Geoscience Reference
In-Depth Information
R
T
M
m
·
p
=
ρ
(9)
ρ
=
N
A
·
=
has been found, when
is density, and the universal gas constant R
k
10
−
23
J
.
/
/
=
.
·
/
/
8
mol. The
state equation (Eq.
9
) also holds for mixtures of gases, e.g., for wet air if density and
molecular weight of wet air are introduced. A simpler form can be found with the
specific gas constant
R
=
3143 J
K
mol with the Boltzmann constant k
1
3806
K
R
/
M
m
, so that
p
ρ
R
T
=
.
(10)
We apply this equation on wet air (no index), dry air (index
d
), and water vapor
(index
w
). The gas laws read for the dry and wet part
p
d
ρ
d
=
R
d
·
T
(11)
p
w
ρ
w
=
R
w
·
T
,
(12)
and applying Dalton's law (Eq.
8
), we get
T
ρ
d
ρ
R
w
R
d
+
ρ
w
R
T
=
.
(13)
ρ
Introducing specific humidity
s
=
ρ
w
/ρ
and
l
=
ρ
d
/ρ
=
1
−
s
we get
R
d
1
s
R
w
1
R
=
R
d
+
R
w
=
·
·
+
R
d
−
.
l
s
(14)
with the molecular weight of water
M
w
=
2
·
1
.
008
+
16
=
18
.
016 g
/
mol and the
mol we find
R
d
/
R
w
=
molecular weight of dry air
M
d
=
.
/
.
28
965 g
1
608 and
R
=
R
d
(
1
+
0
.
608
·
s
) .
(15)
Consequently, the gas law for wet air can be written as
p
ρ
R
T
R
d
(
R
d
·
=
=
1
+
0
.
608
·
s
)
·
T
=
T
v
(16)
with
T
v
=
(
T
(see also Eq.
7
).
T
v
is called virtual temperature, and
it is the temperature of dry air that has the same density at the same pressure as wet
air of temperature
T
and specific humidity
s
. All relationships for dry air are valid
for wet air if we replace temperature
T
by the virtual temperature
T
v
.
1
+
0
.
608
·
s
)
·
