Absolute Zero

Date: 05/11/2001 at 16:07:47
From: Robert Smith
Subject: Absolute zero

My question is, why is absolute zero used in some calculations, e.g. 
temperature + 460?

Thanks,
Rob

Date: 05/14/2001 at 17:36:54
From: Doctor TWE
Subject: Re: Absolute zero

Hi Rob - thanks for writing to Dr. Math.

Suppose you have $10,000 in the bank and an additional $10 in your 
pocket. Now suppose that you find a $20 bill on the ground. Would it 
be fair to say that your wealth has tripled, because you went from 
having $10 in your pocket to having $30? No, because you really went 
from having $10,010 to having $10,030 (which is less than a 0.2% 
increase).

Temperature is the measure of the heat (or average kinetic energy) of 
an object. When measuring it on an "absolute scale" like Kelvin or 
Rankine, we're measuring the total amount of heat (k.e.) present (kind 
of like counting your total dollars). When measuring it on a "relative 
scale" like Celsius or Fahrenheit, we're measuring how much above or 
below a fixed value it is (kind of like only counting the dollars in 
your pocket).

To convert degrees Fahrenheit to degrees Rankine, add 460 because 
absolute zero (no heat) is -460 degrees Fahrenheit. To convert Celsius 
to Kelvin, add 273 because absolute zero is -273 Celsius.

If the temperature goes up from, say, 40 degrees Fahrenheit to 80 
degrees Fahrenheit, the amount of heat in the object hasn't increased 
100% (80F/40F = 2.00), but rather only 8% (540R/500R = 1.08).

Here's another example: What is the percentage increase in heat 
(temperature) if an object goes from -10 degrees Fahrenheit to +10 
degrees Fahrenheit? If we just divide, we get:

     +10F / -10F = -1

but is that negative 100%? That wouldn't make any sense. If we use the 
absolute temperature scale, we get:

     470R / 450R = 1.044

or about 4.4% increase.

Whenever we're dealing with temperature ratios (as we do with Boyle's 
law and the Ideal Gas law), we have to use an absolute temperature 
scale. Only when dealing with temperature differences does it not 
matter. If in doubt, it's always safe to use the absolute scale.

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/