Welcome 2014! And quite a start to the year, with a cold snap that rivals anything we’ve seen in two decades. I don’t remember cold like this since the horrid winter of 1994, when the Northeastern U.S. saw snowstorms and extreme cold that alternated back and forth for weeks. Of course, when I was a child in the 1970s, such chills happened a lot more often; I remember a number of New England mornings where I awoke to a thermometer reading of -20ºFahrenheit (-29ºCelsius) [244 Kelvin].
The scariest negative temperature numbers that one hears about from the media are associated with the “wind chill”, which is a number that is supposed to measure how cold the air “feels” to your skin. But “wind chill” is a rather subjective and controversial measure — there’s no unique way to define it, since you’ll feel differently depending on how much exposed skin you have, on your body weight, on your age and conditioning, etc. By contrast, the temperature measured by a thermometer is defined independent of how humans feel, and experts agree on what it is and means. Oh sure, people use different scales to measure it: Fahrenheit (F), Centigrade or Celsius (C), and Kelvin (K). But the differences are no more than the distinction between meters and feet, or between kilograms and pounds; it’s straightforward, if a bit annoying, to convert from one to the other.
So everyone agrees the temperature is and feels extremely cold, But is it, from the point of nature, really that much colder than usual? To say it another way: it was 84ºF (29ºC) in southern Florida yesterday. How much warmer is that than the -40ºF (-40ºC) that was registered in the cold Minnesota morning?
Well, you might first think: wow, it’s a difference of 124ºF (69ºC), which sounds like a huge difference. But is it really so huge?
Perception and Reality
We humans experience the world through our perceptions and our consciousness — through what we see, hear, feel, and so forth. And as is natural, we tend to assume that what we see, hear and feel correctly represents the world as it is. But in fact, as scientists have learned over the past centuries, the devices we use for our perceptions — eyes, ears, temperature-sensing nerves, and so on — filter and process the information that they receive from the outside world. Our brain then does further processing. By the time the information enters our conscious notion of the world, the world has become a caricature, a cartoon, of the real thing. Much of the world is ignored, and the part that we are conscious of is transformed almost beyond recognition.
Indeed, one of the first things young science students have to do is unlearn almost everything our senses and brains tell us about the world, and relearn it almost from scratch.
So it is with hot and cold. In the real world there is no such thing as a “hot object” or a “cold object.”
However, there really is such a thing as temperature. One can speak of “hotter” and “colder”; if A is hotter than B, then, very simply, A has a higher temperature than B.
But it makes no sense to say “A is hot”. The statement that “A is hot” is a misconception, a trick that our senses play on us. What this really just means is that, to your skin’s nerves, “A feels hot”. And what that usually means, in the real world, is “A is hotter — has a higher temperature — than your skin”. As always the full story’s a bit more complicated, but not too much.
It’s always good when you can do a simple experiment, on your own, to reveal some basic fact about the world. There’s a nice one in this case. Take three bowls; fill one with ice water (literally, water with ice in it), fill a second with water that’s almost too hot for you to put your hand in, and fill the third with ordinary tap water that’s lukewarm. Now put your left hand in the ice water and your right hand in the hot water. After a minute or so, take them out and put them both in the tepid water. How hot is that water?
You will find you are of two minds. Your cold hand will feel the tepid water is hot, and your hot hand will feel it is cold. And this is because the tepid water is hotter than your cold hand, and colder than your hot hand. Thus you may easily learn: what you feel as hot and cold is not a measure of the world, but rather a measure of you relative to the world.
In other words, we humans are not thermometers; our nerves and brains don’t tell us the temperature of a thing, just whether it is hotter or colder than some temperature we find comfortable. [In fact our nerves don't even tell us how much hotter or colder another object is; they actually tell us something about how quickly heat is flowing out of or into our bodies from the object that we're sensing, which is why, when you pull clothing from a hot clothes dryer, the metal zipper feels so much hotter than the cloth does. But more on that another time.]
So what is temperature?
