Pascal's barometer
Pascal's barometer is a lesson in teaching art didactics . It was developed in the years up to 1997 by Bernese physics didacticist Ueli Aeschlimann on the basis of an example by Martin Wagenschein from the 1970s and re-staged in the years up to 2013 by Marc Eyer, now also a professor at the PH Bern .
The didactic piece deals with the phenomena of pressure using original sources and templates from the 17th century by Galileo Galilei , Gasparo Berti , Evangelista Torricelli , Blaise Pascal , Otto von Guericke and Robert Boyle . It falsified in genetic way Aristotle 's theory of horror vacui .
Wagenschein's example
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Martin Wagenschein had appeared frequently as a guest speaker in educational working groups for young Swiss teachers from around 1971. At that time, a special example was part of his regular repertoire: he pulled a beer glass from a wash bowl filled with water with the opening facing downwards. To the astonishment of many viewers, the water remains in the glass as long as its opening is completely under water. On the basis of this phenomenon, Wagenschein held Socratic discussions with the seminar participants who tried to discover the reason for the water remaining in the glass.
In 1983 Wagenschein held a conference in Darmstadt with the presence and participation of Otto Herz and Horst Rumpf as well as the teachers of two alternative schools , the Glockseeschule and the Freie Schule Frankfurt , in which he staged this example. For Hans Christoph Berg , who was also present , this event should have lasting consequences and can be seen as the founding moment of teaching art didactics. Berg later recalled:
“Oh - that's how you can teach Pascal's invention of the barometer - with a beer glass and a water bowl? Don't you have to explain the air pressure beforehand and experiment exactly? He can be so to be discovered? One can! And not only Wagenschein can do that. He composed the barometer lesson so well (Aeschlimann then composed it out) that we were able to stage it successfully in lessons.
(...)
method in examples, example with method. Unfortunately, this is still not used in didactics. But here the teaching art is based on the practice of the other arts: Nobody would only study his theater conception with Brecht without his plays, nobody would only study Schumann's music theory without his musical works, or Paul Klee's 'pictorial thinking' without his pictorial works, or Lessing's Dramaturgy without its dramas: The discovery and practical use of the works, including the work tradition, also in didactics: that is the Eureka of teaching art didactics - thanks to Wagenschein! "
The lesson
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After in 1995, published by Hans Christoph Berg and Theodor Schulze , in the main work Lehrkunst. Didactic textbook. the first eleven doctrines were presented, two years later appeared under identical editorship of the band teaching art workshop I . In this three more didactic pieces are presented in much more detail than in the previous volume. Ueli Aeschlimann presents the barometer lesson; Berg is listed as co-author, and Aeschlimann's production is commented in particular by Horst Rumpf .
Aeschlimann's documented production took place in front of a 10th grade at the Bern teachers' college. Rumpf is amazed that Aeschlimann's Socratic conversation, despite the early suggestion of the actual core findings by some of the graduates, "still has such an interesting, multi-faceted and lively teaching approach, so to speak" . Heiner Ullrich , who in 2001 reviewed the teaching arts workshops I-III for the renowned magazine for pedagogy , particularly emphasizes that Aeschlimann allows the graduates to secure the current state of knowledge in so-called "intermediate stops" by means of protocol-like booklet entries, which documents the individual learning process will. He also emphasizes "admirable ideas of his own" such as the hose test and attests that the author is "serious about driving a car" .
Pascal's barometer also became one of three documented teaching pieces in Aeschlimann's second dissertation from 1999, for which, in addition to the standard first reviewer Berg, Wolfgang Klafki could be won as a second reviewer .
It wasn't until a good decade later, in 2013, that the didactic play was picked up again and staged in the second dissertation by Marc Eyer, also from Bern, who, after Klafki's age-related retirement from around 2007, had his former student Heinz Stübig as a second reviewer . Eyer's production is aimed at a 9th grade at the Neufeld grammar school and therefore differs somewhat from Aeschlimann's. Even before the completion of their dissertation, Eyer and Aeschlimann, on the initiative of the former, published a separate book on the Lehrstück, which Fabienne Freiburghaus documents, analyzes and compares both variants and another at the Solothurn Cantonal School .
