Geoscience Reference
In-Depth Information
respectively. Because the air in the container is thermally isolated, the heat removed
from the air as it cools must equal the latent heat required to evaporate water to
raise the specific humidity of the air to saturation, i.e.:
(
)
(
)
r
VT T c
-
=
r
⎡
q T qV
-
⎤
l
(2.22)
⎣
⎦
a
dry
wet
p
a
sat
wet
where
c
p
(
1.013 kJ kg
−1
K
−1
) is the specific heat at constant pressure for air.
Rewriting Equation (2.22) in terms of vapor pressure:
=
(
)
⎡
⎤
0.622
r
eT e
-
l
(
)
⎣
⎦
a
sat et
r
cT T
-
=
(2.23)
ap dry wet
P
This last equation can be re-written as the so-called
wet bulb equation
, which takes
the form:
(
)
(
)
eeT T T
=
− γ
-
(2.24)
sat
wet
dry
wet
In this last equation the term (
T
dry
-
T
wet
) is often called the
wet bulb depression
and
γ
is the
psychrometric constant
calculated from:
cP
⎛
⎞
γ=
⎜
(2.25)
⎟
0.622
l
⎝
⎠
Actually the
psychrometric 'constant'
is not constant because it varies with
atmospheric pressure and also to some extent with temperature, because the latent
heat of vaporization of water has temperature dependency, see Equation (2.1). For
a temperature of 20
is 0.0677.
Wet and dry bulb temperatures are often routinely measured at climate stations
and if measured using aspirated thermometers the value of
°
C and pressure of 101.2 kPa, the value of
γ
calculated by
Equation (2.25) should be used to calculate the vapor pressure. However, if the
thermometers are not aspirated (which is often the case), a different, empirically
determined value of
γ
γ
* is required to substitute for
γ
when calculating the atmos-
pheric vapor pressure from the wet bulb equation.
Important points in this chapter
Latent heat
: separating water molecules in liquid water to give water vapor
requires energy (
●
2.5 MJ kg
−1
) which is called the
latent heat of vaporization
and which reduces with temperature by about 0.1% per
∼
°
C.
Atmospheric water content
: is quantified in terms of the ratio of the density
of water vapor to that of the (dry) air, called the
mixing ratio
(
r
), or the
●
