GEO165 METEOROLOGY

Kinetic Theory

We will use kinetic theory and the characteristics of molecules in GEO165 to explain a number of seemingly odd,
but elegantly simple phenomena that scientists encounter when investigating the atmosphere.

Some Atmospheric and Related Phenomena
Explained by

Kinetic Theory and Properties of Molecules

Evaporation and Condensation

Formation of Precipitation

Slippery Ice and Not-So slippery Ice

Why Does Ice Float?

Why Does Salt Melt Ice?

The Greenhouse Effect

Liquid Water at -40o

What shape is a falling raindrop?

Why is the sky blue?

How does a microwave oven work?



ASSUMPTIONS OF KINETIC THEORY:
1. All matter is composed of small particles.
2. Molecules are in constant rapid motion, unless at absolute zero (0oK).

3. The number of molecules is very large and molecules are so small that there is plenty of space between molecules. At

atmospheric pressures the average separation is about 10 molecular diameters. Unless molecules collide they do

not exert a force on one another.

4. Collisions are perfectly elastic. A collision is defined as ANY encounter close enough for
the forces of attraction and repulsion to interact; not just when molecules crash into one another (i.e. physically touch).
Perfectly elastic means that when two molecules collide the total KE remains the same, one molecule may gain KE,
but the other has to lose that same amount




Example 1: In a Gas
The most probable speed of an O2 molecule in the is 394 m/s (1417 km/hour, 881 mi/hr) at 25 oC.
The diameter of an O2 molecule is .339 nanometers (.339 billionths of a meter or 3.39 ten-billionths of a meter, 3.39 x10-10meter).
The mean free path (MFP) of O2 at sea level and 25 oC is 7.19 x10-8 meters.
The MFP is 212 times the molecular diameter and 22 times the average molecular separation.
The average molecular separation is 3.3 x10-9 meters (3.3 ten-billionths of a meter)
and the number of collisions the O2 molecule would experience is 5.8 x109 per second
that is -> 5.8 BILLION COLLISIONS PER SECOND!

Click this link to check out HyperPhysics and do your own calculations.


Example 2: Big Numbers
In 1 m3 of air at sea level (1013.25 mb) and 0oC
There are 26,877,618,225,750,776,665,516,051 molecules.
(2.69 x 1025 molecules m-3 that is 26.9 septillion molecules m-3)


If you were to spend a trillion dollars per day!!! it would take you
73.6 billion+ years to spend 26.9 septillion dollars.
How long has the universe been around?

Note the number of molecules is what calculations yield, however displaying it in

standard notation implies an accuracy well beyond our abilities so

scientific notation is preferred. The number above is the number

density of molecules for the given conditions.

 

Despite that large number only 1/1000th of the volume in the example above is occupied by matter, the rest of the volume

99.999% is empty space.

 



The numbers are mind-boggle-ing-ly large (and small),
the velocity is breathtakingly rapid,
the motion is terrifyingly chaotic
and apparently there is no plan.

WELCOME TO THE WORLD OF THE MOLECULE!

Credit for these descriptions
C. Bohren and B. Albrecht Atmospheric Thermodynamics Oxford University Press (1998)




Assumption, not correct but close enough, molecules collide with each other but the collisions are perfectly 

elastic, i.e. when molecules collide, the faster molecule loses energy and the slower gains. None is lost to

translation and  when colliding with a wall of a container, no energy is lost by the molecule it merely bounces off the wall.

 

 

Because the number of molecules is so large and the molecules so small we use the "average velocity" of the

molecules and that is proportional to temperature. Some molecules are moving much faster, some are moving much slower, the

average velocity is proportional to temperature.

 

In liquids, specifically water, increasing the velocity of a molecule can enable it to escape the attractive forces of

surrounding molecules. This is called evaporation and because the kinetic energy of the molecule was increased for it to

escape the total kinetic energy of the liquid is less, the average molecular velocity slower and the temperature lower.

Evaporation is therefore a cooling process. When soaking wet right out of the shower (i.e. naked) stand in front of an

Electric fan on a hot and humid summer day, then you will understand.

 

Evaporation depends on the thermal state (primarily but there are other factors) of the water. Condensation depends on the state

of vapor in the air above a water body. Evaporation and condensation are therefore DISTINCT PHYSICAL PROCESSES with equal

and opposite thermal effects on the body of water.

