As we watch the the global warming gurus - presently impaled upon their thermometers and writhing unhappily in an atmosphere where the temperature just refuses to go up (see, for examples,
(N
2), 2,075 are oxygen (O2), 120 are water (H2O), 93 are argon (Ar), and 3 to 4 are carbon dioxide (CO2). This assumes certain standard and typical conditions (see International Critical Tables 1, p 393, 1926). There are also traces of neon, helium, krypton, hydrogen, xenon, ozone, radon, and other gases (see CRC Handbook of Chemistry and Physics). These values change with altitude primarily by decreases in H2O, O2, and Ar and increases in hydrogen (H2) and N2.Most atmospheric molecules (N
2, O2, and H2) are diatomic, meaning that each contains two atoms joined by a chemical bond. O2 molecules are about 4 angstroms or 4x10-8 centimeters long. Lined up end to end, there would be about 60 million O2 molecules per inch.The "temperature'' of a gas such as the atmosphere is defined as the mean (average) kinetic energy of the molecules in that gas.
The kinetic energy of an object (whether of an airplane full of envi-ros winging their way to another meeting about the immorality of energy use or of a single molecule innocently bouncing around in your breath) is one-half its mass times its velocity squared ( E = 1/2mv
2 ).For a monatomic gas with only only one atom in each unit, the kinetic energy arises only from translational motion - movement of the atom from place to place in three dimensions. For a diatomic molecule, additional motions are possible. These are rotational motion - the two atoms in the molecule spin about their mutual center of mass - and vibrational motion - the two atoms vibrate back and forth by stretching and compressing the chemical bond that holds them together. (Imagine the molecule as a tiny barbell suspended by a string from the bar between the two weights. Now, if you hit one of the weights, the barbell rotates. If, however, the weights were connected by a spring instead of a rod, you could also pull them apart and let go with the result that the two weights would vibrate in and out with respect to one another.) As heat is added to a gas, that energy must be stored in the gas. The storage that takes place in the motion of the molecules of a diatomic gas is in the translational, rotational, and vibrational motions of the molecules of that gas. Some molecules can store more heat than others with the same velocities of motion because they have more or heavier atoms or atoms that are more free to move under certain conditions.
Looking at this another way, each diatomic molecule has two atoms that can move and therefore more degrees of freedom to engage in motions with kinetic energy. The two atoms, however, are bound together and are, therefore, not entirely free. Therefore, it is useful to categorize the new potential motions as rotations and vibrations of the molecule. The more energy that is added to the gas and stored in the gas, the faster its molecules move and therefore the higher its temperature.
For historical reasons, we use temperature scales of degrees Fahren-heit (°F), Centigrade (°C), or Kelvin (°K) and varying definitions of temperature. These can all be related to average molecular kinetic energy by appropriate constants and conversion procedures.
The theory of the behavior of gases was conceptualized in the early 1700s and elegantly worked out by several great theoreticians, culminating with James Clerk Maxwell's classic paper in 1859. These scientists did such careful work that their calculations were mathematically perfect. So, they should have obtained perfect agreement with experiments on simple gases. Maxwell, however, realized that there was something wrong with their molecular model because his calculations of the energy that could be stored in a gas were not in agreement with actual experimental measurements. Feynman quotes Maxwell as saying ten years later, "I have now put before you what I consider to be the greatest difficulty yet encountered by the molecular theory.'' (See
Feynman Lectures on Physics by R. P. Feynman, R. B. Leighton, and M. Sands, Volume 1, p 40-9 (1963), published by Addison-Wesley.To Maxwell and his contemporaries, it appeared that certain motions of molecules, allowed at high temperatures, became impossible at lower temperatures. They had no explanation for this effect. The effect is shown in Figure 1 which is adapted from
General Chemistry third edition by L. Pauling, p 364 (1970), published by W. H. Freeman.
The experimental heat capacities in Figure 1 show perfect agreement with the theoretical value of 2.5 for the monatomic gases, He, Ne, Ar, Kr, and Xe. Only, however, at very high temperatures do the experimental values for the heat capacity of the diatomic gases reach the value of 4.5 equivalently calculated by Maxwell. (The heat capacity arises here as 1.0 units from thermal expansion; 1.5 from translational energy; 1.0 from rotational energy; and 1.0 from vibrational energy.) The problem was that Maxwell and his colleagues did not have access to quantum mechanics because it had not yet been discovered. Figures 2 and 3 show the quantum mechanical explanation that now allows theoretical calculations to agree with experiment. These figures are from Spectra of Diatomic Molecules by G. Herzberg, p 99 and p 107 (1950), published by D. Van Nostrand Company.
