High School Mathematics-Physics SMILE Meeting 1997-2006 Academic Years Climate and Environment

15 September 1998: Karlene Kurth [Lane Tech HS]
She had an idea (source was an old Physics Teacher) to spice up the first experiment---instead of just measuring and avoiding a conclusion give a problem. Find the volume of a room and ask how long there will be enough breathable air. She showed a way of measuring the volume a person breathes. An inverted graduated cylinder in a pot all filled with H2O and a straw to breathe through to get air in the cylinder. Also units and conversion to a common measure could be discussed. One of the ways variables was that if several people were exterminated the others would live longer--of course the obvious variables---level of activity, etc. [5 breaths took 18 seconds and was about 1070 ml or about 1 liter. 2 -5 days was a typical conclusion .]

[editor's note: I have tried to emphasize significant places and accuracy as part of the conclusion. Using the correct device -Calipers for small distance, or using the floor tile as a gauge of distance, I have given something impossible to do with the equipment and see what they came up with--This is an interesting spin.]

Now with newer construction -plastic wrap, double glass windows, etc - there is much less air being changed in the homes. Where in an old home air was replaced in 15 min to 30 min, in newer houses it is much longer. This may cause problems when inside air is being used for combustion. Fireplaces and furnaces now often draw outside air and exhaust that air, avoiding serious problems with the inside air.

Radon gas [http://radon.com/radon/radon_facts.html and http://ace.orst.edu/info/extoxnet/faqs/indoorair/radon.htm] was also brought up as potentially very dangerous, even possibly worse than asbestos. Asbestos doesn't seem to be that deadly, and insurance settlements have been based upon highly questionable estimates of damages. [CNA asbestos settlement of \$2 billion dollars was based upon a premium paid of less than \$10,000.] The problems arising from asbestos removal can be much greater, because of airborne dust.

Radon as a chemical will not react but the problem is that it decays with a half-life of 3.4 days, and may cause serious respiratory damage in the lungs, since the Radon may stick to air sacs in the lung, and do serious damage there. The decay sequence for Uranium is the following:

Radon is formed by this decay of Uranium [present in coal and various shale rocks], and it seeps upward and into basements. Concrete is a fairly porous substance (tar is often placed on the under side of concrete to seal concrete) and if the air pressure is negative (less that outside) Radon is sucked out of the ground. A furnace using air from inside for combustion causes a negative pressure, allowing radon to be sucked in. It was mentioned that one of the products to reduce Radon was a pump to remove air from the basement if the air pressure dropped. Radon levels vary with the geographic area--what is underground and how easily it can escape.

The high voltage in a TV set (27 kV) attracts dust and with a Geiger Counter will show signs of the activity.

12 October 1999:  Discussion

• Why does dew condense on the rear window of a car [away from shelter] preferentially to the front window [close to the shelter]? Presumably, this happens because the rear window is cooler. In vacuum technology one removes noxious substances [such as water] with a "cold trap" on which it will condense [the equilibrium vapor pressure drops off dramatically with temperature]. [Water condensed on the protective outside screen of my new high-tech window, but not on the glass itself during the recent foggy days.]
• One gets fog, heavy dew, and condensation when the temperature of air drops below the "wet bulb" or condensation temperature - 100% relative humidity. By contrast, rain hail, sleet, and snow fall out of clouds when fronts collide ["lake effect" snow looks, feels, and shovels like real snow, but arises from moisture blown from the lake and onto the land]. "Freezing fog" or hoar frost is produced when 100% humidity is reached below 0 C. The spider webs, bushes, and dead flowers look like glittering gossamer "diamond necklaces" in the gleaming sun.  See  http://www.darklightimagery.net/newnature/hoarfrost.html. This effect [mentioned in "Silas Marner" by [Marian Evans / George Eliot] occurs quite frequently in maritime climates [Seattle, Vancouver, Juneau, England, North Sea Coast, even Holland MI], but occasionally occurs in inland climates [Chicago- Kiev, Minneapolis-Moscow, etc]. The word "hoar", meaning "grayish white" [among other things!] is a cognate of the modern German word "Hehr" [venerable or stately], and was already ancient when Geoffrey Chaucer [Merchant's Tale of The Canterbury Tales, 1386] made the wry comment "I feele me nowhere hoor but on myn heed" [so much for interdisciplinary education and Scrabble™ words].
• Liquids can be superheated without boiling [the bubble chamber records ionization tracks briefly, since those tracks are little bubbles that soon become big bubbles. Water can easily be reduced to -2 C [28 old-fashioned F] before it begins to freeze if not agitated, and much lower with special handling. A drop of water very hot surface [frying pay] will scoot on a vapor layer for some time before boiling [Leidenfrost: good for "stump the band" but not Scrabble™].  See the website http://www.varsity.utoronto.ca/archives/118/mar05/scitech/hotcoals.html.

