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HOW LOW CAN YOU GO?
PAT's interest and confusion about cold dates back to whenshe was a little girl—maybe eight or nine years old. Her father told her that heat could not be created nor destroyed. She doesn't remember a context for the remark, but she does remember the discussion that followed.
"Suppose you took some heat and put it in the freezer," she remembers saying. "That would destroy it."
No, it wouldn't. Dad explained that the heat would warm up the freezer a little bit. The heat would spread out, but it wouldn't go away. Heat always flows from hot to cold, evening things out.
Pat now understands that Dad was talking about the conservation of energy—and that the flow of heat would ultimately lead to the Heat Death of the Universe. The Heat Death of the Universe, for those of you who skipped that day in physics class, is when all available energy has been distributed evenly throughout the universe. Nothing is hot and nothing is cold. Everything is the same temperature. Everything has reached maximum entropy or disorder.
When everything's the same temperature, you can't get any more work from heat transfer—which is what runs our cars and factories. All kinds of energy will reach the same equilibrium state—spread evenly all over everywhere. And that's it. The End of the Universe.
Such a bleak scenario! We won't talk about that today. But we are going to talk about the nature of cold, about how temperature can be measured, and about some of the really strange stuff that happens at low temperatures.
Of course, we should mention that many great science fiction stories relate to heat and temperature—tales of ice planets and hot planets, of the cold of space and the heat of stars. But Pat's favorite story related to this column is Pamela Zoline's "The Heat Death of the Universe," which deals with entropy in the suburbs.
Paul is ready to plunge into a description of the fascinating weirdness you find at super-low temperatures, but Pat can't resist a detour into the history of our understanding of cold.
Consider, if you will, the "frigorific particle."
In the first half of the seventeenth century, French scientist and philosopher Pierre Gassendi theorized that cold was caused by frigorific particles that bodies took in as they got colder and released as they warmed up. Search online for "frigorific particles," and you'll turn up some wonderful discussions about the action of these particles and how they tended to settle at the Poles and how they wedge themselves between molecules of water, pushing them apart and causing the water to expand when it cooled and froze.
A decade or so after Gassendi's death in 1655, chemist Robert Boyle did some experiments that convinced a lot of people that the frigorific particle didn't exist.
In one experiment, Boyle carefully weighed a barrel of water. He left it outside in the winter cold until the water froze—and then weighed the barrel of ice. If the water froze because of the addition of frigorific particles, he thought, then surely the ice would weigh more than the water. But the frozen water weighed the same as the liquid water. That was a pretty convincing argument that no frigorific particles had jumped into the water barrel.
One thing that would have helped Boyle and others who did early research into the nature of cold was an accurate thermometer. The human body is just not very good at judging temperature. Without a thermometer, it's pretty tough to tell what's hot and what's not.
You don't believe us? Then check out the experiment in the sidebar—or try this simple thought experiment.
Suppose you have an urgent need to visit an outhouse on a very cold night in winter. Your particular need dictates that you must sit. This outhouse is a two-seater, with a metal toilet seat and a wooden one. Question #1: Would you rather sit on the metal seat or the wooden one? Question #2: Which one is colder?
While you ponder those toilet seats, we'll tell you of a South African man Paul met when he was in Zambia to watch an eclipse. The South African insisted that it must get colder as one descended into the Earth. This fellow said that he had been down into deep gold mines in South Africa. When he felt the walls of the mine, he found they were cold to his touch.
The rock at the deepest part of the gold mine was at 60°C (140°F). To make it possible for people to work down there, the air had to be cooled to 32°C (90°F). The air in contact with the wall made the wall surface 32°C as well. The man admitted that the air temperature felt hot and humid. But he said the wall felt cool.
That wall felt cooler than the air in the mine for the same reason that the metal toilet seat in the cold outhouse feels colder than the wooden one. We suspect your answer to question #1 was the same as ours—you'd choose the wooden seat. But many people get the answer to question #2 wrong. The toilet seats (like the air and the wall in the mine) are the same temperature. But they sure don't feel like it. Why not?
The temperature-sensitive nerve endings in your skin detect the difference between your inside body temperature and your outside skin temperature. When you touch something and your skin cools down, your temperature-sensitive nerves tell you that the object you are touching is cold.
But temperature alone does not determine whether your skin cools when you touch something. To cool your skin, an object must meet two conditions: it must be colder than your hand, and it must carry your body heat away.
