We all are curious about how hot or cold it will be inside, or outside, so we can dress to be comfortable. What most of us do not realize is that the temperature scales that we use are just about completely arbitrary.
The two most common scales are the Fahrenheit one and the Celsius (previously called centigrade) one. Two others are the Rankine (also spelt Rankin) and the Kelvin scales. The basic difference is that Fahrenheit and Celsius are arbitrary, and that Rankine and Kelvin are based on the absolute of zero.
The Fahrenheit scale is likely the oldest in common usage, and just about now confined to the United States. Fahrenheit devised this scale by using a mixture of snow and salt that he defined as to be zero degrees. Since he had designed a fairly small mercury thermometer, he had his wife hold it in her armpit until the reading became stable and called that 100 degrees. As I said, it was a fairly arbitrary system, and woe to the folks who had to collaborate the data, in the days before daily baths and modern soaps. It is a good thing that he was not a bit more kinky, but would have actually, if he had been, gotten a better reading.
Celsius decided that a mixture of snow and salt was too hard to reproduce, and so used thawing ice and water as his zero degrees, and boiling water as his 100 degrees. He corrected for elevation, since it was known at the time that water boils at a lower temperature in higher elevations. His scale is pretty good, but not absolute.
Well, the German Fahrenheit and the Swede Celsius had some conflict in the scientific world, and Celsius finally won since his scale, whilst arbitrary, was less so than that of Fahrenheit, since it did not depend on a particular person's armpit temperature (there are no data concerning her menstrual cycle, which can perturb body temperature by a degree or two on the Fahrenheit scale).
So, in most of the world, the Celsius scale is used. It was later recognized universally that the normal body temperature of a healthy adult is 37 degrees C, (not actually true, because there is a lot of individual variation. For example, I normally run around 97.9 F orally, and feel feverish at 98.6 F) which, when you use the mathematical formulae that I will show later, works out to 98.6 degrees F. So Fahrenheit was not too far off by using 100 F for his wife's armpit, just 1.4 degrees on his scale.
But that leaves us with the problem of negative degrees. Now it gets geeky. Temperature and heat are only loosely related. When you pick up a hot handle on the stove, you say, "S***, that is hot!". But you really are not talking about heat at all, only temperature. I can prove to you that a large iceberg holds much more heat that your little kettle, although your kettle feels hot. What's up with this?
Heat is energy. Temperature is a thermodynamic quantity very different from heat. Temperature is the effect that heat has on a particular collection of matter. It is impossible to have negative heat, in our understanding, and also a negative temperature except for the arbitrary scales that we have give it.
The natural philosophers who studied science from the 16th to the 18th centuries helped us somewhat. They had lots of wrong ideas, phlogiston being one of them (that might be a good topic for a later post), but some good ones. They finally determined that heat and temperature were quite different, but could be related to each other when the properties of the materials were taken into account.
For a given amount of a given substance, heat and temperature are related by the heat capacity of the substance. All substances have different heat capacities, except by coincidence. Heat capacity is defined as the rise (or fall) in temperature of that substance when a definite amount of energy is added (or removed) from the material. Water has the highest heat capacity of commonly encountered materials, so has become the standard. Besides, it is easy with which to work. The heat capacity of water is taken as one calorie per gram per degree C. (These calories are 1/1000 the Calories used to express caloric value of foods, and are related in some strange ways). On the other hand, pure alcohol has a heat capacity of only 0.438 calorie per gram per degree C. What this means is that you add one calorie to one gram of water at 25 C, it becomes 26 C. When you add that same amount of heat to ethanol, it becomes 27.3 degrees C. This was not well recognized in the old days, and until it was figured out made it very difficult to relate heat and temperature.
