## Sunday, July 15, 2012

### Micro States are Not in Micronesia

Note:  I may come back to proof or expand this:

Since I got into an interesting discussion on what heat is, a kinda important subject in physics, I used the old standby joke about falling in an elevator, "it is not the fall, it is the sudden stop that kills ya."  Temperature is an indication of kinetic energy, but not all kinetic energy.

Kinetic energy is motion. Motion does generate heat.  It is resistance to motion that generates heat.   An elevator falling has potential energy even though it is moving, it doesn't release energy until it moves or attempts to move something else which is transferring energy.  So heat is related to energy transfer not energy proper.  Anytime energy is transferred there is a loss associated called Entropy so there will be heat.

An Austria Physicist, Ludwig Boltzman figured that out and determine that there are tiny little energy transfers in substances that are important.  He worked out the Boltzmann constant which not surprisingly has the units, energy per absolute temperature, degrees Kelvin.  Energy per Kelvin are the units for Entropy.

Boltzmann's constant turned out to be the bridge between physics and quantum physics, classical mechanic and statistical mechanics or macro physics and micro physics if you prefer.  Those were grand old times in physics and Boltzmann was THE man for a while.

This lead to the discovery of the source of heat energy in an atom.  A monoatomic gas has three degrees of freedom, space or the Cartesian coordinates up, right and in which are allowed directions of motion.  The atom still doesn't contain measurable heat unless it changes direction as in a collision with something, another atom or a container.  So if the container is large enough and the number of atoms small enough, the atoms could move at any speed they like and there would be no measurable heat until the atom reached the wall of the container.

That concept is useful for most of physics, everything we can see or measure depends on the changes in the direction of something.  Only one problem, just because we can't see it or measure it does not mean it is not there.

Einstein figured that out and mentioned that something is missing, time.  No matter how big the container is, sooner or later that atom is going to hit something.  Einstein correctly figured out that that places a limit on how fast the atom can travel, the speed of light.  If the atom moved faster than the speed of light it would disintegrate.  That is a pretty hard limit.  If the atom disintegrated, every tiny building block of that atom would be measurable energy as it flew off into space.  So time, as in how fast the atom can travel, is another boundary of matter and energy.  Every part of the atom is a degree of freedom only measurable as heat energy when there is a change.   Since the speed of light is the limit, E=mc2   which means the smallest unit of mass is proportional to the smallest unit of energy by,  E/c2.  If you knew what the smallest unit of energy or mass was and could prove it, you would be a hero in physics.  Since Einstein had to add another dimension for relativity, you probably will need another dimension or so for that exotic new discovery of say a graviton.

Going back to the larger micro world, if the molecule was diatomic, two atoms in a bond, the molecule has more degrees of freedom.  Atoms in a smaller molecule, like hydrogen may be able to move more while heavier atoms might be more tightly bond and could move less, but since they have more degrees of freedom to move, they can hold more energy which means they have a higher heat capacity.

The next level is more complex three and more atom molecules.  Each new atom in the bond adds more degrees of freedom to move which means there are more ways to stop moving or change direction of motion.

One atom three dimensional space, three degrees of freedom to move.

Two atoms, three dimensional space plus three directions of rotation in that space, 6 degrees of freedom.

Three atoms, three dimensional space plus three directions of rotation in that space, plus three vibrational directions, 9 degrees of freedom.

Not all of these degrees of freedom matter though or at least to some don't matter.  A single atom can spin in any direction.  Since that spin direction doesn't tend to release energy, it doesn't tend to matter.  With a diatominc molecule, end over end rotation matters, but spinning like at top doesn't tend to release energy so it doesn't tend to matter.  If a molecule is not symmetrical in any orientation, then all of the possible degrees of freedom tend to release energy so they tend to matter.

If you have ever played with a ball, you know that spin does matter sometimes, so it is not smart to just forget about that degree of freedom that generally doesn't tend to matter until it does :)

When it comes to Green House theory, note the small "t", the degrees of freedom that allow the release of a photon of energy are the only ones that appear to matter.

If you look at the Wikipedia link for the Boltzmann constant you will find that the number of microscopic degrees of freedom when considered with the macroscopic constraints, results in a formula for S, Entropy,

From Wikipedia, "

In statistical mechanics, the entropy S of an isolated system at thermodynamic equilibrium is defined as the natural logarithm of W, the number of distinct microscopic states available to the system given the macroscopic constraints (such as a fixed total energy E):
$S = k\,\ln W$
This equation, which relates the microscopic details, or microstates, of the system (via W) to its macroscopic state (via the entropy S), is the central idea of statistical mechanics. Such is its importance that it is inscribed on Boltzmann's tombstone.

Now here is the fun part, the Boltzmann constant was actual never solved to the accuracy needed to be a true constant by Ludwig Boltzmann.  That was done years later by Max Planck.

So now think about what is being measured when you measure heat energy.  If you have a thermometer inserted or in contact with a fluid or solid, you would be measuring the collisional energy transferred to the material in the thermometer.  If you are using a non-contact thermometer, you would be measuring the energy transferred to the instrument by some other means than direct collisional contact.  If the instrument were in a vacuum, then the thermometer would only be measuring photons released by the object that struck the instrument.  If you are using a non contact thermometer inside of the object, you would have to compensate for the "contact" energy to determine the "non-contact" energy or the photons escaping from the object being measured.  The desired "non contact" energy would be Entropy or energy lost from the object being measured.

What happens when we add more CO2 to the atmosphere?  We are adding more molecules with more micro states depending on their degrees of freedom.  The initial Entropy due to CO2 would be k*ln(Wco2), after doubling CO2 the final entropy due to CO2 would be k*ln(2Wco2)

So Ludwig Boltzmann with the help of Max Planck provided an alternate method of looking at global warming over a century ago.