Ideal Gas Law in Meteorology
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Simple equation that relates pressure, temperature, and density or volume
Very relevant to meteorology
Density: mass of air per unit volume.
Decreases as one moves up in
atmosphere.
Pressure: weight of air above you.
Decreases as one moves up in
atmosphere.
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Equation given by pV = nRT
o Where p = pressure, V = volume, n = # of moles of gas, R = gas
constant, and T = temperature
Other ways to write it
o pV = mRdT, where m = mass, Rd = gas constant for dry air
o Also p = mRdT = p = ρRdT
o
V
o density of gas () = mass/volume
For our purposes, since the constants are exactly that—we can ignore them
and just look at the relationship between T, p, and ρ or T, p, and V
Giving:
o p X V is proportional to T
 any change in temperature must be balanced out by the product
of pressure and volume
 If temperature is constant, p and V are inversely proportional
(if one goes up, the other must go down)
o p is proportional to  X T
 any change in pressure must be balanced out by the product of
temperature and density
So…
o Adiabatic compression states that as air sinks, it warms due to
compression.
o Adiabatic expansion states that as air rises, it cools and expands.
Who cares?
- Explains why
o Marshmallows expand in the microwave
o Bags of chips/shampoo bottles expand when you fly or drive up to the
mountains
o Cold objects tend to shrivel up
o Etc.
Questions to think about: Illustrate the answers using the gas law
1) If the temperature of air rises, but the volume stays the same, what happens to
the pressure?
2) If the temperature of an object falls, but the density stays the same, what
happens to the pressure?
3) If the temperature of an inflated balloon is cooled, but remains at the surface,
will the balloon expand or shrink?
4) As a parcel of air (a uniform volume of air) rises up in the atmosphere, what
will happen? What happens when the same parcel sinks?