Further productions are only documented in internal scripts and gray publications. Björn Gemmer, one of the two headmasters of the Steinmühle country school home in the south of Marburg , developed an in-house variant for project lessons in grade 8.
dramaturgy
Pascal's barometer is mainly based on modified historical experiments of the 17th century, which are supplemented by current observations. The division into files is not uniform internally at Aeschlimann and Eyer either or is modified between the individual representations. Since the fund of experiments is for the most part always the same, the fundamental experiments are dealt with in the following in a meaningful order, from which parts can also be deviated from. It is important that the beer glass and water hose experiments are placed first and the experiments by von Guericke and Boyle, who already need a vacuum pump, are at the end. The main sources of the following subsections are the Lehrkunstwerkstatt I , the second dissertations by Aeschlimann and Eyer and their joint book on the Lehrstück.
Wagenschein's beer glass experiment
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At the very beginning there is the beer glass pulled out of the basin, which directly poses the organizational suction question:
- "Why does the water stay in the glass and not flow into the basin?"
Ideally, but also happening several times in real life, two possible explanations emerge among the learners:
- The outflow of the water would create a vacuum, which would contradict the horror vacui .
- The air pressure keeps the water column up.
Although the second explanation is correct, it contradicts intuition: in daily life you do not feel the heaviness of the air. In the Socratic conversation it must now be discussed which further considerations and experiments would support which of the two explanations.
An immediate follow-up experiment is a full pharmacist's bottle, the water of which is held in a tiny Petri dish . The realization that it is not the volume of water that matters, but only the absolute height of the water column, since when using a bottle with a small spout most of the water is held by the walls of the vessel, ideally comes from the student's side in a genetic way. The question of how high the water column can be leads to Berti's experiment.
Berti's water columns and the hose experiment
Gasparo Berti (approx. 1600–1643) demonstrated the maximum height of a water column in Rome in 1641 and at the same time tried to create a vacuum. For this purpose, he used a nearly 12 m high construction with a lead pipe, above which a glass vial was attached airtight and which protruded down into a bowl filled with water. It was filled from above (C), while the tube below (R) was closed. Then the top was closed and the tap was released below. The water sank to a height of 18 cubits (9.7 m), which previously u. a. Galileo Galilei had been known as the maximum suction lift of pumps .
In order to prove that a vacuum was created above the water column, at the suggestion of Athanasius Kircher , Berti placed a magnetically operated bell (M) inside the vial. This proof, however, failed because the sound of the bell was clearly audible, which indicated the presence of air. This is likely to have been due to a reduced tightness of the construction, which in the long run also led to the water column falling.
Berti's attempt is much easier to recreate today. For this purpose, a 12 to 15 m long, transparent hose is completely filled with water, closed at the top and then transported up a stairwell until the water column stops at about ten meters - even if the end of the hose is raised further. This gives you a measure of how far the water can be drawn up in a fictitious, extra-long beer glass. However, it remains unclear whether a vacuum is created above the water or, for example, water vapor.
Chronologically, Berti's attempt took place after the publication of Galileo's considerations set out below, which had also motivated Berti. In the didactic piece, however, he immediately follows the beer glass experiment, which he generalizes.
Galileo's limited power of vacuum
Galileo Galilei (1564–1642) wrote the book Discorsi e Dimostrazioni Matematiche intorno a due nuove scienze in 1633 (or 1638) . At that time he was not a proponent of the air pressure theory, but also doubted the theory of the horror vacui . Rather, he believed that there was a fixed force that could be used to create a vacuum. As an experimental setup, he suggested a cylinder filled with water, which is closed by a piston after all air has been let out. If you now turn the cylinder around, you can measure the “force of the vacuum” using weights attached to the piston.
The force of the vacuum can also be measured using simpler methods. With a plastic syringe, the end of which is held shut, you can use a spring balance to determine the force required to pull out the plunger. This force is apparently proportional to the bore , i.e. H. to the cross-sectional area of the syringe.
Torricelli's barometer and the pressure of gravity
Evangelista Torricelli (1608–1647) was a student of Galileo. In 1643 he rebuilt Berti's water column experiment with the 13-14 times heavier mercury , with which he invented the barometer in particular . It turned out that the maximum height of the mercury column at normal pressure is about 760 mm, i.e. the thirteenth to fourteenth part of 10 m.