26 October 1999: John Bozovsky (Bowen HS),
rushing the season perhaps, explained wind chill temperatures to us. (handout; see http://www.nws.noaa.gov/om/windchill/index.shtml) For example, 0oF is equivalent to -22oF in a 10 mph wind. This is cause the wind lowers body temperature by evaporating perspiration off the surface of our skin and blowing body heat away. The effect increases with wind speed. A graph of wind chill temperature vs air temperature at any given wind speed are approximately straight lines that converge at the warm end - about 85o F or so. Using the data handout from John to make such a graph is a good exercise for students. And now we can figure the wind chill on Hallowe'en, with wind at, say, 20 mph! Thanks, John!

26 September 2000 Bill Colson (Morgan Park HS)
gave us handouts containing an explanation for why dry air is heavier (more dense) than moist air, from Tom Skilling's weather page (website http://wgntv.trb.com/news/weather/) in the Chicago Tribune (http://chicagotribune.com . He wondered about any relevance of Avogadro's number to this. Ideas? [Comment by PJ:  Avogadro's number tells you how many molecules of an ideal gas there are in one mole of the gas, corresponding to a volume  of 22.4 liters at STP. The higher the molecular weight of gas, the heavier one mole will be, and thus the denser the gas. Water vapor [molecular weight 18] thus replaces nitrogen [molecular weight 28] and oxygen [molecular weight 32] molecules, to produce less dense air.  Thus, home runs in baseball are more likely on humid days!

20 January 2002 Bill Shanks (Joliet Central, Physics, Retired) Meterological Winter
Meteorological winter is defined as the period December 1 - March 1, because this is the coldest period of the year in the northern hemisphere. Why? Precisely why is it colder in the winter than in the summer?  Graduating seniors at Harvard a few years ago incorrectly suggested that the earth is closer to the sun in summer than in winter.  A good physics student might refer to the "glancing incidence" of sunlight in winter, but does s/he know what that means?  The total solar flux is about 1400 watts per square meter, as measured for normal incidence.  The angle of the sun with the vertical  in Chicago varies from q = 42°+23° = 65° in winter to q = 42°-23° =19° in summer.  As a consequence, the solar energy delivered to the ground is 1400 ´ cos q Watts/m2, which varies from 1324 Watts/m2 [summer] to 591 Watts/m2 [winter].  Bill illustrated the role of the angle of incidence using his bright flashlight and white paper. The paper was definitely brighter when the light shone directly on it.  In a similar vein, snow cover melts more quickly where it has a southern exposure, because of the heat absorbed from direct sunlight.

20 January 2002: Bill Shanks (Joliet Central, Physics, Retired) Q:  What is a Monolithic Concrete Dome?
A: (given by Ann S Bosley: http://www.bizjournals.com/birmingham/stories/2000/07/31/focus3.html)

The Monolithic Concrete Dome is a super-insulated, steel-reinforced concrete structure. David B. South, president of the Monolithic Dome Institute, and his brothers, Barry and Randy South, developed an efficient method for building a strong dome using a continuous spray-in-place process.
In 1976, following years of planning and development, they built the first Monolithic Dome in Shelley, Idaho. Since then, Monolithic Domes have been constructed for homes, schools, gymnasiums, churches, offices and bulk storage facilities in 45 states and in many foreign countries.

Briefly, here are the steps involved in building such a dome:

• The Monolithic Concrete Dome starts as a concrete ring foundation, reinforced with steel rebar (reinforcing bars). Vertical steel bars embedded in the ring are later attached to the steel reinforcing of the dome itself.
• An Airform, fabricated to the proper shape and size, is attached to the concrete base. Using fans, the Airform is inflated, creating the shape of the dome. In fact, the fans run throughout construction.
• Approximately 3 inches of polyurethane foam insulation is applied to the interior surface of the Airform. entrance into the structure is made through a double-door airlock, which keeps the air pressure inside at a constant level.
• Steel rebar is then attached to the foam using special hooks embedded in the foam.
• Shotcrete, a special spray mix of concrete, is applied to the interior surface of the dome. The steel rebar is
embedded in the concrete. The fans are shut off after the concrete is set.
According to the Monolithic Dome Institute, the advantages of building a Monolithic Concrete Dome include
the strength and permanence of the structure, energy efficiency, cost effectiveness, attractiveness and disaster
resistance.
See the website http://www.monolithicdome.com/.

