applications anJ analogies Revealing the Secret of the Arctic Bomb Earl F. Pearson Western Kentucky University Bowling Green, KY42101 Arctic bombs and hurricanes can provide what appears to be contradictions to concents commonlv taueht to chemistry students. According to ihe ideal gasjaw, the pressure of a confined eas (air) rises with an increase in temnerature. With a n increase in pressure of a fmed amount of gas at constant volume. the temnerature also will rise. However, within an extremely cold high pressure air system, the exact onwsite .. occurs. When a n arctic bomb develops. - . the atmospheric pressure increases as the temperature drons. This anparent contradiction offers a good way to prohde students with a better grasp of the &s laws a n d their limitations. During winter, as heat is lost to space, the cooling rate and low temnerature reached at night depend on the latitude and loEal environmental details sich as elevation, nearness to large bodies of water, and cloud cover, to name a few important factors. If the air within a region becomes trapped, extremely cold weather systems may develop. The temperature plummets, oRen ;caching record lows, and the atmospheric pressure often reaches record highs. This is the birth of an-kctic Bomb. One such arctic bomb developed over Siberia in the former USSR during January of 1989, slowly moved into Alaska, and remained isolated for about two weeks. During this period, overnight lows reached -86 'F (-66 'C) at McGrath and the atmospheric pressure a t Northway reached 31.85 in (Hg) (809 torr), the highest pressure ever recorded in North America ( I ) . While this system broke many records across Canada and the United States, these arctic bombs are not unusual. Weather forecasters watch for their development in the north each winter and carefully monitor their intensity. The movements of these systems are important considerations in long-range weather forecasts. The Great 1938 Hurricane When the atmosphere is gaining heat from the sun in summer, very warm low pressure areas develop, particularly over the southern oceans. These storm centers often develop extremely low atmospheric pressures with wind velocities that may reach 150 mph. On September 21, 1938, one such hurricane, so intense that i t was thought to be "impossible" (2),crashed ashore a t Long Island, hringine with it 25-35-ft tidal waves. The Great 1938 Hurricane, as i t came to be known, killed 700 people and injured thousands more. It destroyed or badly damaged 20,000 homes, 26,000 cars, and aimost 6,000 boats. ?he atmospheric pressure of 27.94 in (Hg) (710 torr) taken a t Bellport Coast Guard Station is the lowest official reading ever recorded on land in the Northeast (3). Presented at the 198th National ACS Meeting, Miami. September 1989. Featured on the ACS radio program: Dimensions in Science, "Weather and Chemistry",Tape #1547.
edited by
RONDELORENZO Middle Georgia Collage Cochran. GA31014
ADDliCatiOn of SimDle Gas Laws .. Both these atmospheric phenomena, the "arctic bomb" and the "monster hurricane" can be explained as applications of simple gas laws. However, the explanation g l l be more effective if an apparent contradiction is drawn between the student's understanding of gas behavior and the observed temperature-pressure relationship in these two examples. Ask the Students 1. What happens to the temperature of a gas as it is compressed to a high pressure? 2. What happens to the temperature of a gas as it is expanded through an orifice? 3. How are pressure and temperature related in an ideal gas svstem. 4. How are the temperature and the pressure related in "Arctic Bombs"? 5. How are the temperature and DreSSOE related in "Manster ~urricanes"? Scientific Principles versus Experience Valid scientific principles have now been brought into direct conflict with experience. As this apparent conflict is resolved, the student can learn a n important lesson. The conditions under which scientific laws are valid must be stated, understood, and rigorously enforced before predictions can be expected to be valid. Good scientists learn this lesson earlv and well. How c a n a n arctic bomb combine high pressure and low temnerature? The temoerature and Dressure annear to beh a 4 just the opposiie to what is'expected'fbr a fixed amount of ideal eas in a rieid container. With the arctic bomb, we are not dealing k t h a n enclosed system, but with a n onen atmospheric system. When the air cools, the volume decreases. When you measure atmospheric pressure, what you actually are measuring is the weight of the air over a unit cross-sectional area. Imaeine .. a one-souare foot area on the surface of the earth extending all the way out through the atmosphere. The weieht of that air under normal omlitions would he about 2160 lb (15 lWin.2x 144 in2)When . the air cools, the column of air cools. Its volume decreases. Other air from the surroundings is brought over that one square foot area. As the air cools, the weight of the atmosphere over that constant area increases rather than decreases. That is the explanation of what happens to pressuretemperature relationshipri. Surrounding air moves in to replace air that is cooling and shrinking in an arctic bomb. This produces the higher pressure and colder temperature simultane(~usly. In class, we usuallv talk about closed svstems, a confined gas with s o many grams in a container. We ;arely talk about open systems. An open system allows matter to enter and leave. The relationship between temperature and pressure in the atmosphere can be understood using the ideal gas laws applied to an open system. Think of the atmosphere as being composed of imaginary rectangular boxes. The area of the base of each box is the same, but the boxes have different heights so that the mass of air is the same within each box. The height of each box decreases as the pressure inside i t increases. The atmospheric pressure Volume 70 Number 4 April 1993
