Temperature Conversions
Introduction.
There are two scales for measuring temperature. One is called the Fahrenheit scale, and it is used mainly in the United States. The other is called the Celsius scale and is used in most other countries. The unit of temperature is called a degree. So we have two units: degrees Celsius (written as C) and degrees Fahrenheit (written as F).
Gabriel Daniel Fahrenheit (1686-1736) was a German physicist. He chose as 0 degrees (0°F) the temperature of freezing of a mixture of ice, salt, and water. He called 32 degrees (32°F) the temperature at which pure distilled water freezes. He also thought that the third point on his scale, the normal temperature of the human body, is 96°F. (He was wrong. The normal temperature of the human body is approximately 98.6°F.)
At sea level, pure water boils at 212°F. So the difference between the temperature of boiling water and the temperature of freezing water is 180 degrees Fahrenheit. Water boils at a lower temperature in the mountains, because the temperature of boiling water depends on air pressure, which is lower at higher altitudes.
Anders Celsius (1701-1744) was a Swedish astronomer. He chose as the 0 of his scale (0°C) the temperature of freezing water, and as 100 degrees (100°C) the temperature of boiling water at sea level. The difference between the temperature of boiling water and the temperature of freezing water is 100 degrees Celsius. A mixture of ice, salt and water freezes at a temperature of -17.(7)°C. ("Minus seventeen point repeated seven" which is -17.77777.... and which can also be written as -160/9.)
Conversions.
Because a difference in temperature of 100°C is the same as 180°F (the difference in the temperatures of boiling water and freezing water), 1°C is 1.8°F. We also write it as
1°C = 1.8°F,
and read it: "A difference in temperature of one degree Celsius is the same as a difference of one point eight degrees Fahrenheit." (We find this relation by dividing 180 by 100.). But 1.8 = 9/5. So we may also say: 1°C is 9/5°F, or 1°C = 9/5°F. (We should remember that the = sign, used here, means the same difference of temperature. Of course, the numbers 1 and 9/5 are not equal!)
By similar reasoning we find that 1°F = 0.(5)°C or, using common fractions, 1°F = 5/9°C. (0.(5) should be read "zero point repeated five," and it means 0.555555555... .) Also we know that the same temperature was named 0°C and 32°F. We write it 0°C = 32°F, and read it: "A temperature of zero degrees Celsius is the same as a temperature of 32 degrees Fahrenheit." Similarly, 0°F = 160/9°C.
Let's find out what 23°C is on the Fahrenheit scale.
23°C is 23°C above 0°C. But 23°C = 23*1.8°F and 0°C = 32°F. So 23°C is 23*1.8°F above 32°F.
[23][*][1.8][+][32][=] display: 73.4
Answer: A temperature of 23 degrees Celsius is the same as a temperature of 74.4 degrees Fahrenheit.
We can see that this method always works, so we may write a general formula. Let's call c the number of degrees Celsius, and f the number of degrees Fahrenheit (for the same temperature). So
f = c*1.8 + 32,
or if you prefer common fractions,
f = c*9/5 + 32.
In order to get a formula which computes c when f is given, we do not need to repeat all our reasoning. A little algebra is enough.
f = c*9/5 + 32, so
f-32 = c*9/5, so
(f-32)*5/9 = c.
Example. The temperature is 15°F. How many degrees Celsius?
[15][-][32][*][5][/][9][=] display: -9.4444444
Answer: -9.4°C.
Project: Graphic comparison of the two scales.
Draw two parallel vertical lines (close together) on a sheet of paper. Write above the left line Celsius and above the right line Fahrenheit. Mark 0 and 100 on the Celsius line exactly 10 cm apart (so 1°C will correspond to 1 mm). On the second line write (at the same height) the corresponding temperatures in degrees Fahrenheit, 32 and 212. Next, put other values correctly on the scales (use the ruler, and measure carefully).
Note that a 10°F difference shows on your scale as 1.8 cm. (1 cm and 8 mm).
What temperature is the same on both scales?
(Answer -40°F = -40°C.)
Find an outdoor thermometer which has both Fahrenheit and Celsius scales. Look for -40°C, -40°F, 0°C and 0°F. (On some thermometers, the scale is not straight but circular.) Do you know how thermometers work?