73
THERMODYNAMICS
±THERMODYNAMICS
PROPERTIES OF SINGLECOMPONENT SYSTEMS
Nomenclature
1. Intensive properties are independent of mass.
2. Extensive properties are proportional to mass.
3. Speci
f
c properties are lowercase (extensive/mass).
State Functions
(properties)
Absolute Pressure,
P
(lbf
/
in
2
or Pa)
Absolute Temperature,
T
(
°
R or K)
Volume,
V
(ft
3
or m
3
)
Speci
f
c Volume,
vVm
=
(ft
3
/
lbm or m
3
/
kg)
Internal Energy,
U
(Btu or kJ)
Speci
f
c Internal Energy,
uUm
=
(usually in Btu
/
lbm or kJ
/
kg)
±Enthalpy,±
H
(Btu or KJ)
Speci
f
c
Enthalpy,
h
=
u
+
Pv = H/m
(usually in Btu
/
lbm or kJ
/
kg)
Entropy,
S
(Btu
/
°
R or kJ
/
K)
Speci
f
c Entropy,
s = S/m
[Btu
/(
lbm
°
R) or kJ
/
(kg•K)]
Gibbs Free Energy,
g
=
h
–
Ts
(usually in Btu
/
lbm or kJ
/
kg)
Helmholz Free Energy,
a
=
u
–
(usually in Btu
/
lbm or kJ
/
kg)
Heat Capacity at Constant Pressure,
c
T
h
p
P
2
2
=
bl
Heat Capacity at Constant Volume,
c
T
u
v
v
2
2
=
Quality
x
(applies to liquidvapor systems at saturation) is
de
f
ned as the mass fraction of the vapor phase:
x = m
g
/
(
m
g
+ m
f
)
,
where
m
g
= mass of vapor, and
m
f
= mass of liquid.
Speci
f
c volume of a twophase system
can be written:
v
=
xv
g
+ (1 –
x
)
v
f
or
v
=
v
f
+
xv
fg
, where
v
f
= speci
f
c volume of saturated liquid,
v
g
= speci
f
c volume of saturated vapor, and
v
fg
= speci
f
c volume change upon vaporization.
=
v
g
–
v
f
Similar expressions exist for
u
,
h
, and
s
:
u
=
xu
g
+ (1 –
x
)
u
f
or
u = u
f
+ xu
fg
h
=
xh
g
+ (1 –
x
)
h
f
or
h = h
f
+ xh
fg
s
=
xs
g
+ (1 –
x
)
s
f
or
s = s
f
+ xs
fg
For a simple substance, speci
f
cation of any two intensive,
independent properties is suf
f
cient to
f
x all the rest.
For an ideal gas,
Pv
=
RT
or
PV
=
mRT
, and
P
1
v
1
/T
1
=
P
2
v
2
/T
2
, where
P
= pressure,
v
= speci
f
c volume,
m
= mass of gas,
R
=
gas constant, and
T
= absolute temperature.
V
= volume
R
is
speci
f
c to each gas
but can be found from
.
,
R
mol wt
R
where
=
^h
R
= the universal
gas constant
= 1,545 ftlbf/(lbmol
°
R) = 8,314 J
/
(kmol
⋅
K).
For
ideal gases
,
c
p
–
c
v
=
R
Also, for
ideal gases
:
P
h
v
u
00
TT
2
2
2
2
==
bb
ll
For cold air standard,
heat capacities are assumed to be
constant
at their room temperature values. In that case, the
following are true:
Δ
u
=
c
v
Δ
T
;
Δ
h
=
c
p
Δ
T
Δ
s
=
c
p
ln (
T
2
/T
1
) –
R
ln (
P
2
/P
1
); and
Δ
s
=
c
v
ln (
T
2
/T
1
) +
R
ln (
v
2
/v
1
).
For heat capacities that are temperature dependent, the value
to be used in the above equations for
Δ
h
is known as the mean
heat capacity
c
p
`j
and is given by
c
cdT
p
p
T
T
21
1
2
=

#
Also, for
constant entropy
processes:
;
,
P
P
v
v
T
T
P
P
T
T
v
v
kcc
where
k
k
k
k
pv
1
2
2
1
1
2
1
2
1
1
2
2
1
1


d
d
d
n
n
n
For real gases, several equations of state are available; one
such equation is the van der Waals equation with constants
based on the critical point:
,
P
v
a
vb R
T
a
P
RT
b
P
RT
64
27
8
where
2
c
c
c
c
2
2
+
=
c
^
c
f
m
h
m
p
where
P
c
and
T
c
are the pressure and temperature at the critical
point, respectively, and
v
is the molar speci
f
c volume.
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THERMODYNAMICS
FIRST LAW OF THERMODYNAMICS
The
First Law of Thermodynamics
is a statement of
conservation of energy in a
thermodynamic system. The net
energy crossing the system boundary is equal to the change in
energy inside the system.
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 Fall '06
 OLER
 Thermodynamics, Energy, Entropy

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