Figure 2 shows the distances between the H
2 atoms in a hydrogen molecule as they vibrate back and forth (horizontal axis) vs. the energy contained in that vibration (vertical axis). Quantum mechanics shows that these vibrations can only take place at discrete energies and are not allowed for energies in between these discrete levels. These levels for H2 are labeled 0, 1, 2, 3, and so on in the figure. At high levels, vibration tears the molecule apart as indicated by the gray area at the top.Until the temperature is sufficiently high to cause some of the hydrogen molecules to vibrate vigorously enough to be in level 1, they all must stay in level 0. They cannot, therefore, store additional energy in vibration when at low temperature.
As shown in Figure 3, molecular rotation is also quantized. The first five vibrational levels (0, 1, 2, 3 and 4 labeled '
v') are those in Figure 2. Superimposed on each of these, we see the sets of rotational levels allowed in each vibrational level. No energy can be stored in rotation until the temperature is high enough to provide energy for the molecules to move to the next higher quantized 'J' rotational state above 0.
Returning to Figure 1, we see that H2 is unable to store energy in either vibration or rotation at temperatures between its boiling point (about 20 °K) and 50 °K. Above 50 °K, H2 gradually accumulates rotational energy storage which is mostly complete above 400 °K, but is still unable to store energy in vibration. Above 700 °K, vibrational energy storage begins to become possible for the more energetic H2 molecules. The other diatomic molecules shown in Figure 1 have different curves because their atoms have different masses and chemical bonding ability, so their quantum levels have different spacings.
Different individual molecules in the same gas can have differing energy contents at different times. The actual detailed theory calculates distribution functions for the different energy configurations. These functions give the indicated overall results.
The O
2 and N2 (and, at high altitude, H2) which comprise most atmospheric molecules have quantum levels such that, at ordinary temperatures of 0 °C to 100 °C (32 °F to 212 °F or 273 °K to 373 °K), additional rotational energy can be stored but vibrational energy cannot. Too few molecules are able to reach energies high enough to occupy the first vibrational level above the 0 state.As our atmosphere warms and cools, therefore, the diatomic molecules of nitrogen, oxygen, and hydrogen and the atoms of argon store and release heat energy by increasing or decreasing their average translational velocities. In addition, nitrogen, oxygen, and hydrogen are able to store energy by increasing their rates of rotation. At ordinary temperatures, however, increases in molecular vibration do not take place.
Energy transfer to atmospheric molecules occurs primarily by collisions between those molecules and the molecules of warmer bodies and by absorption of energy from electromagnetic radiation.
As you read, you cannot see the tiny diatomic benefactors in the air between your eyes and this page. If they were not there, however, tirelessly bumping into your body and storing and releasing energy by increasing or decreasing their rates of translational and rotational motion, you would be immediately uncomfortable and soon dead.
In these few words, we can communicate only a little about the subject of energy storage in atmospheric gases and the measure of that storage - which is called 'temperature.' This is, however, a very beautiful and exact part of physical science. If you know a student 16 years of age or older to whom you wish to give a lasting gift, get copies of the three books listed above (as sources for Figures 1 to 3) from your library or from interlibrary loan and suggest that he study these books until he understands this subject and all of its associated mathematics.
Notice three things. First, as complicated as this simplified explanation may sound, it is child's play in comparison with understanding the atmosphere of the whole earth - an ability the global warming industry falsely claims to have acquired. Second, Maxwell insisted that theory agree with experiment if theory were to be considered correct. Global warming calculations have a common characteristic - they do not agree with experiment because they fail to agree with measured atmospheric temperatures. These calculations are fundamentally flawed and cannot be corrected with fudge factors designed to give a politically desirable answer. Third, we are very fortunate to live at a time when the world that surrounds us has been enhanced by science. In previous times, people lived out their entire lives without ever having an opportunity to know about and enjoy the truth about the air around them.
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Vol. 23, No. 1
Newsletter: Access to Energy Newsletter Archive Volume: Issues Issue/No.: Vol. 23, No. 1 Date: September 01, 1995 12:45 PM Title: Secrecy
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