# What Marilyn omitted about the Fahrenheit Thermometer

Ask Marilyn ® by Marilyn vos Savant is a column in Parade Magazine, published by PARADE, 711 Third Avenue, New York, NY 10017, USA. According to Parade, Marilyn vos Savant is listed in the "Guinness Book of World Records Hall of Fame" for "Highest IQ."

In her Parade Magazine column of March 22, 1998, Marilyn fails to completely answer a reader's question about the Fahrenheit temperature scale.

## The Readers Respond!

Charles Kluepfel <ChasKlu@aol.com> has the following comments:
In this week's Parade, Marilyn is asked for logical correlations of the Fahrenheit scale with natural occurrences (what's special about zero Fahrenheit, for example). Her reply mentions a few interesting facts, including the over-precision in converting the rounded 37-degree-Celsius normal temperature of the human body to 98.6 degrees Fahrenheit. She also editorializes about the suitability of the Fahrenheit scale to human needs. But she never mentions how 32 was chosen, rather than something that is "rounder", like 30, 35, 40 or even 50. Perhaps the first two paragraphs from her answer would have been more like the following paragraph, quoted from Isaac Asimov's Biographical Encyclopedia of Science and Technology:

Fahrenheit, however, added salt to water to get the lowest freezing point he could and called that zero. (He wanted to avoid negative temperatures on winter days that were well below the freezing point of pure water.) He then divided the difference in level between that point and that reached at body temperature not into twelve parts [as Newton is described as suggesting, in Asimov's preceding paragraph] but into eight times that many (in line with the high precision of his instrument) or ninety-six "degrees." He later adjusted that slightly in order to make the boiling point of water come out to 212 degrees, exactly 180 degrees above the freezing point of pure water, set at 32 degrees. On this Fahrenheit scale, body temperature is 98.6 degrees.

Marilyn is right to correct Asimov's last quoted sentence, but she leaves out the physical derivation of the zero point, which is what the questioner had asked. She makes it sound that it was chosen as an extreme of discomfort (a nebulous observation, at best) when in fact is was the lowest temperature for which Fahrenheit could reasonably get a physically meaningful match to a natural occurrence. She also leaves out the later adjustment to the scale to make exactly 180 degrees (direct opposite, in geometry) between the freezing (or melting) and boiling points of pure water.

In the 3/22/98 Parade, she "explains" why the Fahrenheit temperature scale is what it is. She says that Fahrenheit just picked the scale so that 32 was the freezing point of water. According to Merriam Webster's Collegiate dictionary, the 0 point on the Fahrenheit scale "approximates the temperature produced my mixing equal quantities by weight of snow and common salt". So that is how the zero point was determined.

Allan S. Wagman <Allan_Wagman@cc.chiron.com> sent this letter to Marilyn:

I happened upon your column in the March 22 issue of Parade Magazine which quite incompletely answers to a very good question posed by Baker Smith - What is the logical correlation between the Fahrenheit scale and natural calibration points. The answer is very simple. There are 180 degrees between the melting point of water and the boiling point. This number was considered rational at the time since it was based on the number of degrees in half of a circle. Fahrenheit was an instrument maker in Amsterdam who is famous for inventing the mercury thermometer. He based his temperature scale on the work of many others, but mostly that of Robert Hook and Ole Roemer. Fahrenheit's scale is fixed by the known simple constant temperature baths at the time which were that of melting water-ice in a saturated aqueous salt solution and that of melting water-ice in pure water. The saturated salt bath and ice was assigned the value of 0 degrees while that of ice and pure water was assigned the value of 30 degrees. (see D. G. Fahrenheit Phil. Trans. (London) 1724, 33, 78.) The temperature of the body was measured at 96 degrees. This scale was later arbitrarily changed when the temperature of boiling water was measured at 212 degrees. Fahrenheit changed the value of freezing water from 30 to 32 degrees to achieve the more attractive scale of 180 degrees between the melting point of water and that of boiling water. There are many other interesting connections in the history of thermodynamics and the personalities that are famous for making the great intellectual leaps that drive our science and civilization. (for more information see the references below)

There are many other inaccuracies in your column such as the assertion that there are not normally temperatures above 100 or below 0 degrees Fahrenheit. I have lived in Texas and in Pittsburgh PA, and I can assure you that these temperatures are exceeded regularly. As for using temperatures above 50 degrees Celsius, most of us use a stove every night. The Celsius scale is very intuitive since it is a base ten system. It is very easy to understand exactly how hot something is because the math is made simple. Freezing water is 0 C, room temperature is 25 C, a hot day is 30 to 38 C, boiling water is 100, we cook a roast at 200 C, and broil at 250. Also since a lot of data concerning the temperature of the human body was collected in Centigrate (pre 1948) which has values just a little bit higher than that of Celsius, I wonder if Prof. Paulos of Temple U. took this into account. I guess I'll have to read Innumeracy a little bit more closely.

In an era of this country's history where science is so misunderstood and scientists are held in such poor regard, we need national spokespeople who portray science and education as interesting and worthwhile pursuits. I believe that the best service that we, the teachers and educators, can provide our children is accurate, complete, thought provoking, and if at all possible, entertaining answers to their questions. There is currently a great need in our country's education system and in the general public for scientific outreach programs and emphasis on the basics of critical thinking. Keep in mind that the information that you provide the public is for some, one of few sources of scientific knowledge and examples of problem solving for which they have access. Not only does the accuracy of your answer count, but also does its tone and delivery. I challenge you and every other provider of information in the public media to set your standards high.

