|We are wondering about some weather data. It
seems like there is an indirect relationship
between air pressure and relative humidity. We
thought wet air would have greater air pressure
(weigh more) than dry air! What's up with that?
I consulted with another graduate student friend
of mine who is taking a meteorology (weather)
class, and he said that the average water content
of the atmosphere is about 2 grams per kg, or 1/5
of a percent of the mass of the atmosphere. That
being the case, it is unlikely that humidity
variation will have a great effect. On the other
hand, the natural pressure variation that we tend
to see do to weather changes is less than a
percent (I am remembering variation between about
29.8 and 30.0 inches of mercury, which is a little
over a 0.6% variation), so the added effect due to
moisture could in fact be a sizable, although not
dominant, factor in the pressure equation!
I believe wet air
would in fact be heavier and would thus add to the
air pressure, but I don't think the effect would
be very great. The difference between dry air (0%
humidity) and saturated air (100% humidity), if a
friend of mine did the calculations correctly,
would produce about a change equivalent to about a
third of the difference between commonly observed
extremes in barametric pressure. In other words,
humidity will play a part but cannot account for
that we see.
Relative humidity is the partial pressure of water
in the air divided by the vapor pressure of water
at the air temperature. Vapor pressure is the
pressure at which liquid is in equilibrium with
it's gaseous state; water at a given temperature
boils when the partial pressure of water is at or
below its vapor pressure (at 100 degrees Celsius,
the vapor pressure of water is one atmosphere).
The vapor pressure of water is relatively low at
room temperature, less than 0.1 atmosphere. So,
humidity (as defined) really doesn't seem to
depend on the air pressure. Air at high pressure
or lower pressure with the same humidity and
temperature would have the same amount of water in
I don't know much about weather, so I
can't really say much about the relationship
between air pressure and humidity. As I recall
though, high pressure seems to keep storms and
moisture away whereas storms seem to move into low
pressure areas. This would seem to explain your
discovery that humidity in inversely proportional
to air pressure. If I can come up with a better
answer I'll let you
think a better way to think about relative
humidity is that it is the ratio between the
amount of water in the air and the amount of water
that can be stored in the air. 100% humidity
would mean that the air is holding as much water
as it can. The amount of water that can be in air
depends on temperature. Colder air can hold less
water than warm air.
It turns out that in a
high pressure area, air is flowing out to areas of
lower pressure. This air is replaced by air from
the upper atmosphere which is colder and thus
drier. So people inside a high pressure area
notice that the air is drier than usual.
Likewise, low pressure areas draw in warmer, moist
air so people in a low pressure area would notice
Storms occur when a cold
air mass and a warm air mass meet. Since the warm
air and cold air don't mix very well, one air mass
rises and the other doesn't. Which air mass
rises? When this air mass rises to high altitude
what do you think happens to its temperature? How
would this effect its humidity? What happens if
the humidity become higher than 100%?
the way, I made a mistake before when I was
talking about vapor pressure. A liquid boils at a
temperature at which the vapor pressure equals the
total pressure over the liquid. Thus water boils
at 100 Celsius because the vapor pressure of water
at that temperature is one atmosphere. Sorry
about any confusion I caused!
This is one of the things that go somewhat against
general experience. Humidity is defined to
actual partial pressure of water in air
at a given temperature
divided by partial
pressure of water in air in equilibrium with
liquid water at that temperature.
way of saying this is that humidity is the mole
fraction of water vapor in the air divided by the
mole fraction of water vapor in air in equilibrium
with liquid water.
During a rainstorm, or a
heavy fog, liquid drops are suspended in the air
(for longer or shorter times) and the air is fully
saturated with water vapor in equilibrium with the
water drops at that temperature. This is 100%
There can only be so much water
vapor in air at a given temperature, and this
amount increases very quickly with increasing
temperature. So 100% humidity means different
mole fractions of water vapor in the air at
different temperatures. Generally, when an
atmosphere at 100% humidity at a high temperature
is cooled to a lower temperature, liquid water
condenses - that is, it rains.
air is actually less dense than dry air. If you
think about air as an ideal gas, there is a simple
relationship between the density and the average
molecular weight of the air. Since the molecular
weight of air is about 29 gr/mol and water is 18
gr/mol, increasing the fraction of water in the
air decreases the average molecular weight, and so
decreases the density.
(Pressure x Molecular Weight)
(Temperature x Gas Constant) = density
wet air is less dense than dry air, until it
starts to condense.
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