Thursday, August 19, 2010

Fun With Math (?): Converting Centigrade to Fahrenheit and Vice Versa

Some Background:
The global warming alarmists often live in Europe, so we see lots of references to temperatures in centigrade.  Here in the U.S. we are still used to reading temperatures in Fahrenheit.  It's useful to be able to convert from one temperature scale to another, especially to put alarmists arguments into a more familiar perspective.

My Screw Up at YouTube:
There is a National Geographic video at YouTube showing the ecological disaster that would allegedly occur if global temperatures increased even 5°C.  Well I whipped out the conversion formula I learned in high school and tried to convert that increase to its Fahrenheit equivalent, which has more meaning for me as an American.  So I computed 5°C * (9/5) +32 = 41°F.  Well now, I thought, we'd have to have the sun become a supernova before such an increase would happen, so the whole argument is moot, cause it ain't ever gonna happen, at least not for billions of years.

Thinking It Through
However, my thinking was wrong.  We weren't comparing two temperatures, we were comparing an increase in temperature, an interval rather than a point on the thermometer.  So how do you convert an interval, say, how is an increase in 5°C converted into °F?

Well, let's see.  The centigrade thermometer is based on a 100 degree scale:  start at 0 degrees (freezing point for water) and end at 100 degrees (boiling point for water).  The Fahrenheit thermometer is based on a 212 degree scale.  It starts at 0 and ends at 212 degrees.  Freezing (for water) is at 32 degrees and boiling of water occurs at 212 degrees.  Okay, so converting an interval, C to F, should be C * 212/100, I thought.  That converted 5°C to 10.6°F.  Sounds reasonable.  If correct, I should be able to convert back to C by the upside down version of the formula:  C = F*(100/212).  However, this did not convert 10.6 °F back to 5°C. It converted it to 2.36°C.  My formula didn't work, but why?

Aha, it dawned on me.  Water freezes at 0°C and at 32°F.  The scales are not really comparable because the F scale covers a greater range of temperatures.  To make them comparable, I had to knock off the first 32° from the F scale (212 - 32 = 180).  So the formula for comparing temperature intervals are these:  F = C*(180/100) and C = F*(100/180).

So an increase of 5°C is equal to an increase of 9.0°F, and vice versa.  This formula works both ways, so it seems correct.

So now, in order to evaluate National Geographic's nightmare scenario, I have to think:  what ecological disaster would occur if global temperatures increased 9.0 °F?  That would be hot, indeed.  The Medieval Warming Period is said to have increased only 7°F, at the most.  However, that period saw longer growing seasons, easier living conditions and greater longevity.  The warming was beneficial to man, not deleterious.

So even if temperatures did increase 5°C, would it really destroy the planet?  I doubt it.  I also doubt that the temperatures ever will increase that much, barring some unforeseen ecological change (man made carbon emissions won't do it.)

Okay, for those who are interested, here are the formulas for converting temperatures.

Converting From Centigrade to Fahrenheit:
It the temperature is 5 degrees C, what is the temperature in Fahrenheit?  Use the formula:

F = (9/5 * C) + 32

So to convert 5°C to F:  (9/5 * 5) + 32 = 41°F.

Converting From Fahrenheit to Centigrade:
If the temperature is 41°F, what is it in centigrade?  Use the formula:

C=(F-32) * 5/9

So to convert 41°F to C:  (41-32) * 5/9 = 5°C

Now, if the temperature increases by 5°C, how much did it increase in F?  The answer is not 41 degrees, because we aren't measuring two temperatures, but the interval between two temperatures. The formula to compute this is:  C * 180/100 = F.

So an increase in 5°C = 5* (180/100) = an increase of 9.0°F

To convert a temperature interval from F to C, the opposite formula is used:
F * (100/180) = C.

So an increase in temperature of 9.0 °F, expressed in C, is as follows:
9.0 * (100/180) = 5°C.

Now that I have put you all to sleep, pleasant dreams!


Stogie said...

Crazy CPAs!

Stogie said...

I do have fun with math and Excel!   :)

Stogie said...

That's the hard way to solve nine-fifths times 5. Are you sure you're a CPA?

Careful, buddy. If you keep messing around with gateway skills like math and the metric system, you could end up strung out on science literacy! 



Stogie said...

Sven, yes it dawned on me today that 180/100 is the same as 9/5.  However, the 180/100 is what makes it clear, since the figures are of thermometer degrees.

By the way, I was a Zoology and Chemistry major before I switched to accounting and I worked in a commercial Chemistry lab (as a lab tech running experiments) for six years.  I am not a stranger to science.