I'll leave you with a related teaser. What is the relationship between the modern estimate of absolute zero and that of the theoretical value in K. 0 Kelvin is defined with respect to an ideal reversible heat engine working on a Carnot cycle between two temperatures; high and low. The modern estimates are based on observation of super-cooled gasses. Which one is correct? -- well, both really, but why. Its a trick question, but I'll give you a hint. The relationship can be derived from the ideal gas law and a little knowledge of the atom.

• Adkins, C. J., Thermal Physics, 1987 Cambridge University Press, ISBN 0-521-33715-1
• Cork, James M., Heat, 1942, John Wiley & Sons
• Herzfeld, Charles M. Editor, Temperature: Its Measurement and Control in Science and Industry, 1962, Reinhold
• Quinn, T. J., Temperature, 1990, Academic Press, ISBN 0-12-569681-7
• Weber, Robert L., Heat and Temperature Measurement, 1950, Prentice-Hall, Inc
• Zemansky, Mark W., Heat and Thermodynamics, 1968, Mc Graw Hill

Rick Strickert <Rick_Strickert@radian.com> contributed this version:

Ole Christensen Roemer (1644-1710) was a contemporary (and friend) of Isaac Newton and best remembered for his (controversial for many years) discovery of the finite speed of light. However, Roemer was a most versatile person with many accomplishments for his native Denmark in astromomy, mathematics, engineering, tax reform, weight standards, military ballistics, law, government, international trade, to name a few. He also had another under recognized accomplishment.

It was Roemer who designed and constructed his own more accurate thermometers and was the first to realize and use *two* fixed points (rather than one) to calibrate the scale of a thermometer. Roemer's upper point was the boiling point of water, which he set as 60 degrees. (Roemer apparently did not realize that water's b.p. depended on atmospheric pressure, a fact that Fahrenheit later discovered.)

Roemer's lower calibration point has been the subject of some debate. Some have said that a 0 value was assigned to a mixture of water, ice, and ammonium chloride; others claim Roemer used the melting point of snow (which he marked as 7.5 deg.). Because much of Roemer's records were destroyed in a fire in Copenhagen in 1728, we may never know for sure. (I might note here that 7.5 is one-eighth of 60, and accurately dividing a thermometer scale by powers of 2 is easily accomplished with simple tools.)

In 1708, the German physicist, Daniel Gabriel Fahrenheit (not "Gabriel Daniel"), visited Ole Roemer in Copenhagen. Roemer showed him the two-point calibration system he had developed. Roemer was also testing small thermometers designed for meteorological use which had divisions marked from 0 to 22.5 deg. (normal blood temperature) using Roemer's scale.

Fahrenheit was so impressed with Roemer's thermometers and the two-point calibration scale that he adopted them for use back in Germany. While it appears that Fahrenheit used the same lower calibration point as that of Roemer, it is clear (from a letter written by Fahrenheit to Boerhaave in 1729 and rediscovered in 1936) that Fahrenheit used Roemer's 22.5 deg ("normal body temperature") as the upper point. From a 1724 paper, Fahrenheit determined the upper point either in the mouth or under the armpit (the third alternative technique was not noted :-)). It is not clear whether Fahrenheit (or Roemer) distinguished a male or female body temperature (in his Latin paper Fahrenheit used the word "hominis").

Fahrenheit later multiplied Roemer's scale numbers by four for easier reading. This made the melting point of ice 30 deg. and body temperature 90 deg.

Eventually Fahrenheit adjusted the calibration points to 32 (ice melting point) and 96 (body temperature) to simplify marking the scale divisions (i.e., 64 divisions). Thus the boiling point of water would be measured experimentally near 212 deg. Later, the b.p. of water, at a fixed atmospheric pressure, was used as the upper calibration point of 212, returning to Roemer's initial calibration concept. (With these two calibration points, the experimentally determined temperature of a healthy person is now accepted to be approximately 98.6 deg.)

Thus, as noted by historian I.B. Cohen, Ole Roemer's thermometer scale design is really the basis of the thermometer scale used by Daniel Gabriel Fahrenheit (1686-1736).

For more information on Roemer, the thermometer, and his other accomplishments, see Roemer and the First Determination on the Velocity of Light, I. Bernard Cohen (Burndy Library, New York, 1944). Cohen's short book has many references, mostly in Danish, French, German, or Latin; and mostly very old. Fahrenheit's own acknowledgement of Roemer's contribution is in a letter he wrote in 1729 and reprinted in Kon. Akad. Wet. Verhand., Vol.xvi, 1936, pp.1-37. A more recent discussion of Roemer's temperature scale was given by Robert H. Romer, "Temperature scales: Celsius, Fahrenheit, Kelvin, Reamur, and Romer", The Physics Teacher, 20 (Oct. 1982), pp.450-454)

For the extremely adventurous, one can peruse a bibliography on Roemer by Per Friedrichsen, "Dansk Astronomi Gennem Firhundrede År", Bind 3, ISBN 87-7245-281-1, Produktion Rhodos, 1990, then stop by the Ole Roemer Museum in Tåstrup, Denmark.

Roger Geffen <pater@gis.net> found Dr. Johnson's Temperature Conversion Toolkit in Java, which converts between Fahrenheit, Celcius, Kelvin, Rankine, and Réaumur.

http://www.wiskit.com/marilyn/fahrenheit.html last updated September 15, 1998 by herbw@wiskit.com