Article pubs.acs.org/jchemeduc
Hurricane Ike versus an Atomic Bomb Earl F. Pearson* Department of Chemistry, Middle Tennessee State University, Murfreesboro, Tennessee 37132, United States ABSTRACT: The destructive potential of one of nature’s most destructive forces, the hurricane, is compared to one of human’s most destructive devices, an atomic bomb. Both can create near absolute devastation at “ground zero”. However, how do they really compare in terms of destructive energy? This discussion compares the energy, the power, and the power per unit volume of Hurricane Ike with “Little Boy”, the smaller, in terms of TNT equivalent, of the two nuclear bombs used during World War II. By far, Hurricane Ike wins on the basis of energy comparison. However, on both power and power per unit volume, Little Boy wins. The details of the calculations are presented and the tremendous redistribution of energy that is accomplished by evaporation and condensation of water is dramatically illustrated by this discussion.
KEYWORDS: High School/Introductory Chemistry, First-Year Undergraduate/General, Environmental Chemistry, Public Understanding/Outreach, Applications of Chemistry, Atmospheric Chemistry, Nuclear/Radiochemistry, Thermodynamics, Transport Properties, Water/Water Chemistry
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courses, such as inorganic chemistry or physical chemistry, could be required to submit the detailed calculations and verify the results presented here as a homework assignment. For many years, I have summarized the results presented here any time heat of vaporization (ΔvapH) of water is discussed in any of my courses. I now plan to give my students copies of the article and put one question on the next exam from the paper.
he destructive potential of one of nature’s most destructive forces, the hurricane, is compared to one of human’s most destructive devices, an atomic bomb. Both can create near absolute devastation at “ground zero”. However how do they compare in terms of destructive energy? This discussion compares the energy, the power, and the power per unit volume of Hurricane Ike with “Little Boy”, the smaller of the two nuclear bombs used during World War II. This discussion is appropriate for the first course in chemistry at either the high school or college level, as well as for more advanced courses such as inorganic and physical chemistry at the college level. It provides an interesting application of the concepts used in teaching unit conversion. It is especially useful in teaching complex unit conversions, for example, converting distances usually measured in miles (mi) to volumes in cm3. It requires the use of the density and volume of water in cm3 for conversion to mass for determining the enthalpy involved in vaporizing and condensing the volume of rain produced by a hurricane. Depending on the level of the course, the material can be presented in lecture in detail or as a summary of the results and a reference to this article. If you say nothing more than “A 1 inch rainfall over a one square mile area has an energy equivalent to 2.5 nuclear bombs,” you will immediately spark interest in your students. Energy transport through water evaporation and condensation would also make a very interesting addition to the discussion of the hydrologic cycle in an environmental chemistry course. Students in advanced © XXXX American Chemical Society and Division of Chemical Education, Inc.
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ENERGY OF HURRICANE IKE Hurricane Ike1 is shown in Figure 1 as the eye made landfall in the Houston−Galveston area at 2:10 a.m. CDT, September 13, 2008. Ike was expected to produce rainfall quantities of 5 to 10 in. (0.13−0.25 m) over eastern Texas and extreme southwestern Louisiana, with isolated quantities of 15 in. (0.38 m) possible. Tropical storm force winds extended 275 mi (443 km) outward from the center. The diameter of the storm was greater than the distance from Richmond, Virginia to Boston, Massachusetts, 546 mi (879 km).2 Assuming a circular pattern, the area occupied by Ike is estimated to have been 2.38 × 105 mi2 (6.16 × 1011 m2) or approximately 9.54 × 1014 in2. If it is assumed that the average rainfall in this area was 7.5 in. (0.19 m), the volume of water falling over the area is 7.2 × 1015 in.3 (1.2 × 1017 cm3). From the density of water, this was approximately 1.2 × 1017 g of water (6.5 × 1015 mol). Although the heat of vaporization (ΔvapH) of water is readily found in literature, it is a good exercise for students to calculate
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When 1.0 kg of U-235 fissions by the equation shown, 8.5 × 1010 kJ is released.5 This energy is equivalent to the explosion of 20 kilotons (kT) of TNT (8.5 × 1010 kJ × 2.39 × 10−10 kT/ kJ). The Little Boy nuclear bomb explosion that helped to end World War II released 6.3 × 1010 kJ of energy, the explosive equivalent of about 15 kT of TNT.6 Hurricane Ike was estimated above to have released 2.9 × 1017 kJ, more than 4.6 million nuclear bombs! Students find it unbelievable that a 1 in. rainfall over a one square mile area releases as much energy as 2.5 World War II nuclear fission (“atomic”) bombs.