In most ordinary situations, you can think of temperature in a simple way (though I should note that a more sophisticated view is sometimes needed.) Every material object that we find around us — tables, air, bricks, glass, alcohol — is made from molecules characteristic of that material. In any material, the molecules, vastly too small for you and I to see, are moving, fast and randomly, and banging into each other. Some are moving faster than others, and they’re heading in all directions. In a solid, they don’t move far; they just rattle in place. In a liquid or gas, they can move all around, but they don’t go far without banging into each other, and when they collide their speed and direction change. Because they’re constantly running into each other, each molecule is moving sometimes faster, sometimes slower… but the molecules never stop moving.
[This might confuse your intuition. You're used to large objects that you can see, like soccer balls and cardboard boxes and pens, slowing down and stopping. That's because, on the Earth's surface, large objects generally end up sliding over the ground or the floor, and friction slows them down. Molecules aren't subject to friction, so they keep moving. In fact friction is a process in which large objects gradually lose their motion-energy (technically, "kinetic" energy) and hand it over to molecules!]
The temperature of an ordinary material is simply a measure of the average amount of random, invisible motion that the molecules in that material are undergoing, or, more precisely, a measure of the average speed and motion-energy that those molecules have. Molecules in colder objects move more slowly than molecules in hotter objects; that’s all there is to temperature!
Here again, our senses fail us. Look at the table in front of you. Your senses do not tell you that the molecules in that table are randomly wiggling around. Of course your senses don’t even tell you that the table is made from molecules, so it’s not surprising they don’t reveal their motion… but there aren’t even apparent fuzzy edges to the table, which you might have naively expected. And our senses don’t tell us that even on a calm day, with no wind, the molecules of the air surrounding us are zipping around at a cool 1600 feet (500 meters) per second — faster than the speed of sound, and around five times the wind speeds of the most powerful hurricanes.
This incredible rain of molecules against your body doesn’t knock you over because, unlike hurricane wind, which pushes you in a particular direction, the random motions of the molecules push you in all directions, and therefore, in no direction at all. The molecules do exert pressure on your skin, but your body pushes back; if it didn’t it would collapse, so of course evolution has assured that it does. Yet your senses don’t even bother to tell you that all this is happening. Why? Because this pressure is just part of the scenery of being alive on the surface of the Earth, and your survival doesn’t depend upon you knowing about it, anymore than it depends upon you knowing that molecules exist at all.
How much hotter is Florida than Minnesota?
Now that it’s clear what temperature is, we can ask how large, really, is the change from the 84ºF (29ºC) [301 K] temperature felt in daytime in southern Florida and the -40ºF (-40ºC) [233 K] temperatures felt in early morning in northern Minnesota? The temperature difference, subtracting the colder number from the hotter one, sounds dramatic, but doesn’t answer to the question. We have to focus something else.
For this purpose, the outdated Fahrenheit scale is hopeless. The number of degrees doesn’t correspond to anything very easy to remember. You just have to memorize how the Fahrenheit scale works: water boils at 212ºF and freezes at 32ºF, and that’s for weird historical reasons.
The Centigrade, or Celsius, system (Celsius invented it in 1743) is much easier to remember, and almost the whole world uses it in daily life. 0ºC is where water freezes; 100ºC is where it boils. But while that’s convenient when you want to know if the temperature is below freezing, it’s not convenient to determine the answer to our question.
No, if you want to understand really how much hotter is air at 84ºF (29ºC) than air at -40ºF (-40ºC), you need the Kelvin scale. The Kelvin scale is very easy to use. For one thing, it’s really the same as the number of degrees in Centigrade/Celsius scale, plus 273.15 — and that’s it. I’ll just approximate this shift by 273, to keep my numbers simple.
- freezes at 273 K, and
- boils at 100 + 273 = 373 K.
What’s this magic number “273.15”? Well, 0 K = -273.15 ºC = -459.67 F is the temperature at which the amount of motion-energy per molecule reaches zero, and the molecules stop moving. [Almost true! Due to the jitter inherent in quantum mechanics, the molecules never quite stop moving, and the motion-energy is never quite zero. But the motion and the motion-energy are far too small for us to worry about for today.] In other words, it is impossible to have a lower temperature than zero Kelvin! This lowest possible temperature is called “absolute zero”, which is why the Kelvin scale starts there. 0 K simply corresponds to the lowest possible motion-energy per molecule, which for most practical purposes might as well be literally zero.