06 May 2003
Earl Zwicker passed around an Environmental Disclosure Statement distributed by Commonwealth Edison, which indicated 65 % of their energy is obtained from nuclear power, 30 % from coal-fired power, 2 % natural gas-fired power, and 3 % is purchased from other companies.  Because of their reliance upon nuclear energy, their emissions are significantly below the averages in the Midwest, which is 75 % coal-powered and 22 % nuclear.  Very interesting!

09 September 2003: Don Kanner [Lane Tech HS, physics]        Hygroscope
Don
showed us the String Thing executive toy manufactured by Can You Imagine http://www.cyi.net/.  The following entry is excerpted from that site:

"The Amazing String Thing creates magical string effect nearly 3 feet in the air! Point it up, down, even sideways and watch as the string playfully dances in mid-air, gently touching the string generates wave patterns and interactive shapes that seem to defy gravity. The String Thing can be used with its own display cradle or you can hold the lightweight unit in your hand! Blacklight Responsive string looks great under any light. Battery Operated."
Don also presented Earl Zwicker with the device, which very nicely displays the "dimple effect" discussed in the Mathematics-Physics SMILE meeting of 05 February 2002. mp020502.html. Very visual, Don!

Don touted the venerable book A History of Physics by Florian Cajori [1899].  The book is readable, and contains a number of interesting quotes, insights, and examples that refer to original sources.  For example, Count Rumford [American Loyalist who died as a Bavarian nobleman] is quoted as saying that he expected to live long enough to see Caloric entombed along with Phlogiston--but he did not live that long.  In addition, he learned about the Hygroscope, a device used by Nicclaes de Cusa [1401-1446] to measure the moisture content of air.  The idea is to balance a scale with rocks on one side, and dry wool on the other side.  As time goes on, the wool will absorb water from the atmosphere, and become heavier than the rocks.  Don used a digital scale with a micro-camera attached to a small television set to show the scale reading.  He began by putting 11.78 grams of dry wool on the scale.  Here is a record of the readings (taken by Porter Johnson) every five minutes

 Time Mass (grams) change in mass Elapsed time   (minutes) Calculated mass change 4:45 11.78 0.00 0 0.00 4:50 12.11 0.33 5 0.19 4:55 12.24 0.46 10 0.35 5:00 12.34 0.56 15 0.47 5:05 12.41 0.63 20 0.57 5:10 12.46 0.68 25 0.66 5:15 12.51 0.73 30 0.73 5:20 12.57 0.79 35 0.78 5:15 12.60 0.82 40 0.81 5:30 12.63 0.85 45 0.85 5:35 12.66 0.88 50 0.88 5:40 12.68 0.90 55 0.90 5:45 12.70 0.92 60 0.92 5:50 12.72 0.94 65 0.93 5:55 12.73 0.95 70 0.94 6:00 12.74 0.96 75 0.95 6:05 12.75 0.97 80 0.96

The dry wool was prepared by heating ordinary wool in an oven at 95 - 100 °C for 30 minutes, and then enclosing it in a sealed container.  After it is placed on the scale in the open air, the mass of the wool continually increases with time.  That rate of increase decreases with time, and it appears to level off after a little over an hour.

Note by Porter Johnson:  Let us make the simplifying assumption that the increase of mass of  the wool gradually levels off according to the formula

Dm (t) = Dm (¥) [ 1 - e -t / T ]
where T is a characteristic time for the wool to come into equilibrium.  From the facts that Dm = 0.73 g at t = 30 minutes and Dm = 0.92 g at t = 60 minutes, we obtain T = 22.3 minutes and D m (¥) = 0.99 grams. The data calculated using this formula appear in the last column above.  The simple exponential is not an adequate representation of the data, so that the effect cannot be explained by this single absorption time.

Don, you certainly pulled the wool over our eyes! Good work, and keep reading those ancient tomes!