This knowledge leads to the concept of gravitational pressure . It suggests that the air above us also has a weight that corresponds to exactly 760 mm of mercury or 10 m of water per unit area. By comparing a (partially) evacuated bottle with the same in air, one can calculate the density of air to be about 1.3 grams per liter, which corresponds to about the 800th part of the density of water. Accordingly, the air would have to be 8 km high in order to press on your surface with the same force per surface. The fact that the earth's atmosphere extends even further is also due to the fact that air, unlike liquids, is relatively compressible and the density of air decreases with distance from the earth.
The following quote comes from Torricelli, and it now comes to mind:
"We live submerged at the bottom of a sea of elemental air."
Pascal's demonstration at the Puy de dôme
In 1647 Blaise Pascal (1623–1662) had already demonstrated through his experiment emptiness in emptiness or made plausible that a vacuum was created above the water and mercury columns. In addition, he is said to have made a bet with friends the following year that he could burst a full barrel of wine with a glass of wine. He achieved this by making a corresponding difference in altitude (see left).
Much better known, however, was his experiment in the French Massif Central , which he had his brother-in-law Florin Périer carry out in the same year (1648). Périer had the task of transporting a mercury manometer from the city of Clermont-Ferrand up to the approximately 1000 m higher Puy de Dôme ( 1465 m ) and thereby regularly documenting the level of the mercury column. According to Pascal's considerations, the gravity pressure, if it should be responsible, must be lower at higher altitudes, since there a smaller amount of air is loaded on the observer.
Pascal's assumption was confirmed. Aside from the altitude dependence of the air pressure, he also recognized that the weather depends on the air pressure, and thus initiated the use of the barometer for weather forecasting.
Since mercury thermometers are bulky and the toxic metal is no longer as inexperienced as in Pascal's time, Périer's experiment will not be carried out on the local mountain in the classroom. However, even with a height difference of z. B. 20 m, as it can usually be produced within a school building, a corresponding difference in the mercury column can be measured in the millimeter range.
Guericke's hemispheres and the power of vacuum
In 1649 Otto von Guericke (1602–1686) invented the air pump by extending the principle of the reciprocating piston pump , which had long been in use for water, to include gases. It was now possible to generate an approximate vacuum with simple means.
From 1856 he staged a particularly haunting demonstration experiment on the “power of vacuum” with the Magdeburg hemispheres . Two hemispheres, which were only united to form a ball by airtight contact, were evacuated. Now not even two teams with 8 horses each managed to separate the hemispheres from each other, in later attempts it was twice as much as 15 horses.
In the usual collections of schools there are mostly significantly reduced copies of the hemispheres, which instead of the original diameter of 42 cm have only a fraction of that. But hemispheres with an inner diameter of z. B. 10 cm close an area of almost 80 cm² = 0.008 m². If this is multiplied by the pressure of 1 bar = 100,000 Pascal , the mathematical result is a force of almost 800 Newtons , which corresponds to a weight of at least 80 kg. The original hemispheres even weighed around 1.4 t!
Von Guericke's experiment basically starts again with Galileo's “power of the vacuum” and is just as easy to do mathematically as drawing a known cross-section with a closed syringe, but is much more difficult to grasp for schoolchildren. While you can actually pull the plunger of a syringe a few centimeters without air being able to penetrate, the hemispheres can basically only be pulled infinitesimally far before air penetrating would destroy the vacuum. It is also sometimes not immediately clear to the learner that the force acts on the inner cross-sectional area of the sphere, although the external air pressure initially presses the hemispheres immediately. The very counterintuitive attempt therefore requires further investigation and explanation. As long as the ball is filled with air at atmospheric pressure, the inner air presses the halves of the ball apart with the exact force with which the outer air compresses them. Only when the ball is pumped out does this equilibrium lapse until there is almost no counterforce from inside.
Boyle's demonstration and the return to the beer glass experiment
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Robert Boyle (1627–1692) took advantage of Guericke's invention of the air pump in 1660 by observing the column height of a barometer under a glass bell that was provided with a negative pressure. A similar experiment can be carried out at school with a scaled-down “water barometer”, a miniature of the beer glass experiment. With sufficient negative pressure, the water itself flows out of a miniature glass that is only a few cm long. This closes the circle that began with the beer glass experiment.
