Environmental Engineering Reference
In-Depth Information
In practice, the formula (2.2.3) can be rearranged for example to the frequently
applied form for the exergy
b
, J/kg, of an ideal gas of temperature
T
and pressure
p
:
T
0
c
p
ln
T
R
ln
p
p
0
b
=
c
p
(
T
−
T
0
)
−
T
0
−
(2.2.15)
where
c
p
is the specific heat of gas at constant pressure,
R
is the individual gas constant,
T
0
is the absolute temperature of environment and
p
0
is the partial pressure of the
considered gas in equilibrium with environment.
2.2.3.2 Gravitational interpretation of exergy
Solar heating of a surface on Earth, combined with the gravity field, creates specific
effects, e.g., a driving force for solar chimney power plant. The full role of the Earth's
gravity field in such processes could be better analyzed by introducing the additional
component of mechanical exergy
b
m
(called shortly ezergy) and by additional terms of
gravity input
G
in the exergy balance, both proposed by Petela (2010).
The mechanical exergy concept
b
m
is derived from the difference between density
ρ
of considered substance and density
ρ
0
of environment. Regardless of the temperature
T
and pressure
p
of the substance under consideration, the buoyancy of the substance
is unstable, and thus the ability to work in the environment at respective parameters
T
0
and
p
0
is sensed if removed as either an anchor (
ρ<ρ
0
) or a supports (
ρ>ρ
0
). In
the first case, the substance moves upwards, in other case, the substance sinks.
The altitude of the considered substance is measured from the actual level
x
=
0.
In both the above cases the substance tends to achieve an equilibrium altitude (
x
H
),
at which the density of local environment
ρ
0,
x
is equal to density of the considered
substance;
ρ
=
ρ
0,
x
. The motion of substance (remaining at constant
T
and
p
)to
the equilibrium altitude would generate work which is called the buoyant exergy
b
b
,
which does not depend on the kind of the substance. During repositioning of the sub-
stance, from actual altitude
x
=
H
, the gravity acceleration
g
x
is changing,
e.g. decreasing with growing altitude
x
, thus:
=
0to
x
=
g
x
ρ
0,
x
ρ
1
dx
x
=
H
b
b
=
−
(2.2.16)
x
=
0
The solution of equation (2.2.16) is discussed by Petela (2010).
At level
H
the substance could be allowed to generate additional work, denoted
by
b
H
, which would occur during a reversible process of equalization of parameters
T
and
p
with the respective local environment parameters
T
0,
H
and
p
0,
H
. In case of
a gas, during equalizing of the gas parameters
T
and
p
with the parameters
T
0,
H
and
p
0,
H
at the altitude
H
, based on Formula (2.2.15), the following work (exergy
b
H
) can
be done:
T
0,
H
c
p
ln
T
T
0,
H
−
p
p
0,
H
b
H
=
c
p
(
T
−
T
0,
H
)
−
R
ln
(2.2.17)
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