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POWER AND POWER DENSITY COMPARISONS Although energy released is an indication of potential destruction, power generation is a better measure. The rainfall from Hurricane Ike was estimated to be approximately 2.0 in./ h. 2 At this rate of rainfall, Hurricane Ike generated approximately (1.6 × 1011 kJ mi−2 in.−1)(2.38 × 105 mi2)(2.0 in./h)(1 h/60 min)(1 min/60 s) = 2.1 × 1013 kJ/s (kJ s−1 = kW). The energy of Little Boy was calculated to be generated in about 1 μs,6 releasing a power of (6.3 × 1010 kJ)/(1 × 10−6 s) = 6.3 × 1016 kW. Comparing power generation, Little Boy was equivalent to about 3000 Hurricane Ikes and 1850 (15 kT) TNT explosions. To get a better estimate of destructive force, we need to consider the power density, that is, power generated per unit volume. If we assume that Hurricane Ike was about 5 mi high (26,000 ft), its volume would have been approximately 1.2 × 106 mi3 (5.0 × 1015 m3). Hurricane Ike’s power density would have been (2.1 × 1013 kW)/(5.0 × 1015 m3) = 4.2 × 10−3 kW/ m3. The density of uranium is 19.05 g/cm37 and so the volume of the approximately 0.77 kg of U-235 that fissioned in Little Boy was approximately 40.3 cm3 (4.03 × 10−5 m3). The power density inside this atomic bomb was approximately (6.3 × 1016 kW)/(4.03 × 10−5m3) = 1.6 × 1021 kW/m3. The destructive potential of Little Boy within its critical mass was equivalent to about 3.8 × 1023 Hurricane Ikes, almost 2/3 mol of Hurricane Ikes!
Figure 1. Satellite infrared image showing landfall of hurricane Ike. Image credit NASA/JPL.2
it from the heat of formation of liquid water and gaseous water.3
H 2O(l) → H 2O(g) Δ vapH = [−241.818 − ( −285.82)] kJ/mol = 44.00 kJ/mol
The quantity of solar energy absorbed by seawater upon vaporization and subsequently deposited when the water vapor condensed in the clouds of Hurricane Ike was 2.9 × 1017 kJ. This is equivalent to 1.6 × 1011 kJ mi−2 in.−1 of rainfall (2.4 × 1010 kJ km−2 cm−1).
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ENERGY OF LITTLE BOY It is interesting to compare the energy of Hurricane Ike to the energy released in a nuclear fission explosion. Uranium-235 was used in the first nuclear bomb dropped during World War II. The spontaneous nuclear fission of U-235 induced by absorption of neutrons produces Sr-90, Xe-143, and additional neutrons, a net gain of two neutrons:4 235
U + 1n →
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90
Sr + 143 Xe + 3 1n + energy
CHEMICAL EXPLOSION (TNT) COMPARISONS Because nuclear fission explosions are often described by their kiloton TNT equivalent (kT), it is interesting to compare the power density of a nuclear explosion with the power density of its equivalent TNT explosion. The energy equivalent of Little Boy was about 15 kT TNT, 6.3 × 1010 kJ. The detonation speed of TNT is 6900 m/s8 and the density of TNT is 1.6 g/ cm3. The volume of a sphere containing 15 kT TNT is 8500 m3. A detonation beginning at the center of the sphere would take 1.8 ms to traverse the entire volume. The power generated is 3.4 × 1013 kW, and the power density in the explosion of 15 kT of TNT would be 4.0 × 109 kW/m3. Thus, the destructive potential of Little Boy, judged by power density, would be equivalent to 4.0 × 1011 times the destructive potential of 15 kT of TNT! Whereas the energy of Little Boy was equivalent to 15 kT of TNT, the power density within Little Boy when it exploded was 4.0 × 1011 times that of 15 kT of TNT. However, one cannot simply scale up and compare the destructive potential of Little Boy to 6.3 × 1012 kT of TNT to reach the same power density (destructive potential). Both the energy and the volume of the TNT (and the explosion time as well) will increase as the mass increases. Because density is an intrinsic property, the energy per unit volume does not change if the quantity of TNT is increased. However, the power
Other decay schemes also occur. The nuclear fission is regulated by the supply of neutrons with proper velocity for absorption. Each uranium atom that fissions produces two extra neutrons that can initiate two additional fissions in the next generation, creating a chain reaction as illustrated below in Figure 2. The circles represent 235 U nuclei and the arrows represent neutrons.
