Geoscience Reference
In-Depth Information
Table 2.1 Some physical constants
Dry air
Molecular weight: 28.966 g mol
−
1
Gas constant:
R
d
=
04 J kg
−
1
K
−
1
287
.
1005 J kg
−
1
K
−
1
Specific heat:
c
pd
=
716 J kg
−
1
K
−
1
Density:
ρ
=
1
.
2923 kg m
−
3
(
p
=
1013
.
25 hPa
,
c
vd
=
T
=
273
.
16 K)
Water vapor
Molecular weight: 18
.
016 g mol
−
1
Gas constant:
R
w
=
461
.
5Jkg
−
1
K
−
1
Specific heat:
c
pw
=
1846 J kg
−
1
K
−
1
c
vw
=
1386 J kg
−
1
K
−
1
Note
. The values listed in Tables 2.1, 2.4 and 2.5, are adapted from
the Smithsonian Meteorological Tables (List, 1971), where the orig-
inal references are cited.
for dry air. Similarly, the density of water vapor is
0
.
622
e
R
d
T
ρ
v
=
(2.5)
where 0.622
=
(18.016/28.966) is the ratio of the molecular weights of water and dry air.
The density of moist air from Equations (2.4) and (2.5) is
1
−
p
R
d
T
0
.
378
e
p
ρ
=
(2.6)
showing that it is smaller than that of dry air at pressure
p
. This means that water vapor
stratification plays a role in determining the stability of the atmosphere. The equation of
state of moist air can be obtained by eliminating
e
from Equations (2.4) and (2.5)
p
=
ρ
TR
d
(1
+
0
.
61
q
)
(2.7)
This indicates that the air mixture behaves as a perfect gas provided it has a specific gas
constant
R
m
=
R
d
(1
+
0
.
61
q
)
(2.8)
that is a function of the water vapor content. Therefore, Equation (2.7) is often expressed
as
p
=
R
d
ρ
T
V
(2.9)
where
T
V
is the virtual temperature defined by
T
V
=
(1
+
0
.
61
q
)
T
.
(2.10)
The virtual temperature is the temperature that dry air should have in order to have the same
density as moist air with given
q
,
T
and
p
.