Finale and possible prospects
While Ueli Aeschlimann applies the knowledge gained directly to the connection between air pressure and weather in his finale, Marc Eyer prefers a final discussion of the historical protagonists of the didactic play, in whose roles individual students slip.
Even in the actual stagings, observations are made on everyday phenomena that deviate from the historical experiments documented above. Mention should be made of the principle of the water tower , communicating pipes such as the siphon and the hose level , the drinking straw and the principle of hydraulics . Various other types of barometer, including the Goethe barometer and the can barometer , are usually presented and analyzed; as a created work u. U. a self-made membrane barometer can be taken along.
The teaching piece can also be used as a basis for dealing with the gas laws , which require significantly more quantitative-mathematical procedures.
literature
The following list is arranged chronologically:
- Galileo Galilei: Discorsi e Dimostrazioni Matematiche intorno a due nuove scienze . Rome 1633
- Blaise Pascal: Lettre de Monsieur Pascal jeune a Monsieur Perier, du November 15, 1647 , in Brunschvigg, Boutroux Oeuvres de Blaise Pascal , Volume 2, pp. 153–162, Archives - documents in particular emptiness in emptiness ; s. Berg / Schulze (1997)
- Caspar Schott : Technica curiosa, sive mirabilia artis. Endterus, Nuremberg 1664
- Robert Boyle: Hydrostatical paradoxes, made out by new experiments… 1666. (online) .
- Otto von Guericke: New "Magdeburg" experiments on empty space . Ostwald's classics series, vol. 59. Thun, Frankfurt / M. 1996, ISBN 3-8171-3059-7 ; Translated by: Ottonis De Guericke Experimenta nova Magdeburgica de vacuo spatio , Waesberge, Amsterdam 1672.
- Ernst Mach : The mechanics in their development. Edition Classic Verlag Dr. Müller, Saarbrücken 2006 (reprint of the 9th edition 1933; orig. 1883); ISBN 978-3-86550-525-5
- Martin Wagenschein: Memories for tomorrow. An educational autobiography. Beltz, Weinheim / Basel 1983, ISBN 3-407-83075-0 ; in this:
- Young Swiss (PDF; 120 kB; pp. 116–119)
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Hans Christoph Berg , Theodor Schulze (Ed.): Lehrkunstwerkstatt I, didactics in teaching examples, with an introduction by Wolfgang Klafki . Luchterhand, Neuwied 1997; ISBN 978-3-472-03010-2 ; in this:
-
Pascal's barometer (pp. 81–124)
- Hans Christoph Berg, Theodor Schulze: Editorial (pp. 83–84)
- Blaise Pascal: Letter to ask for an experimental investigation of the air pressure (to Florin Périer; pp. 85–86)
- Florin Périer: Report on the barometer observations at the foot and on the summit of the Puy de Dôme (to Blaise Pascal; pp. 86–88)
- Susanne Mumm: In the seminar with Martin Wagenschein (pp. 88–89)
- Ueli Aeschlimann with Hans Christoph Berg: Pascal's barometer. A lesson according to Wagenschein. (Pp. 90–116)
- Horst Rumpf : A short comment on "Pascal's Barometer" (pp. 116–119)
- Peter Gasser: Case study on the lesson "Pascal's Barometer" (pp. 119–12)
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Pascal's barometer (pp. 81–124)
- Ueli Aeschlimann: With a car license to the art of teaching. Design, testing and interpretation of three teaching examples on physics, chemistry and astronomy using the genetic-dramaturgical method. Marburg 1999; DNB 969920059 ( download of the original dissertation ), therein:
- "Pascals Barometer" - a first lesson (pp. 15–61)
- Heiner Ullrich : Lehrkunstwerkstätten I – III (Berg / Schulze 1997 and 1998, Berg / Klafki / Schulze 2000) in: Zeitschrift für Pädagogik , Issue 4 (2001) ( PDF ; 1.0 MB); the barometer lesson is discussed on p. 611
