Environmental Engineering Reference
In-Depth Information
the heat release is sharper than for heat transport. This character of heat processes
is of universal character and may be applied to some processes in ionized gases.
We considered above a thermal wave of vibrational relaxation in a nonequilibrium
molecular gas, and below we consider one more process of this type, which results
in decomposition of ozone in air or other gases and proceeds in the form of a ther-
mal wave. The propagation of the thermal wave results from chemical processes
whose basic stages are
M
k
dis
M
K
k
1
!
O
3
C
!
O
2
C
O
C
M, O
C
O
2
C
!
O
3
C
M, O
C
O
3
2O
2
(5.43)
where M is a gas molecule and the relevant rate constants for the processes are
given above the arrows. If these processes proceed in air, the temperature
T
m
after
the thermal wave is connected to the initial gas temperature
T
0
by
T
m
D
T
0
C
48
c
,
(5.44)
where the temperatures are expressed in Kelvin and
c
is the ozone concentration
in air expressed as a percentage.
On the basis of scheme (5.43), we obtain the set of balance equations
d
[O
3
]
dt
D
k
dis
[M][O
3
]
C
K
[O][O
2
][M]
k
1
[O][O
3
],
d
[O]
dt
D
k
dis
[M][O
3
]
K
[O][O
2
][M]
k
1
[O][O
3
] ,
(5.45)
where [X] is the number density of particles X. Estimates show that at gas pressure
p
k
1
[O
3
], that is, the second term
on the right-hand side of each equation in (5.45) is smaller than the third one.
In addition, we know that [O]
1atmand
T
m
>
500 K we have
K
[O
2
][M]
[O
3
], that is,
d
[O]/
dt
d
[O
3
]/
dt
.Thisgives
d
[O]/
dt
D
0and[O]
D
k
dis
[M]/
k
1
. Using this result in the first equation in (5.45),
we obtain
d
[O
3
]
dt
D
2
k
dis
[M][O
3
].
Then, with (5.36) and (5.37), we obtain for the thermal wave
D
d
2
[O
3
]
dx
2
u
d
[O
3
]
dx
C
2
k
dis
[M][O
3
]
D
0,
d
2
T
dx
2
u
dT
2
c
p
Δ
ε
dx
C
C
k
dis
[O
3
]
D
0 ,
(5.46)
where
Δ
ε
D
1.5 eV is the energy released from the decomposition of one ozone
molecule.
We can now substitute numerical parameters of the above processes for a
thermal wave in air at atmospheric pressure, namely,
D
0.16 cm
2
/s and
D
0.22 cm
2
/
s
. These quantities are almost equal numerically and have simi-
lartemperaturedependence,sowetakethemtobeequalandgivenby
D
T
300
1.78
0.19
p
D
D
D
.
