# Temperature scale redux

## Numerous scales and units have been devised for measuring temperature—the most commonly sensed and monitored physical parameter—but only two major units now find everyday usage. Two 18th century European scientists are credited for today's degrees Fahrenheit (°F) and degrees Celsius (°C) scales, of which the latter is virtually universally used except in the U.

By Frank J. Bartos July 1, 2004

Numerous scales and units have been devised for measuring temperature—the most commonly sensed and monitored physical parameter—but only two major units now find everyday usage. Two 18thcentury European scientists are credited for today’s degrees Fahrenheit (°F) and degrees Celsius (°C) scales, of which the latter is virtually universally used except in the U.S.

Key to establishing a reliable temperature scale is a foundation of repeatable standard points, for example, the change of state of water. German-born physicist Gabriel Fahrenheit (1686-1736) originally based his scale on three points: An ice-salt-water mixture designated as zero; plain ice-water mixture set as 30; and the oral temperature of a ‘healthy’ human designated as 96. On that scale, the boiling point of water (at standard atmospheric pressure) came in at 212. Adjustments followed, like designating water’s freezing point as 32, which made the interval to the boiling point a more reasonable number (180).

Swedish astronomer Anders Celsius (1701-1744) applied his careful experimenter’s approach to establish a more logical scale, with 0 as the boiling point of water and 100 for its freezing point. The scale was reversed to its present form after his death. Because of the C Scale’s ‘100-point’ interval between the freezing and boiling points of water, it was also referred to as the Centigrade scale. More in our time (1948), the designation ‘degrees Celsius’ was adopted for °C.

Since the C and F scales are based on the same physical points (changes of state of water), they’re easily related. A graph of the relationship—a straight line connecting standard points 1 and 2 and continuing in both directions, serves as a useful visualization tool. Besides providing a physical feel for the temperature scales, the line gives us an equation of the C and F relation virtually by inspection. I recommend such a graph for anyone working with temperature conversions.

Since we know the slope of the line (2z/1z = 180/100 or 1.8) and its F-axis intercept of 32 (point where C = 0), then from basic math, the slope-intercept equation of a line directly yields:

F = 1.8C + 32, which is easily solved for C to give C = (F – 32)/1.8.

These are all the conversion formulas you need. I believe they’re simpler than often-cited forms involving fractions. The graph further explains why the C and F scales have one point of numerical equivalency at -40 (which I call the ‘unique’ point). This occurs at point A in the third quadrant where xA = yA. Graph points B through G provide physical perspective on other temperature points of interest.

 Basis of both Celsius and Fahrenheit temperature scales is the interval between the freezing and boiling points of water at standard conditions. These are points 1 (0 °C; 32 °F) and 2 (100 °C; 212 °F) along the relationship line.

Downward extension of the line has a defined ending at point 3, known as absolute zero (-273.15 °C; -459.67 °F). This theoretical coldest possible temperature of matter is the zero point of the Kelvin scale , proposed by British scientist William Thomson (Lord Kelvin) in 1848. Kelvin temperature scale has application in scientific and engineering fields and is specified without the term ‘degree’ (e.g., 283 K = 10 °C = 50 °F).

Upward extension of the line has no defined limit. Many industrial and physical processes operate at up to thousands of degrees F or C.