Is water at 200 degrees Fahrenheit twice as hot as water at 100 degrees Fahrenheit?

The popular but incorrect answer is yes.

The inaccuracy is perpetrated even on science programs on TV as well as in articles about science in popular science magazines.

Figuring that 200 degrees is twice as hot as 100 degrees is a simple division problem, although most of us would see intuitively that 200 divided by 100 equals 2.

How much hotter is water when it is at boiling temperature, 212 degrees F, compared with freezing temperature, 32 degrees F?

Using that simple ratio, boiling divided by freezing would be 212 divided by 32, which equals six and five-eights, or 6.625. So, is it correct to say that boiling water is a little more than 6-1/2 times hotter than freezing water?

Let us investigate. What about the same question posed in Celsius? Then it would be 100 C (boiling) divided by 0 C (freezing).

Oops! We cannot do that. Division by zero is an undefined operation. The reason for that is a little complex in detail.

It boils down to if division by zero were defined, then we would also have to be able to multiply by zero and get a nonzero answer. Most everyone knows that anything multiplied by zero is zero. No exceptions. No division by zero.

There is obviously something wrong. What is it?

It is simple. Our common, temperature scales are relative, not absolute. There are negative temperatures. Dry ice sublimates at minus 109 F. Liquid nitrogen boils at minus 320 F, liquid oxygen at minus 297 F, liquid hydrogen at minus 432 F and liquid helium at minus 452 F.

How low can we go? It seems that we need an absolute temperature in order to compare “hotness.” To get that we need to know what is the coldest that anything can be.

It would obviously be absolute zero as opposed to the relative zeros of Fahrenheit and Celsius.

Over the past 150 years, scientists have developed different ways of calculating the value of absolute zero precisely in terms of the relative Fahrenheit and Celsius scales.

Absolute zero is minus 459.67 F and minus 273.15 C.

The Kelvin scale

In the late nineteenth century Sir William Thompson, aka Lord Kelvin, tested a new theory that heat is due to molecules moving around in a substance. Using the change in volume of a gas with temperature, he extrapolated to find the lowest possible temperature and created a new temperature scale that began there.

The Kelvin temperature scale starts at absolute zero, 0 K. It is related to the Celsius scale in that the degree is the same size. This is unlike the relationship between Celsius and Fahrenheit, where 1 degree C equals 1.8 degrees F.

Now returning to the original questions, it is clear that only the Kelvin temperature accurately reflects the amount of internal energy in a substance. On the Kelvin scale, water freezes at 273 K and boils at 373 K.

So boiling water is 373 divided by 273, or 1.37 times hotter than freezing water.

A good analogy is to think of a linear measurement such as a person’s height. Suppose that a tailor measures height relative to the top of a yardstick tacked to the wall at floor level because it is monotonous measuring the lower three feet each time. She becomes accustomed to this measurement such that a 5-foot person would be a “2” and a 6-foot person would be a “3.”

Is a 6-footer 1-1/2 times as tall as a 5-footer? Of course not!

Richard Brill is a professor of science at Honolulu Community College. His column runs the first and third Friday of the month. Email questions and comments to brill@hawaii.edu.