⋅
⋅
⋅
⋅
Some Relationships for Gases
define some units
these are extracted from Van Wylen & Sonntag, Fudamentals of Classical
3
kJ
:=
10
⋅
J
Thermodynamics, Third Edition to which page numbers and equation numbers apply
2006: included reference to text: Woud section 2.23 in [W n.nn]
3
kmol
:=
10 mole
section 3.4 Equations of state for the vapor phase
of a simple compressile substance  page 41
(Woud page 20)
⎯
⎯
⎯
gas at low density (experiment)
pv
=
R
R
=
universal_gas_constant
(3.1)
⋅
⋅
T
⎯
xxx
=
mole_basis
kJ
kJ
R_bar
:=
8.3144
units sometimes .
..
kmol K
⋅
kg_mol K
⋅
⎯
R
R
=
mw
mw
=
molecular_weight
for R_bar above
mw
=
kg
kmol
p
1
⋅
v
1
p
2
⋅
v
2
[W 2.32, 2.33[
(3.5)
pV
=
mR
⋅
T
or .
..
pv
=
RT
(3.2)
=
T
1
T
2
section 4.3 Work done at moveable boundary of
simple compressible system  page 63
⋅
W
1_2
p
1
V
1
p
1
V
1
⎜
⎟
(4.5)
if .
..
n
=
constant
n
=
1
=
⎮
⌠
V
2
p dV
=
⋅
⋅
⎮
⌠
V
2
1
dV
=
⋅
⋅
ln
⎛
V
2
⎞
⌡
V
1
⎮
⌡
V
1
V
⎝
V
1
⎠
section 5.6 The ConstantVolume and
ConstantPressure Specific Heats  page 98
specific heat = increment of heat Q to change T by 1 deg
c
=
1
⋅
δ
Q
1
=
specfic
m
δ
T
m
two cases: 1) constant volume
c
v
=
1
⋅
δ
Q
constant volume
m
δ
T
=
δ
W
(5.4)
1st law .
..
δ
Qd
E
+ δ
W
=
dU
+
dKE
+
dPE
+
δ
U
+
p
⋅δ
V
dKE
=
dPE
=
0
δ
W
=
p
V
=
=
0
1
δ
Q
1
δ
U
δ
u
c
v
δ
u
δ
T
=
constant volume
(5.14)
[W 2.36]
c
v
=
⋅
=
⋅
=
m
δ
T
m
δ
T
δ
T
2) constant pressure
δ
+
p
V
=
δ
H
as .
...
dH
=
d U
+
⋅
)
=
dU
+
p dV
+
⋅
=
(
p V
⋅
Vdp dp
=
0
1
δ
Q
1
δ
H
δ
h
c
p
δ
h
δ
T
=
constant pressure
(5.15)
[W 2.37]
c
p
=
⋅
=
⋅
=
m
δ
T
m
δ
T
δ
T
10/23/2006
1
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View Full Documentsection 5.7 The Internal Energy, Enthalpy
and Specific Heats of Ideal Gases  page 100
⋅
⋅
u ()
experiment (Joule)
ideal gas
pv
=
RT
=
f
T
=> constant volume
δ
u
c
v
=
u not a function of v =>
du
=
c
vo
⋅
dT
vo
ideal gas
(5.20)
δ
T
also .
..
p v
() RT
=
hT
h
=
u
+
⋅
=
uT
+
⋅
()
i.e. h = F(T) only
(5.24)
δ
h
dh
=
c
po
⋅
dT
po
=> constant pressure
δ
T
c
p
=
=>
ideal gas
dh
du
relation between c
vo
and c
po
...
h
=
u
+
p
v
=
u
+
R T
⋅
=
+
R
differentiate w.r.t T
dT
dT
c
po
=
c
vo
+
R
or .
..
c
po
−
c
vo
=
R
(5.27)
with constant c
h
2
−
h
1
=
c
po
⋅
(
T
2
−
T
1
)
otherwise integrate if c(T) known or tables
(5.29)
[W 2.38]
section 7.10 Entropy Change of an
Ideal Gas  page 206
Tds
=
du
⋅
(7.7)
[W 2.18]
⋅
+
p dv
T
=>
T
du
=
c
vo
⋅
dT
and .
..
=
=>
p
=
R
⋅
⋅
=
c
vo
⋅
dT
+
R
⋅
⋅
dv
⋅
⋅
v
v
⎛
T
2
⎞
⎛
v
2
⎞
c
vo
=
constant
dT
dv
ds
=
⋅
+
R
⋅
(7.19)
c
vo
⎜
T
1
Rln
v
1
s
2
−
s
1
=
⋅
ln
⎟
+
⋅
⎜
⎟
(7.24)
c
vo
T
v
⎝
⎠
⎝
⎠
otherwise integrate or use
tables
⋅
v dp
=
dh
−
⋅
(7.7)
[W 2.21]
T
T
dh
=
c
po
⋅
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 Fall '06
 DavidBurke
 Thermodynamics, vinitial Tfinal, Tfinal sfinal

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