Though the metal and wood are the same temperature, they carry heat away from your body at different rates. The metal seat and the rock wall of the mine are good conductors of heat. When you touch them, heat flows from your bare skin to the metal or rock, where it is rapidly conducted away. This leaves your skin cold—and therefore the object you are touching feels cold.
The wooden seat and the air in the mine are poor conductors of heat. Because heat is not conducted away quickly, the surface of the seat and the air near your skin soon become as warm as your skin. After this happens, little or no additional heat leaves your skin and the object feels warm.
BACK TO BOYLE
To understand temperature (and how to measure it), Pat finds it useful to begin with how freezers work. That brings us back to Robert Boyle, the guy with the barrel of ice. Today, Boyle is remembered best for Boyle's Law, which describes the relationship between the pressure and volume of an ideal gas at a constant temperature in a closed system.
Here's the deal. Let's say you have a fixed amount of an ideal gas. Squeeze that gas into a smaller volume and the pressure goes up. Expand the size of the container (without adding any more gas) and the pressure goes down. Boyle figured out that if you multiply the pressure of the gas by the volume of the gas, you always get the same constant. That is—you get the same constant as long as the temperature doesn't change.
Boyle's Law was followed by a trilogy of ideal gas laws—all of which were combined in a single law that states the relationship between pressure, volume, temperature, and number of molecules of gas. (For those who prefer equations to words, the combined ideal gas law is PV=kNT, where P is pressure, V is volume, N is the number of molecules, T is temperature, and k is the Boltzmann constant.)
Like so many phenomena, the details get a little tricky. But the bottom line is this: when gasses expand, they cool. You can feel this when you let air out of a bicycle tire. The expanding air from the tire is cooler than the surrounding air.
And that brings us to how freezers work. In the coils of the freezer, a compressed liquid expands and evaporates as it passes through a small opening. When a liquid evaporates, it absorbs energy from its surroundings, cooling the gas and the remaining liquid. (That's why evaporating sweat cools you off.) In addition, the expansion of the gas cools it. The result is cold air in the freezer.
How cold is the air in that freezer? For that, you need a thermometer.
A thermometer has a visible and consistent response to temperature that can be measured on a scale. Mercury, like most materials, expands as it gets warmer. If you have a bulb containing mercury at the bottom of a glass tube of a constant diameter and you warm the tube, the mercury will rise with an increase in temperature.
Early thermometer makers Daniel Gabriel Fahrenheit and Anders Celsius had to figure out how to calibrate that rise. They had to come up with a scale that they could use to measure temperature.
Back in 1724, Fahrenheit established a temperature scale. He made a mixture of water, ice, and salt to create the lowest easily reachable temperature and made this his zero. He then measured human body temperature and made this 100. (We now know that the average human body temperature is 98.6 on his scale.) On Fahrenheit's scale, most everyday temperatures were positive numbers.
In 1742, Anders Celsius created a different scale. His zero was the boiling point of water and his 100 was the freezing point. That's right—his scale was upside down from our modern scale. Right after his death, Swedish botanist Carolus Linnaeus flipped Celsius's scale over, making a thermometer where zero represented the melting point of ice and 100 represented water's boiling point.
SCIENTIFIC SCIENCE FICTION
Mercury will freeze at -38.83°C (-37.89°F); pure ethanol alcohol freezes at -114°C (-173.2°F). So if you want to measure really low temperatures, neither a mercury nor an alcohol thermometer will work for you.
For lower temperatures, scientists came up with the ideal gas thermometer—which is a bit of science fiction right there. You see, there are no real ideal gasses. In an ideal gas, the molecules don't interact with each other at all; they bounce off each other and off the walls of the container without losing any energy.
But scientists are capable of stretching a point when they need to, and ideal gas behavior can be approximated using a dilute inert gas such as helium. Helium that's at a constant pressure changes volume as temperature rises. In a helium thermometer, the volume of the gas is calibrated to correspond to temperature.
Now, maybe you're wondering what the thermometer is actually measuring. What is temperature, anyway?
Pat says it's a measure of how much the molecules of something are bouncing around. When you add energy (maybe by lighting a fire under the object in question), the molecules bounce around faster and the temperature increases.
Paul has a much more rigorous definition of temperature. Being more rigorous, he needs to be more specific as well. He says you get the temperature of a gas by measuring the average random kinetic energy of translational motion per molecule, then dividing by a conversion factor. (For those of you who like equations, the conversion factor is k, the Boltzmann constant from the ideal gas law.)