07 October 2003: Roy Coleman passed out information on weather and rain, that came from articles by Tom Skilling, which appeared in recent issues of the Chicago Tribune. They contained the following information:

• The earth's atmosphere weighs about 6 ´1012 tons, corresponding to 7 ´1015 kg.
• Within the United States, there are about 105 thunderstorms per year, generating about 9 ´ 107 lightning discharges.
• One inch of rain falling across metropolitan Chicago represents a weight of  about 1012 pounds, corresponding to 5´1011 kg.
• Drizzle is defined as water droplets of diameter less than 0.02 inches (0.5 mm); they fall at speeds from 1-4 mph.
• Water droplets are found  to be large in diameter as 0.2 inches (5 mm); above that size they become unstable and shatter into smaller droplets.  They fall at 5-20 mph, with an average speed of 14 mph. The bigger they are, the faster they fall!
Properties of Typical Clouds:
 Cloud Type Water vapor density Vertical height Horizontal spread Mass Cirrus 0.1 g/m3 1 km 25 km ´ 25 km 8 ´108 kg Cumulus 0.2 g/m3 1 km 1 km ´ 1 km 2 ´105 kg Cumulus Congestus 0.8 g/m3 5 km 2 km ´ 2 km 2 ´10 8 kg Cumulonimbus 1.0 g/m3 10 km 6 km ´ 6 km 4 ´109 kg
Useful data for developing physics problems! Thanks, Roy!

Roy Coleman [Morgan Park HS, Physics]     Estimating the Speed of Falling Rain Drops
First, go out and buy a car in which the rear window slopes at a modest angle (say, q » 30°) to the horizontal.  Then, drive your car during a rainstorm, and find the minimum speed v0 at which falling raindrops do not strike that rear window.  If there is no wind, the speed of the falling raindrops vf  should satisfy the relation vf / v0 = tan qSimple, non?  If the wind is blowing, repeat the observation while going in the opposite direction as well, and take the average.  Be sure not to crash into anything while doing this experiment!
Now, there's a good reason to get rid of the old clunker and get a new car.  Nice work, Roy!

21 October 2003: Jane Shields [Calumet HS,  science]        Weather Frog
Jane
made a "blow by blow" description of her attempts to construct a Weather Frog, which hops up a ladder during periods of high atmospheric pressure and down the ladder at low atmospheric pressure.  The idea is to place a flexible plastic seal over the top of a quart [liter] glass jar, with a string wrapped around a (sewing needle) shaft a few times.  One end of the string is attached to the underside of the plastic seal, and a small weight is suspended from the other end.  The shaft is free to rotate.  One end of a rigid metal wire is attached perpendicularly to the shaft, and the paper frog is hooked to its other end.  As air pressure changes, the seal moves slightly up or down, so the shaft rotates, and the frog moves up or down.  Jane's apparatus almost worked, and she was determined to succeed with it.  Very good, Jane!

A nice description of the principles behind the operation of the Weather Frog, as well as details for its construction, are contained on the Science and Education Partnership website: An Elementary Unit about Air Pressurehttp://www.seplessons.org/node/287, from which the following has been paraphrased:

HOW A BAROMETER WORKS: "A barometer has a piece of special metal in it called corrugated metal that squeezes down when heavier air pushes on it and expands up when lighter air does not push so much on it. There is a needle attached to the metal that points to a number on the dial to tell the air pressure. There are also words on the barometer to tell what the weather conditions will do according to the air pressure: rain, change, and fair. Lower numbers indicate low pressure and higher numbers indicate high pressure. Air pressures usually range from 29.00 to 31.00 inches [of mercury] in Nebraska."
Jane also passed around an RD Challenge --- illusions that appeared in the September 2003 issue of The Readers Digest [http://www.rd.com]. Other illusions, appeared in the January 2002 issue. This website also contains links to the Counter-rotating Spirals Illusion [http://dogfeathers.com/java/spirals.html], Grand Illusions [http://www.grand-illusions.com/opticalillusions/], and Artful Illusions [http://members.aol.com/Ryanbut/illusion1.html].  Neato!

Nice stuff, Jane!

24 February 2004: Porter Johnson passed out a table obtained from the website Beaufort Scale of Wind Force and Its Probable Wave Height:  http://www.r-p-r.co.uk/beaufort.htm. The Beaufort Scale is the international standard for describing wind velocity ( as measured 11 meters above the surface -- called "Wind Force" by Marine Meteorologists) and relating it to steady-state probable and maximum (crest to trough) wave heights on deep, open water.  For example, Wind Force 4 (Moderate breeze) corresponds to winds around 7 meters/second and average wave heights of about 1 meter, whereas Wind Force 8 (Gale) corresponds to 20 m/sec winds and 6 meter waves, and Wind Force 12 (Hurricane threshold) corresponds to 35 m/sec winds and 14 meter waves.  For more details check the website, as well as other sites linked to it.

15 November 2005: Ann Brandon (Joliet West HS, retired)            Strange Temperatures on Shipboard
Ann
recently made a voyage through the Panama Canal, on which there were daily weather reports.  She was struck by some of the temperatures:  57 °C = 14 °F and 69 °C = 20 °F.  Very strange temperatures --- even for the tropics!  Thanks, Ann.