So here’s the advantage of the Kelvin scale: the temperature of the object in Kelvin is directly proportional to the energy of its molecules. An object with a temperature of 200 K has twice as much motion-energy per molecule as one with a temperature of 100 K, and half as much motion-energy per molecule as one with a temperature of 400 K.
Well, that suggests to us how we should answer the question: How much hotter is object B than object A? Now that we have a scale for which all temperatures are positive, we can take a ratio of their two temperatures, TB/TA. If B is hotter than A, the ratio is greater than 1; if B is colder, the ratio is less than 1. If that ratio is, say, 1.2 — if the temperature of B is 20% larger than the temperature of A — that tells us that the molecules in B have energy 20% larger than those in A. Remember this is only true if we use the Kelvin scale, and not Fahrenheit or Celsius.
Meanwhile, the reason not to use the temperature difference, TB – TA, is that its meaning is ambiguous. A difference of 5 K would be very large if B is at 6 K and A at 1 K — B is six times hotter than A — but would be a tiny effect if B is at 60,000 K and A is at 59,995 K, in which case the difference in the two temperatures is a very small fraction of a percent.
I hope you now begin to see why scientists use the Kelvin scale. It is a scale that relates a property of visible macroscopic objects, as measured in temperature, to the level of activity of the invisible microscopic molecules out of which the objects are made, as measured in motion-energy (or “kinetic” energy). If the temperature is large, so is the energy per molecule; as one drops to zero, so does the other.
So how cold is this week’s cold snap?
Yesterday, in southern Florida the high temperature was 301 K, and the low temperature was 233 K in northern Minnesota. The ratio of the two temperatures is simply 301/233 = 1.29. We may say that Florida was as much as 29% hotter than Minnesota, meaning, specifically, that the average air molecule in Miami in the afternoon had 29% more energy than the average air molecule in Duluth at dawn.
Is that a lot, or not? Motion-energy increases as speed squared (Emotion = ½mv², for an object of mass m traveling at a speed v that is much slower than the speed of light) so it only takes 14% more speed to give you 29% more motion-energy. That means a car driving 68 miles per hour (114 km/hour) has 29% more motion-energy than a car driving 60 miles per hour (100 km/hour). So think about that when you are commuting to work. When you accelerate from 60 to 68 miles per hour, you’ve increased your speed by enough to turn this morning’s Duluth into this afternoon’s Miami.
That said, the molecules are a bit speedier. Compared to those slow-pokes in Duluth, which crawl along at a mere 980 miles per hour (1640 km/hour), the average molecule in Miami is traveling about 1100 miles per hour (1850 km/hour), about 14% faster.
So it’s a matter of perspective. Biologically speaking, the difference between Florida and Minnesota is enormous; you can survive in one for months, and in the other for minutes. This is in large part because between comfortable Key West and dangerous Duluth lies the temperature where water turns to ice, and so your body, being more than half water, will start to freeze solid in the cold, not to mention being unable to maintain the internal warmth it needs to function. And yet, for the nitrogen and oxygen molecules in the air, the cool-down is a rather small change… no more than slowing down on the highway from 68 miles an hour to 60 miles an hour (114 km per hour to 100 km per hour.) They barely notice the difference!
We should be very grateful to live on such a stable planet, whose hottest surface temperature (about 130ºF= 54ºC = 328 K) and coldest surface temperature (about -130ºF = -90ºC = 183 K) are only different by a factor of 328/183 = 1.8 — and of course those temperatures are unusual, and only occur in unique places. Compare that with the Moon, where high temperatures (214ºF = 101ºC = 374 K) and low temperatures (-300ºF = -184ºC = 89 K) vary by a factor of 374/89 = 4.2. Out in the wider universe, it’s a little more drastic. The center of the sun reaches a blazing temperature of 27,000,000ºF = 15,000,000ºC = 15,000,000 K (approximately). Meanwhile the ancient photons (the particles of electromagnetic radiation which make up the “cosmic microwave background”) that fill outer space would warm you to just under 3 K. The ratio of the two temperatures is about 5,000,000.
Home Sweet Home. Even when it runs a little cold.