How do you derive the conversion of temperature?

Answer 1

First thing is first, defining the different scales, their basis.

Im not sure on the sciency specifics of the definition... but on the Celsius, or Centigrade scale, 0 degrees is defined something along the lines of "freezing point of water". Im not sure at what pressure or purity, but essentially the freezing point. Simiarly, 100 degrees is defined to be the boiling point of water. These are definition. They set the positions of certain particular events, and the distance in between. Namely, 0 is freezing water, 100 is boiling water, and there is a 100 degree gap between the two.

On the Fahrenheit scale... oh golly... 0 degrees has something to do with the lowest temperature a salt-water mixture can reach before it freezes. 100 F is supposed to be the average human body temperature... (unfortunately, the early statistics were off by a little). Thus, there is also a 100 degree gap between those two events.

Okay... how do you derive the conversion?

If you look on a thermometer properly guaged in celsius and Fahrenheit degrees in accordance with their definition... you will notice two things...

One, you will notice that there are far more tack marks on the Fahrenheit side... the markings for each degree is closer together than the markings on the Celsius side. For each Celsius degree, there is about 1.8 (or 9/5) Fahrenheit degrees. Or, for ever Fahrenheit degree there is about 5/9 (0.555...) Celsius degrees.

This is because the actual temperature difference (in terms of actual heat energy) between events separated by 100 degrees is... is closer together in Fahrenheit than in Celsius. Their associated definitions place these events at different energy levels... but they both have a 100 degree gap on their respective scales. In Celsius, the distance between events is still 100... but the difference in energy level is far greater.

The other thing you will notice is that a 0 on one scale is not at the same spot as a 0 on the other scale. The definition of zero in Fahrenheit is not the same as the definition in celsius... and so zero is placed at a particular energy level too.

So not only are their zeros not in the same spot (The zero on the celsius scale is equivalent to the 32 on the Fahrenheit scale), but there are more Fahrenheit degrees in a given change in heat.

The conversion is then:

(F-32) 5/9 = C

(9/5)C + 32 = F

I hope that answers your question.

Answer 2

Celsius to Kelvin: add 273

K = 273+ C

C = K - 273

Celsius/Fahrenheit:

C = (F +40)*5/9 - 40

F =(C +40)*9/5 - 40

F to Rankine

R = F + 459.67

Réaumur

C = R*1.25

F = R*2.25 + 32

Answer 3

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