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its physical properties without the step of thermal coupling of this gas to a sensor which would
otherwise be necessary.
The advantages of this measuring method are firstly its inertia-free reaction to the actual gas
temperature, and secondly, the avoidance of measuring errors such as those that occur for
example when a solid-state temperature sensor is heated by radiation or cooled through the
evaporation of water on the sensor.
Many comparative tests between different weather and thermal radiation shield housings show the
indirect effect of the above-mentioned sources of measurement errors on the temperature sensor.
[1]
At sites with a high likelihood of icing-up ultrasonic anemometers are also used already as acoustic
thermometers, as classical temperature sensors are no longer vented with weather and thermal
radiation shield housings after icing-up. Due to the deteriorated thermal coupling to the outer world
they response only extremely time-delayed, or due to the missing discharge of the own power
dissipation the measured temperature is too high. [2]
2.2.1 Correction of the acoustic-virtual temperature from Influence of air humidity
Given the dependence, albeit low, of the sound propagation velocity on the air humidity level, the
"acoustic virtual temperature" relates to dry air without any water vapour content.
The deviation of the measured "acoustic temperature" from the real air temperature shows linear
dependence on the absolute humidity level of the air.
The amount of water vapour in the air proportionately increases the velocity of sound as H
2
O
molecules only have around half the mass of the other air molecules (O
2
and N
2
).
The velocity of sound however only increases with the molar mass fraction of water vapour in the
air to a disproportionately low degree.
The reason for this is the lower mean translatory velocity of the water vapour molecules in
comparison with the other air molecules. With the more complex H
2
O molecules greater degrees of
freedom of motion are possible than with the more simple O
2
and N
2
molecules so that the total
energy content (temperature) is divided between the possible degrees of freedom of translation
and rotation as kinetic energy.
O
2
and N
2
molecules have 3 degrees of freedom of translation and 2 degrees of freedom of
rotation, and H
2
O molecules 3 degrees of freedom of translation and 3 degrees of freedom of
rotation.
The adiabatic exponent
γ
of each gas is determined by the total number of degrees of freedom
according to the following interrelationship:
n
2
1
+
=
γ
The adiabatic exponents measured for dry air
d
γ
and water vapour
v
γ
are:
399463
.
1
=
d
γ
and
331
.
1
=
v
γ
The dependence of the acoustic virtual temperature
Tv
on the water vapour content of the air can
be calculated using the following relationship:
•
−
−
•
−
+
•
=
e
M
M
p
e
M
M
Tt
Tv
d
v
d
v
d
v
1
1
γ
γ
[1]