 

Example 3: In Liquid Water
In 1 m3 of water there are 30,000,000,000,000,000,000,000,000,000 molecules.
(3.0 x 1028 molecules m-3) (30 octillion m-3)

The number above is the number density of molecules in liquid water.

At an air/water interface (0oC, 1013.25 mb or hPa) the number density of molecules in the liquid is 3.0 x 1028 m-3
and the number density of molecules in the air is 2.69 x 1025 m-3 .

So...the ratio(3.0 x 1028/  2.69 x 1025) = 1,100 tells us there are 1100 times more water-water interactions
than water-air interactions between molecules where evaporation and condensation occur - at the air/water interface.


To a very good approximation the thermal state atmosphere
is at best of minor importance in evaporation.

 

However air can be considered a kinetic energy delivery system for the process of evaporation, especially on windy days.


Just like with any object with mass for a molecule in a gas to accelerate (change velocity or direction) a force must act on it. The
more massive a molecule is the more energy required to attain the same speed as a less massive molecule.

Keep this in mind when looking at the graph below showing the most probable speeds for atmospheric molecules..


Using the graph decide which molecule is the most massive? Which is the least massive? Why?

Note: Dry air includes all the permanent gasses of the atmosphere, O2, N2
and the others. By weighting the velocity based on proportion of the gas in the atmosphere the
line for dry air represents the average velocity for the dry air components.


Adding energy to a volume of air will increase the velocity (rate of translation)
of the molecules, but that is not the only way molecules can move.

Molecules can be made to rotate and vibrate, and just like anything else with mass to get vibrational movement and rotational movement energy is required. This is be the reason the “greenhouse effect” works with carbon dioxide and water vapor.

 

Vibrational Modes of Oxygen (O2) and Nitrogen (N2)

O2

N2

 

 

 

 

O-O Stretching
Activated by UV wavelength radiation

 

N-N Stretching
Activated by UV wavelength radiation

 

 

 

 

 

Vibrational Modes of Water Vapor (H2O)

 

 

 

 

 

 

O-H Symmetric Stretching
Activated by Infrared

wavelength radiation

O-H Asymmetric Stretching
Activated by Infrared

wavelength radiation

H-O-H Bending
Activated by Infrared

wavelength radiation

 

 

 

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Movies courtesy of Peter R. Bannon at Penn. State U.

TRANSLATION MOVIE

ROTATION MOVIES

VIBRATION MOVIES

ARGON 

CO2
O2
N2
H2O
O3  

CO2
H2O
O3  

 

The States of Matter

SOLID

LIQUID

GAS

Solid - a substance whose particles have a low kinetic energy. The particles of a solid are held close together by intermolecular forces of attraction called bonds. Because the particles are so close together, they appear to vibrate and jiggle around a fixed point. When the temperature of a solid is raised, the velocity of the particles increases. The collisions between the particles occur with greater force, causing the particles to more farther apart and eventually he bonds are broken. The ordered arrangement of the solid breaks down and a change in physical state occurs.

Liquid - a substance whose particles have enough kinetic energy to stretch the intermolecular forces of attraction. Collisions between the particles a strong enough to force the particles apart. The particles appear to have a moving vibration because they are still under the influence of the intermolecular forces of attraction. As the temperature of a liquid is raised, the velocity of the particles increases. The collisions eventually become so great that the particles break all intermolecular forces, begin moving independently between collisions, and a change in physical state occurs.

Gas - a substance whose particles have enough kinetic energy to break all intermolecular forces of attraction. The particles of a gas move independently of each other. The particles move at random because they have overcome the intermolecular forces of attraction. When a gas is raised to extreme temperatures, over 5000 oC, they have so much kinetic energy that their collisions will break electrons out of the atoms, and a change in physical state occurs.

Plasma - a substance whose particles have enough kinetic energy to strip electrons from molecules and atoms. A plasma is a special form of a gas made of free moving ions, and electrons. Plasmas are a 4thstate of matter like a gas but with many unique properties. The density and temperature of plasmas vary widely. Plasmas are encountered in meteorology when studying aurora and lightning to name two.

VARIOUS FORMS OF PLASMA