We all know that in the Fahrenheit scale that freezing is 32 degrees F, and boiling is 212 degrees F, so there are 180 degrees F between to two. In the Celsius scale, freezing is zero degrees C and boiling is 100 degrees C, so 180 F degrees represent 100 C degrees. Thus, a degree C is 1.8 times "bigger" than an F degree. There is a simple formula to convert the two:
C = (F-32)/1.8
When you plug in 98.6 for F, you get 37 C out of the relationship. It can be rearranged to read
F = 1.8C + 32, and when you plug in, say, 20 degrees C (near room temperature, and it was in norther Europe, you get 68 degrees F. There are tables on the Tubes where you can just enter one temperature and out pops the other.
Fun exercise: find the single temperature where the Fahrenheit and the Celsius scales intersect. Geeks are not allowed in this one, since we are all descendants of Mercury (there is a very subtle joke there).
By the time that folks were investigating the gas laws (I have some previous posts about those in this series), it was found that having a zero as an arbitrary setting did not work well. After careful experimentation, it was found that any gas expands by 1/273 by each increase in a degree Celsius. Likewise, they contract by the same fraction. (Remember, this was before the kinetic theory of gasses and atomic theory was well understood). Taking this relation to the point where a gas would have zero volume, it was postulated that the coldest temperature possible would be negative 273 Celsius. This is the so-called absolute of zero temperature, commonly called absolute zero.
Thus, Lord Kelvin devised a temperature scale based on this temperature as the lowest possible. He kept the "size" of the degrees that Celsius used, and the Kelvin scale goes from 0 K (the convention is not to use degree signs with the Kelvin scale) to infinity. Thus, on the Kelvin scale, water freezes at 273 K, and boils at 373 K. Rankine modified it to use the old Fahrenheit degree sizes, and the Rankine scale is still used in engineering for Imperial units. Otherwise, they are the same in that the zero point has nothing below it, since a true negative temperature is not in keeping with the laws of physics. These are the absolute scales, and as any junior high student will tell you must be used when going gas calculations.
Later work showed that the offset was actually 273.15 degrees C, but that was pretty close for the time. Now comes the interest part.
The absolute scale was postulated on the behavior of gasses being cooled, before it was known that they were composed of either single atoms or molecules. But it works. Interestingly, regardless of how we try (and we have, believe me), we have never found any evidence that it is possible to go below that temperature. This is quite a statement to make for a constant that was determined on very shaky theoretical grounds. In fact, I find it to be amazing.
Here is what happens at absolute zero: all motion stops. Everything. No motion at all, translational (straight line), rotational (spinning), vibrational (atoms moving back and forth), everything. It is as if time stops. If you could cool something to absolute zero instantly, time would appear to have stopped.
We have come close to it, but never have quite attained it. Here is one way to try to get there: get a gas, say helium, and compress it. Then let some evaporate so that the rest is cooled. Repeat the process, and you finally get liquid helium. Then do some very complex work, like adiabatic nuclear decoupling and you can get closer. We have attained the value of a few microdegrees above absolute zero, but never have attained it. There are a couple of theoretical reasons why.
First, there is no such of a thing as a perfect thermal insulator. On this hot rock of Earth, some heat will leak into the system. Second, there is not any such of a thing as a perfect engine, and because of those imperfections, nothing can remove all of the heat from any system. Third, entropic considerations come into play. It is hard to make the entropy of a system go to zero, as required at the absolute of zero, since the entropy somewhere else has to balloon, that that costs tremendous amounts of energy to make it go.
Well, I hope that this irregular installment of Pique the Geek is entertaining and thought provoking. As always, questions, comments, criticisms, and other science and technology topics are welcome in the comment section. Right now it is 8.6 degrees F here, or a warm 260 K. If I were liquid nitrogen, I would be warmly bubbling (the boiling point of nitrogen is 77 K), but since I am a bag of mostly water, I am cold, or would be outside. To save energy, I have dressed in layers and set the thermostat to 66 degrees F. I did put a 100 w bulb in the droplight in the shelter that I built for my fig bush to hope to keep it over 5 degrees F (it is supposed to go negative here tonight), since the branches die if under 5 degrees F).