# Notes on Temperature Scales

### Steve Sconfienza, Ph.D.

Airline Transport Pilot

Flight Instructor: Airplane Single and Multiengine; Instrument Airplane

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e-mail: docsteve@localnet.com

## Fahrenheit

(thermometric scale)

Named after Gabriel Daniel Fahrenheit (1686-1736), German physicist.

Freezing-point of water is 32° and the boiling-point 212° (there are 180 degrees in the Fahrenheit scale freezing/boiling interval).

Around 1714 Fahrenheit proposed the scale with the freezing-point of water 32° and the boiling-point 212°, but the actual genesis of this scale is clouded by various explanations and legends, including the following:

• Fahrenheit based his scale on the work of Olaus Roemer, who devised the alcohol thermometer and developed a scale with the boiling point of water at 60° and the freezing point of an ice/salt mixture at 0°.
• F is based on the freezing point of a mixture of equal quantities by weight of snow and NaCl.
• Ice and salt together in a more-or-less equal mixture constitute a "frigorific" mixture that — regardless of the ambient temperature — stabilizes at 0° F.
• 100° F (or 90°) is based (roughly) on human body temperature.
• Continuing that thought, the human body temperature is 64 units (26 units) above the water/ice stabilization point.
• The freezing-point of water is set at 32° to avoid negative temperatures.
• 0° and 100° represent the mean high and low temperatures in some city over some period of time (pick your favorite city here).
• Given the determined range of temperatures (0° to 100° for whatever reason), the freezing point of water came out to about 30°, later determined as 32°.

Nevertheless, Fahrenheit is a much more intuitive and human scale than Celsius, because its 100 degree range roughly corresponds to most mid-latitudes areas. Given this, it is surprising that the Celsius scale has found the acceptance that it has outside of the laboratory. (This has led to a lot of philosophical questions, such as, "Do residents of socialist countries [read that as western European industrial democracies, which often vote for socialist parties] accept government dictates concerning everyday life more readily than residents of other countries [read that as the United States, which has a more laissez faire economy]?")

First used: 1753

## Rankine

(absolute scale)

Named after William John Macquorn Rankine (1820-1872), Scottish engineer and physicist.

Uses Fahrenheit degree units, but sets zero equal to absolute zero.

Rankine promoted the Kelvin scale, but using the 180-degree increment of the Fahrenheit scale. Absolute zero on the Rankine scale is -459.67° Fahrenheit. Scientific computations involving gasses are often done in Rankine or Kelvin.

First used: 1926

(thermometric scale)

Named after Anders Celsius (1701-1744), Swedish astronomer.

C based on freezing point of water and 100° C on the boiling point.

In 1742 Celsius proposed a 100-degree (centigrade) scale (from 0° to 100°), and improved the Centigrade scale by defining 0.01° C as the triple point of water and 100° C as the boiling point.

Because "centigrades" and "grades" were also measures of angle, the Centigrade scale was officially renamed the Celsius scale in 1948.

First used: Centigrade, 1801; Improved (with basis on tripple-point), 1850

## Kelvin

(absolute scale)

Named after William Thomson, 1st Lord Kelvin (1824-1907), Scottish engineer, mathematician and physicist.

Uses Celsius degree units but sets zero equal to absolute zero.

The Kelvin scale uses the same size degree increments as the Celsius scale, and is widely used by astronomers and physicists.

Around 1862, Kelvin (in collaboration with J.P. Joule) proposed an absolute scale of temperature based on laws of heat rather than the on the freezing/boiling-points of water. From this work came the idea of absolute zero -- the temperature below which it is not possible to go (the point at which all molecular movement theoretically ceases). Absolute zero is 0°K (-273.15° Celsius).

First used: 1908

## RÉaumur

(thermometric scale)

Named after René-Antoine Ferchault de Réaumur (1683-1757), French scientist.

Freezing-point of water is 0° and the boiling-point is 80°.

This scale is now obsolete (but may be of some historical interest).

Réaumur proposed a new scale in 1730 that set the freezing-point of water at 0° and the boiling-point at 80°. Each °Réaumur is equal to 5/4 of a °C, so °*5/4=°C, °Ré*9/4+32=°F, and °Ré*5/4+273.15=°K.

First used: 1814

## Conversion Formulas

Briefly, the big two:

• F to C: C = (5/9)(F - 32)
• C to F: F = (9/5)C + 32
But did you know . . .
• F to C: C= (5/9)(F + 40) - 40
• C to F: F= (9/5)(C + 40) - 40
And it may help to know that . . .
• 9/5 = 1.80
• 5/9 = 0.555555...
All conversions:
• F to C: C=(5/9)*(F-32)
• F to K: K=((5/9)*(F-32))+273.15
• F to R: R=F + 459.67
• F to Ré Ré=((5/9)*(F-32))*(4/5)
• C to F: F=((9/5)*C)+32
• C to K: K=C+273.15
• C to R: R=((9/5)*C)+491.67
• C to Ré: Ré=C*(4/5)
• K to F: F=((9/5)*(K-273.15))+32
• K to C: C=K-273.15
• K to R: R=(9/5)*K
• K to Ré: Ré=(K-273.15)*(4/5)
• R to F: F=R-459.67
• R to C: C=((5/9)*(R-491.67))
• R to K: K=(5/9)*R
• R to Ré: Ré=((5/9)*(R-491.67))*(4/5)
• Ré to F: F=((9/5)*(Ré*(5/4))+32
• Ré to C: C=Ré*(5/4)
• Ré to K: K=(Ré*(5/4))+273.15
• Ré to R: R=((9/5)*(Ré*(5/4)))+491.67

## Triple Point of Water

The triple point of water is defined as the state (p=611 Pa, t=+0.01° C [i.e., t=273.16 K]) where all different forms of the substance can co-exist (i.e. liquid, solid, gas). This is only possible at one temperature and one pressure. It is therefore used as the second fixed point to define the temperature scale, absolute zero being the other fixed point. When water freezes on earth it is affected by many other factors like contamination, changes in air pressure, and so forth.