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decreases with altitude, because there are fewer boxes (less weight) between the high altitude point and the edge of the atmosphere. Experimentally, we find that a gas tends to flow spontaneously from regions of high pressure to regions of lower pressure. However, air near the surface does not spontaneously flow to a higher altitude, because boxes near the surface experience a greater force due to gravity. The difference in the force of gravity at each altitude is exactly sufficient so that ifa box from any altitude were brought to the surface, its height would shrink to the same height as other boxes on the surface, and its new pressure would become equal to the pressure inside a surface box. In this manner, vertical pressure gradients are stabilized by the corresponding vertical gradient in the force of gravity. If something Get stream) stacks more boxes over a given area than over & surroundinm, the atmospheric over that area will be greater than the pressure in the surroundine area. What about the exoected lateral movement of air frim these high pressure rigions to the lower pressure sumundines at the same altitude? As lone as the atmosphere is cooling (winter) the bulges in t h i atmosohere (hieh oressure reeions) cool faster than the vallevs (surround&). If the ~hhnkin~caused by faster wolingk the high pressure region is equal to the expansion caused by diffusion out of it due to the pressure difference, the lateral pressure gradient is stabilized by the lateral gradient in cooling. As in the gravity example above, if a box from the surroundings were brought into the high pressure region, it would cool to the same temperature. Its height and pressure would be the same as other boxes in the high pressure region at the same altitude. However, unlike the gravity example, the pressure inside a high pressure region will increase or decrease depending on whether the cooling rate is above or below this critical value. During winter in the northern hemisphere, the cooling rate at far northern latitudes exceeds this critical value and high pressure regions intensify ifthey do not move south where the cooling rate is below that needed to stabilize them. For those interested in the mathematics, a simplified, noncalculus derivation of the atmospheric pressure-atmospheric temperature relationship follows. P=fM P(atm)= (mg)lA P(atm)= (nMg)lA where f = force; A = area; m = mass; g = gravitational acceleration constant; M = average mole mass of air; n = number of moles If the air is originally at an internal gas pressure, p, and temperature, TI, then the number of moles, (nl) in a column of air reaching from the surface into space is: n1 = pVIRTl where V = volume of the air column. But since v=Ah where h = height (thickness) of air. Then nl =pAhlRT1 and the atmospheric pressure may now be written as Pl(atm)= pMghlRT, Now suppose the air is cooled at constant internal gas pressure, p, from TI to Tz. The number of moles, nz, over the same area (A) is: 316
Journal of Chemical Education
nz = pAhlRTz
and the new atmospheric pressure is:
Notice that
and
Therefore
P(atrn)T= constant and P(atm)= eonstant/T That is, the atmospheric pressure is inversely proportional to the absolute temperature of the atmosphere (4). Contrast this result with the internal pressure-temperature relationship for a closed (fixed mass and volume) ideal gas system:
and, since nRNis constant
or the pressure is directly proportional to the absolute temperature. This relationship was tested using data (5)for Oklahoma City, Oklahoma (7:00 EST) during February 114, 1989, during the passage of an arctic bomb. The P(atm)Tproduct averaged 277,200 (mbar*K) with a standard deviation of only 1.5%, which is in reasonable agreement with prediction. Why Arctic Bombs Develop One "secret" is revealed, but another one remains hidden. Why does the temperature continue to drop and the pressure wntinue to rise when the jet stream traps the air of a northern region in winter? That is, why do "arctic bombs" develop and why do they wntinue to intensify? The answer to this question is qualitatively simple. The atmosphere is a gigantic "sea" of fluid air containing ripples or waves like waves on the oceans. The crests correspond to high pressure regions, and the valleys correspond to regions of low atmospheric pressure. The jet stream steers these regions, trapping them at times, and occasionally shoving them along. While the thermal conductivity of eas oressure. the thermal a eas is inde~endentof internal . co>ductivity of a column of air is proportional to the amount of matter in the column. Aa the atmosoheric oressure increases, a greater mass of air is present in the wlumn between the Earth's surface and the cold of space. Thus, a high atmospheric pressure region is a better thermal wnductor than its surroundings at lower atmospheric pressure. Cooling occurs faster in the high pressure region than in its surroundings. Air is drawn into the cooler region to replace air that is cooling and shrinking. This causes further increases in the atmospheric pressure. The cycle of cooling and increasing atmospheric pressure followed by more rapid cooling and faster increasing atmo-
spheric pressure continues as long as the high pressure system remains trapped. If the jet stream does not move, these high pressure systems continue to intensify, a n arctic bomb is born, and conditions are favorable for its continued growth and development. Acknowledgment I would like to express my appreciation to the reviewers and the Editor of this Feature for many helpful sugges-
tions for improving the manuscript and to Judy Dee1 for typing the manuscript and the revisions. ~iteratureCited
1. ~ a t i a n aweather l summary, NationalOceanicand~tmoapherie~ d ~ i n i s t ~ ~ t i ~ ~ . ~ ~ . tional Weather Seruiee, Washington, DC, Jan. 29-Feb. 4. 1989. 2. W s g n e ~ AJames. . Weathrw& 1988.41, 219. 3. Ludlum. Davis M. Weolherwlse 1988.41.214.
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