Environmental Engineering Reference
In-Depth Information
of transmissivity
τ
0 is zero, however this pressure grows with the growing trans-
missivity and is maximum for
τ
=
1. In the second case, the photons can transfer
momentum to other particles upon impact and such possibility of potential pressure
exists regardless of the properties (e.g. transmissivity) of any target. As in the consid-
eration of substance pressure, the equipartition theorem can be applied to the energy
in a three-dimension system and accordingly the pressure
p
of black radiation is:
=
u
3
p
=
(2.2.26)
and using (2.2.24) in (2.2.26):
a
3
T
4
=
p
(2.2.27)
One of the possible processes of photon gas is the isentropic process during which
the photon gas does not exchange heat with the surroundings. For example such a
process can be imagined for a photon gas trapped in the space surrounded with an
expandable wall of perfect reflectivity. The isentropic process occurs reversibly and
the entropy in each elemental process stage remains constant. The entropy in J/K of
the gas occupying volume
V
is determined based on formula (2.2.25) and the condition
of constant entropy in the process is:
V
4
3
aT
3
=
const
.
(2.2.28)
or eliminating temperature
T
by pressure
p
with use of formula (2.2.27):
pV
4
/
3
=
const
.
(2.2.29)
Exergy of black radiation was determined for the first time by Petela (1964), by
consideration of the isentropic process in which the
V
1m
3
of radiation of tem-
perature
T
changes the initial pressure
p
to the final pressure
p
0
at temperature of
the environment. The final state of the considered radiation is in equilibrium with
the environment and the exergy of this radiation is zero. Therefore, according to the
exergy definition, the initial density
b
b
,
S
, J/m
3
, of black radiation within the system is
equal to the useful work performed during the process:
=
V
0
=
−
−
b
b
,
S
pdV
p
0
(
V
0
V
)
(2.2.30)
V
Using (2.2.27) and (2.2.29) in (2.2.30):
a
3
(3
T
4
T
0
−
4
T
0
T
3
)
b
b
,
S
=
+
(2.2.31)
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