Paul and Pat don't talk about temperature the same way, but we agree that temperature relates to the movement of molecules. And since temperature relates to molecular movement, the zero point might be defined as the point at which all molecular motion stops.
That brings us to yet another temperature scale. This is the Kelvin temperature scale, named after Lord Kelvin, a mathematician, physicist, and natural philosopher. Back in 1848, Kelvin published a paper about the need for a scale on which "infinite cold" or absolute zero was the zero point. He figured that absolute zero would be -273°C—and he was pretty close to right. Absolute zero is -273.15°C. On the Kelvin scale, water freezes at 273.15K. Since kinetic energy is always greater than or equal to zero, there can't be negative temperatures on the Kelvin scale.
Just to keep things interesting, the possibility of a temperature at which all motion ceases raises a slight problem with quantum mechanics. Werner Heisenberg discovered that it was impossible to know the position and velocity of a particle exactly at the same time. So if you have a particle in any sort of a box (and the universe counts as a box!) it must have some uncertainty in its velocity—which means that its velocity can't be zero.
Consequently, at absolute zero atoms and molecules are still in motion. This motion is large enough that helium atoms at atmospheric pressure will not form a solid even as they approach absolute zero! This so-called "zero point motion" keeps them moving enough to make them a liquid.
What absolute zero means then is that the atoms have the minimum possible motion. This energy of this minimum motion cannot be extracted. (So Paul suggests you save your money and do not fall for the Web scams that claim to harvest zero point motion.)
In the darkness of space, temperatures get close to absolute zero. An object in space cools off as energy radiates away it and is not replaced. Anyone who has been in the desert at night understands this cooling effect well. When the sun goes down, you radiate your heat and cool off fast.
For a more extreme example of cooling by radiation, suppose you take an ideal gas thermometer out into space and shield it from nearby stars. Its temperature drops as it radiates away energy and receives little in return. (Pat insists on pointing out that this method helps advance the Heat Death of the Universe. Thermos bottles and cozy blankets, which prevent the dissipation of heat, fight against the Heat Death of the Universe. People who leave the heat on and the front door open or abandon their ideal gas thermometers in space encourage the Heat Death of the Universe.)
The temperature of that ideal gas thermometer would eventually stabilize at 2.725 Kelvins. That is the temperature of space, maintained by the cosmic microwave background radiation that's constantly striking the thermometer.
What, you ask, is cosmic microwave background radiation? Paul is very glad you asked. Cosmic microwave background radiation is left over from the "Big Bang." An absurdly long time ago, that radiation started out as orange light at a temperature of 3000 Kelvins. As the universe expanded, the wavelength of the electromagnetic radiation traveling through the vacuum of space expanded along with the vacuum itself. The light changed from orange to red to infrared and is now stretched a thousand times into the microwave region of the electromagnetic spectrum. The microwave spectrum of this radiation from the big bang warms our thermometer all the way up to 2.725 Kelvins.
But you remember, of course, that we mentioned the ideal gas thermometer was science fiction. We've had to fake an ideal gas by using an almost ideal gas—helium at atmospheric pressure. But at very low temperatures, we get caught in our web of fabrications (Pat, as a fiction writer, is quite familiar with what can happen in a tangle of fabrications—at any temperature).
Anyway, here's the problem: helium gas liquefies at 4.22 K. So our (almost) ideal gas thermometer is no good at all in space.
To measure the very cold temperature of space, scientists had to create a new way of measuring temperature by noting how the spectrum of light emitted by an object depends on temperature. By noting the light emitted by objects of known temperature, scientists have calibrated a virtual "blackbody spectrum thermometer."
This means we can measure the temperature of an object just by analyzing the radiation it emits. In fact, you may have had this method of temperature measurement used on you. Have you ever had a doctor take your temperature by pointing a thermometer at your forehead or in your ear? That thermometer measured the infrared radiation you were emitting—your own personal blackbody radiation—and used that to calculate your temperature.
The dark "surface" (where surface could be the cloud tops) of a planet will cool by radiation. This is why the bottoms of craters near the poles of the Moon and Mercury, where the Sun never shines, are extremely cold. On the Moon, which lacks the Earth's insulating blanket of atmosphere, temperatures as low as 26 K have been discovered.