Figure 2. Chain reaction. B
dx.doi.org/10.1021/ed200712s | J. Chem. Educ. XXXX, XXX, XXX−XXX
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Table 1. Comparisons of Energy, Power, and Power Density Event
Energy/kJ
Hurricane Ike TNT explosion (15 kT) Little Boy Bomb (15 kT)
2.9 × 10 6.3 × 1010 6.3 × 1010 17
Energy Equivalent
Power/(kW)
Power Equivalent
Power Density/(kW/m3)
Power Density Equivalent
1 4.6 million 4.6 million
2.1 × 10 3.4 × 1013 6.3 × 1016
3000 1850 1
4.2 × 10−3 4.0 × 109 1.6 × 1021
3.8 × 1023 4 × 1011 1
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impressive. However, it would take about 2/3 mol of Hurricane Ikes concentrated into the volume of one Hurricane Ike to be equivalent to one Little Boy nuclear bomb. Try to imagine the destructive potential of the largest thermonuclear bomb! (Tsar, 50 million tons TNT, exploded by the USSR in 1961.) A video of a very small atomic explosion can be viewed on YouTube.11
density decreases because the time for the explosion of the larger sample would also increase. Thus, exploding 15 kT of TNT has a power density 9.5 × 1011 times greater than the power density of Hurricane Ike. These data are summarized in Table 1.
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SUMMARY
It should be emphasized that this article compares three very different energy-releasing events: a hurricane (condensation of water vapor), a nuclear reaction (nuclear fission), and a chemical explosion (bond breaking and making). Hurricanes generate their enormous quantity of energy over a long period of time, days or weeks, and are not explosions, per se. Their energy is generated by reforming the hydrogen bonds in liquid water that were broken by solar energy when the water originally evaporated, a phase change. Both nuclear fissions and chemical explosions may generate less energy than a hurricane, but generate it in fractions of a second. A nuclear fission explosion derives its energy from mass to energy conversion because of the mass lost when an atom fissions into other nuclei with a slightly lower total mass, E = mc2. The energy of a TNT explosion is chemical energy that appears as weaker chemical bonds in the some or all of the reactants are converted to bonds that are stronger in some or all of the products. The destructive effect of the explosion is actually determined by the brisance of the reaction, which expresses the rapidity with which an explosion generates its maximum pressure. The rapid increase in pressure generates a supersonic, highly heated, shock wave that results in the destructive potential of the explosion. A comparison based on the brisance of TNT and Little Boy might more accurately compare the destructive potential. The volume of the shock wave generated by Little Boy would be much larger than the volume of U-235 (40.3 cm3) used in these calculations and would lower the destructive potential of the nuclear fission explosion. However, nuclear fission is so much more destructive than its equivalent TNT explosion, a comparison using any reasonable volume for the fissionable material would remain astounding. Water is an unusual liquid responsible for moving tremendous quantities of energy around the planet. The average yearly rainfall on earth is estimated as 1.05 m/y, a volume of 5.1 × 1014 m3 of water evaporated and condensed each year.9 The mass of water involved is 2.8 × 1019 mol. The energy redistributed by the evaporation and condensation of this quantity of water is 1.25 × 1024 J/y. The earth receives 1.73 × 1017 W of power from the sun,10 amounting to a total of 5.5 × 1024 J/y. Thus, evaporation and condensation of water redistributes about 23% of the total energy received by the sun each year. Water in the seas is also heated by the sun, storing additional energy that moderates climate on the earth. The land surface absorbs thermal energy from the sun, but quickly radiates the heat at night. A typical hurricane redistributes the energy equivalent of several millions nuclear bombs; even a gentle rain redistributes the energy equivalent of about 2.5 nuclear bombs per inch of rainfall per square mile. The destructive force of hurricanes is
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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REFERENCES
(1) A more familiar hurricane could have been chosen, but there will always be the next more familiar hurricane. The relative order of the energy, power, and power density would be similar for any hurricane chosen for comparison with nuclear or TNT explosions. (2) Hurricanes and Tropical Cyclones. http://www.nasa.gov/mission_ pages/hurricanes/archives/2008/h2008_ike.html (accessed Oct 2012). (3) Moore, J. W.; Stanitski, C. L.; Jurs, P. C. Chemistry: The Molecular Science, 4th ed.; Thompson Brooks/Cole Publishing: Belmont, CA, 2011; p A39. (4) ChemistryA Project of the American Chemical Society; W.H. Freeman Co. Inc.: New York, 2005; p 188. (5) Burdge, J.; Overby, J. ChemistryAtoms First; McGraw-Hill Publishing Co.: New York, 2012; p 868. (6) General Chemistry Case Studies. http://www.chemcases.com/ nuclear/nc-09.html (accessed Oct 2012). (7) CRC Handbook of Chemistry and Physics, 53rd ed.; Lide, D. R., Ed.; CRC Press, Inc.: Boca Raton, FL, 1972; p B-151. (8) Encyclopedia. http://en.encydia.com/de/Trinitrotoluol (accessed Oct 2012). (9) The Physics Facebook. http://www.hypertextbook.com/facts/ 2008/VernonWu.shtml (accessed Oct 2012). (10) Hill, J. W.; Kolb, D. K. Chemistry for Changing Times, 8th ed.; Prentice Hall Publishing Co.; Upper Saddle River, NJ, 1998; p 350. (11) Nuclear Bomb. http://www.youtube.com/watch?v= H1sS1TmXF38&feature=related (accessed Oct 2012).
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