- Swiss Conference of Cantonal Education Directors (EDK; ed.): Lesson development - on the status of the discussion. Studies and reports 2nd Biel / Bern 2004 (EDK report 2004)
- Marc Eyer, Ueli Aeschlimann (et al): Pascals Barometer. hep (Volume 8), Bern 2013; ISBN 978-3-0355-0008-0
- Marc Eyer: Lehrstück lesson in the horizon of cultural genesis. Didactic didactic composition and staging of Galileo's law of the fall - Pascal's barometer - Fermat's mirror optics. Marburg 2013; DNB 1049818873 ( download of the original dissertation ), therein:
- Pascal's barometer (pp. 79–145)
- Marc Eyer: Lehrstück lesson in the horizon of cultural genesis. A model for didactic teaching in the natural sciences. Springer, Wiesbaden 2015; ISBN 978-3-658-10997-4 (reprinted by Eyer (2013))
- Björn Gemmer: Pascal's barometer. Physics project for the eighth grade to introduce aero- and hydrostatics. Script, Marburg 2016
Web links
- Pascal's barometer on lehrkunst.ch
- Ueli Aeschlimann: With a car license to the art of teaching. Design, testing and interpretation of three teaching examples on physics, chemistry and astronomy using the genetic-dramaturgical method. Marburg 1999; DNB 969920059 ( download of the original dissertation )
- Marc Eyer: Lehrstück lesson in the horizon of cultural genesis. Didactic didactic composition and staging of Galileo's law of the fall - Pascal's barometer - Fermat's mirror optics. Marburg 2013; DNB 1049818873 ( download of the original dissertation ), therein:
- Pascal's barometer (pp. 79–145)
- Heiner Ullrich: Lehrkunstwerkstätten I – III (Berg / Schulze 1997 and 1998, Berg / Klafki / Schulze 2000) in: Zeitschrift für Pädagogik , Issue 4 (2001) ( PDF ; 1.0 MB); the barometer lesson is discussed on p. 611
Footnotes
- ↑ Ueli Aeschlimann at the PH Bern, memento from February 2017
- ↑ Marc Eyer ( Memento of the original from February 13, 2017 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. at the PH Bern
- ↑ see en: Gasparo Berti
- ↑ cf. Wagenschein (1983), pp. 116-119
- ↑ s. EDK (2004), pp. 85f.
- ↑ s. Berg / Schulze (1997)
- ↑ s. Rumpf in Berg / Schulze (1997)
- ↑ cf. Ullrich (2001), p. 611
- ↑ s. Aeschlimann (1999), pp. 15-61
- ↑ s. Eyer (2013), pp. 79-145
- ↑ s. Eyer / Aeschlimann (2013)
- ↑ cf. Gemmer (2016)
- ↑ The order shown here corresponds to that of the section Das Lehrstück on a double page from Eyer / Aeschlimann (2013), pp. 12–13.
- ↑ See Aeschlimann in Berg / Schulze (1997), Aeschlimann (1999), Eyer (2013) and Eyer / Aeschlimann (2013).
- ↑ s. Bulkhead (1664)
- ↑ A description can also be found in Friedrich Jaeger's Enzyklopädie der Neuzeit 13 , Metzler, Stuttgart 2011; ISBN 978-3-476-02003-1 ( Google Books ).
- ↑ See, for example, History of the Barometer on strange-loops.com
- ↑ Galileo wrote the book in 1633, but it was initially not published due to his house arrest; A Latin translation was published in Strasbourg in 1635 and the Italian version did not follow until 1638.
- ↑ cf. Galilei (1633), pp. 14-15 and Aeschlimann (1999), pp. 59-60 and sketch
- ↑ quoted from Shmuel Sambursky : Der Weg der Physik ; P. 337; see. also Aeschlimann (1999), p. 55
- ↑ cf. Pascal (1647) and Pascal in Berg / Schulze (1997)
- ↑ s. from Guericke (1672)
- ↑ Strictly speaking, it is of course a question of the force of pressure (difference); Von Guericke's pump was unable to generate a total vacuum, but it was able to generate a negative pressure of approximately 0 bar.
- ↑ Gemmer has even the basic gas laws into lesson integrated , but this genetic sequence somewhat hampered; see. Gemmer (2016).