At very low temperatures, strange stuff happens.
In 1910, Heike Kamerlingh Onnes was looking into the behavior of metals at low temperatures. He cooled mercury down to a couple of degrees Kelvin in a magnetic field. As he cooled the mercury, his very expensive glass apparatus suddenly blew apart.
So he tried it again, destroying another expensive set of glassware. A lot of broken glass later, Onnes realized he had discovered a new property of matter. At low temperatures, the mercury had no resistance to the flow of electric current. In the presence of a magnetic field, the electrons moved inside the mercury. When the magnetic field pushed on these moving electrons (as magnetic fields do), it shoved the mercury sample so hard it broke through the walls of the glass vessels used in the experiment. Onnes had discovered superconductivity.
Here's what's going on in a metal that's supercool. When electricity flows through a metal (let's say a copper wire), electrons flow. Atoms in a solid copper wire are in motion. As the electrons flow through this array of copper atoms, the vibrating atoms get into the way of the electrons, slowing their motion and turning some of the energy of the electron motion into increased motion of the copper atoms. As a result, the metal gets warm. We say the metal has electrical resistance.
When we cool copper down the vibration of the atoms decreases and its resistance decreases. At temperatures near absolute zero, resistance in some materials also drops to zero. (Paul notes that a more complete understanding of zero resistance requires quantum mechanics—and we aren't going there right now.) Because these materials have no electrical resistance, electrons can travel through them freely. They can carry large amounts of electrical current for long periods of time without losing energy as heat. In demonstrations, superconducting loops of wire have carried electrical currents for several years with no measurable loss.
Today we make superconducting wires to carry electricity without loss. These wires are used in underground transmission lines connecting power plants in Detroit and also to make the magnetic fields that steer the electron beams in the accelerator at CERN, the European Organization for Nuclear Research. (CERN suffered tremendous damage when one connector in the superconducting circuit warmed up enough to become non-superconducting. A small city's worth of energy was suddenly deposited into a piece of metal, and the resulting heat vaporized a cubic meter of the accelerator.)
There are other strange properties that appear at low temperatures. Cool liquid helium to 2.17 K and it becomes a superfluid, a fluid that can flow without viscosity.
Take an empty beaker and lower it into a normal fluid like water. As long as you keep the top of the beaker above the top of the water, the beaker will remain empty.
Lower the beaker into superfluid helium and the helium liquid will flow up and over the rim of the beaker filling the inside of the beaker to the same level as the outside.
How can this happen? The water and the superfluid helium wet the beaker and rise up making a meniscus. Look closely at the place where water meets the inside of a glass and see this for yourself.
The meniscus forms because the fluid sticks to the glass. It stops rising because the fluid sticks to itself. Water, which sticks to itself very well, doesn't rise very far. But superfluids, which flow without sticking to themselves, just keep rising, crawl over the lip of the glass, and down the other side.
These superfluids are also called "quantum fluids." At these low temperatures, the rules of quantum mechanics dictate behavior at macroscopic scales. Superfluids can flow freely through infinitesimal holes, move around a closed loop forever, and climb up the walls of their containers.
ABSOLUTELY THE END
Pat and Paul both prefer the excitement of the super cool (and the super hot, which we might deal with in another column) to the bland sameness of even temperature at the Heat Death of the Universe. But we are aware that the Heat Death of the Universe is inevitable. We are also aware that thermometers (unlike thermos bottles and cozy blankets) actually contribute to the Heat Death of the Universe.
The zeroth law of thermodynamics (yes, really—the zeroth law) says that the temperatures of two objects in contact with each other for a long enough time will be the same. When you touch a thermometer to an object, heat flows from whichever one is warmer to whichever one is colder until they are both the same. Then you can read the thermometer to find out the temperature of both.
Of course, you have changed the temperature of the thing you are measuring—however slightly. And you've helped spread heat around a little more evenly, bringing Heat Death just a little closer.
Even the simple act of measurement can change the universe.
--------The Exploratorium is San Francisco's museum of science, art, and human perception—where science and science fiction meet. Paul Doherty works there. Pat Murphy used to work there, but now she works at Klutz Press (www.klutz.com), a publisher of how-to books for kids. To learn more about Pat Murphy's science fiction writing, visit her website at www.brazenhussies.net/murphy. For more on Paul Doherty's work and his latest adventures, visit www.exo.net/~pauld.
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