEs &Esurr
w/dv
Priv
du
then ,
Erot
.
linexact
+
V
+
cases ,
differential
=
U
y
k/v = 0
in
lab ,
how we
do
Enthalpy
33
most
.
processes done
-not
at
in
lab ,
most
chemical/physical
1V =
q
=
define
ap
enthalpy ?
at constant p !
let
how
define
us
general
(works out
the
AV , DH ?
-
for
solids/liquids ?
H = V
to
of
both
rep
terms
consider :
b/c
su
=
DV
=
It
q
1U
(V , + PV) =
-
VAP
+
+
P , V.
+
is
whatis
one
qp
-
SH = DU + PSV
put
account
defnet
-A
small
(aq)
change
367 5k5
for constant P
+
blc
differ
H2(g)
DV ??
↑
key rule
that
,
Heat
at
to
q
CAT
:
=
q
=
same
367 5 k5
.
volume
solution
internal
energy
VHz
.
=
24 5Lv
.
PAV =
24 5 atm L
.
.
=
2 5k]
.
.
of
some
for
the
gases given
IPV = O
DH
-
=
by
SCPV
dep
substance
constant
molar
paths
su =
dU = CrdT
AV =
note : not
slightly
smaller
SCRT
or
on
.
.
added
heat
substance
(2) amt
present
(3) chemical/physical prop . substance
addition
(4) conditions of
rise
.
I depends
(5/k) : extensive
form ;
that
constant
at
:
.
Iso
PV work
energy
<
is
will
its T
,
intensive
come
(Cv)
be
can
:
.
2
umie
on
experimentally
path
heating
constant
at
:
SH = SCpdT
(300K)
at
lOWT
if
ST50K , mostly
,
only
assumption
to
trans/rot motions
fair
to
i
dH = CpdT
=
fair
(C)
wine
say
say
indep
Cp/C
contribute
.
T
ab
indep T
const
.
to
heat
cap
.
where
Cp = a + bT ,
SCrdT
actually
BUT
heating
=
g x qu
+
measured
often
up
=
indep T ?
explain .
released a
DU
Capacities
I
two
heating
key rule SH ??
is C
added
consider
.
not
conditions
In = 0
capacity
1
AH
2 SK5
-
.
S
will
function ,
.
JU/AH
solids/liquids
heat
together
heat
state
in
DH = 367 5 kJ
=
ignore
=
values
but
,
[NaOH
-
qp
PSV
difference
,
when
when
change
APAV
(l) amt
heating
restrictingchangetospecific put
&p
negligible
S(PV)
+
2128 (1)
+
°
A Closer Look
.
are
SH = (V2 + P2Vz)-(V ,
-
equation
T = 25 C ,
into
wh
rxns
34
( , + PV)
-
.
takes
or
easier ! !
370 0KJ
-
in general
for
PV
change in energy
.
=
w
+
,
function !!
+
PAV
AH = Au
constant P ,
at
assume
we
=
same
2 NaOH
done
U , P, V
but
1H = (V2 + PVz)
1H
,
fn .,
I safer
constant V
sink)
heat
=
not
,
DU , DH
comparison
if
+
expansion
-
state
new
a
(H)
in
else ,
is
state
at constantl
P(Vz V ,) = (Vz + P(z)
V,) +
-
constant R process ,
for
what
(Vz
=
lqp blc
PA
-
not
a
enthalpy
difference
qp
su + PAV
=
notice
full eq?
w
+
done
processes
(vib.
at
higher)
.
given
T
range
why
conceptually ,
Cp + Cv ?
,
does
Cp
for constant R process
compute
let
H = V + PV =
solids/liquids though
dH = du
sink
CpdT
Cp
C + nR
CrdT
really
(p = Cv for
for
IT
same
solid/liquid though
for
not
condensed
...
phases
nRT
(recall
dH = CpdT ; dU =
:
CvdT)
nRdT
+
[p =
or
woah
R
+
.
emphasis
sm
gas expansion
?
Expansion
3 5 Gas
.
isot
V +
needed
heat
more
-
Cu
vs .
nRdT
+
=
=
Cp
compute
us
what is it for
for
a
h eat
is
expansion
,
the
difference .
why
equal !
Cr-not
vs .
expansion ,
of
expansion
ideal
an
consider
will
two
is
gascases simple
process
can
we
use
applyIst
to
special
law
thermodynamics
derive
AV q
,
,
w ,
H
1
b/c T = 0
then
T
expansion
isothermal
.
SV = 0
,
(as per
SV = q + w = 0
,
SH = AV +
then ,
constant
-
APV
const
=
gases point masses/no int )
, pet
.
(and recall
w
O
,
w =
-
nRT()
SH = 0
-
.
KMT , where
q
P .. V , T
p
bl
T const
1
derive
the
MASSIVE
adiabatic
exp
is
8?
if
8
w
adiabatic
exp .
why
is it
see
in
.
ok to
term ?
,
:
=
Cp
adiabatic
du
expansion
= du
+
=
-
Cu + nR
=
[p =
=
PdV
+
R
↑
recala n
recall :P-CV = R
(5)
in()
=
<P
=
-
ideal
gas
(in()
[Rin()
Sin
capacity
neat
ratio
finally,
()
: For = multiplying previous equation
one
Wher, isot
Wrev ad-
q 0
expansion
reversible
1st law
.
what happens
= 1 ?
derive
adiabatic
a
relation
If
.
just multiply is
for adiabatic
....
-
process
,
P, V ,
8
=
PaVzO-differs from Boyle's
by 8
law
(if U
=
1
,
Boyle-like !)
wh
w
=
can
·
1
take
=
ST
=
advantage
cT =
newh? Why
ofI V
being state
. othermalexpansion
actual path :
V
on
st
BV = nEvBT
.
I
is
C
from
showing up during
graph
for isot
,
heat
for adiabatic
graphically
:
see
can
,
,
abs
.
Onto
Wher, ad
from
cannot
new
expansion ?
an
surr
.
happen
>
=
Wrev
Wgas
and T
isotherm !
,
isoT
drops
0
