56
THERMODYNAMICS
PROPERTIES OF SINGLE-COMPONENT
SYSTEMS
Nomenclature
1.
Intensive properties are independent of mass.
2. Extensive properties are proportional to mass.
3.
Specific properties are lower case (extensive/mass).
State Functions
(properties)
Absolute Pressure,
p
(lbf
/
in
2
or Pa)
Absolute Temperature,
T
(
°
R or K)
Specific Volume,
v
(ft
3
/
lbm or m
3
/
kg)
Internal Energy,
u
(usually in Btu
/
lbm or kJ
/
kg)
Enthalpy,
h
=
u
+
Pv
(same units as
u
)
Entropy,
s
[Btu
/
(lbm-
°
R) or kJ
/
(kg
⋅
K)]
Gibbs Free Energy,
g
=
h
–
Ts
(same units as
u
)
Helmholz Free Energy,
a
=
u
–
Ts
(same units as
u
)
Heat Capacity at Constant Pressure,
P
p
T
h
c
⎟
⎠
⎞
⎜
⎝
⎛
∂
∂
=
Heat Capacity at Constant Volume,
v
v
T
u
c
⎟
⎠
⎞
⎜
⎝
⎛
∂
∂
=
Quality
x
(applies to liquid-vapor systems at saturation) is
defined 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.
Specific volume of a two-phase system
can be written:
v
=
xv
g
+ (1 –
x
)
v
f
or
v
=
xv
fg
+
v
f
, where
v
f
=
specific volume of saturated liquid,
v
g
=
specific volume of saturated vapor, and
v
fg
=
specific volume change upon vaporization.
=
v
g
–
v
f
Similar expressions exist for
u
,
h
, and
s
:
u
=
xu
g
+ (1 –
x
)
u
f
h
=
xh
g
+ (1 –
x
)
h
f
s
=
xs
g
+ (1 –
x
)
s
f
For a simple substance, specification of any two intensive,
independent properties is sufficient to fix 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
= specific volume,
m
=
mass of gas,
R
= gas constant, and
T
= absolute temperature.
R
is
specific to each gas
but can be found from
()
wt.
mol.
R
R
=
, where
=
the universal gas constant
= 1,545 ft-lbf/(lbmol-
°
R) = 8,314 J
/
(kmol
⋅
K).
For
Ideal Gases
,
c
P
–
c
v
=
R
Also, for
Ideal Gases
:
0
0
=
⎟
⎠
⎞
⎜
⎝
⎛
∂
∂
=
⎟
⎠
⎞
⎜
⎝
⎛
∂
∂
T
T
ν
u
v
h
For cold air standard,
heat capacities are assumed to be
constant
at their room temperature values. In that case, the
following are true:
∆
u
=
c
v
∆
T
;
∆
h
=
c
P
∆
T
∆
s
=
c
P
ln (
T
2
/T
1
) –
R
ln (
P
2
/P
1
); and
∆
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
∆
h is known as the
mean heat capacity (
) and is given by
1
2
2
1
T
T
dT
c
c
T
T
p
p
−
∫
=
Also, for
constant entropy
processes:
P
1
v
1
k
=
P
2
v
2
k
;
T
1
P
1
(1–
k
)/
k
=
T
2
P
2
(1–
k
)/
k
T
1
v
1
(
k
–1)
=
T
2
v
2
(
k
–1)
, where
k
=
c
p
/
c
v
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.
Heat
Q
is
energy transferred
due to temperature difference
and is considered positive if it is inward or added to the
system.
Closed Thermodynamic System
No mass crosses system boundary
Q
–
W
=
∆
U
+
∆
KE +
∆
PE
where
∆
KE
= change in kinetic energy, and
∆
PE
= change in potential energy.