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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