What is Entropy - REALLY?

As far as obscure concepts in Thermodynamics go, Entropy gets way more than its share of media attention.  Unfortunately most of what is shouted and written  about Entropy is complete nonsense.  Utter bollocks.  Somewhat inaccurate or wanting in veracity, shall we say.

People often repeat the mindless slogan that entropy means disorder, disarray, crumbling and decay.  It can't possibly mean any of those things, because Entropy is not a property of matter at all.  It is only a property of Energy.

It is also said that the existence of Entropy (to be precise, the existence of the Second Law of Thermodynamics which defines Entropy) means that organized structures cannot arise spontaneously and therefore the very existence of "complex" structures has various bizarre philosophical implications. This is also pure bottled nonsense.

Entropy is a property of Energy and has nothing to do with matter, atoms, crystals, structures, buildings, organisms or automobiles except for the extent to which energy in its various forms is lurking inside those things.

Energy is nothing more than motion or the possibility of motion.  One big car in motion has as much kinetic energy as two smaller cars that together weigh the same as the big car and that are moving at the same speed.  One car moving 100 mph has the same energy as four cars identical to the first traveling 50 mph.  Doubling the speed of something requires quadrupling its kinetic energy.

But the most important thing about energy is that it cannot come from nothing and it cannot disappear into nothing.  Energy always comes from something else and always goes somewhere else. That is the First Law of Thermodynamics ("how energy works") in which Nature demands that all energy is always conserved.

But if energy is always conserved in every physical process, why do things seem to run out of energy after a while?  AHA!!! This is where Entropy comes in.

Entropy is the property of Energy which states that Energy always tries to spread itself out as evenly as possible.  Energy never gets destroyed; it always exists in exactly the same amount.  But energy always gets more and more uniformly distributed as time goes on.

If you wind up a clockwork toy and let it go, the energy stored in the spring doesn't stay there: it gets used to move the parts, and eventually friction (heating) slows the toy down until it stops.  The energy was transformed into heat, work (which eventually became heat) and sound waves (which eventually became heat).  The exact same amount of energy still exists, but that energy became widely dispersed.  Mission accomplished.

When energy spreads out, a numerical quantity known as Entropy increases.  Entropy is a measure of the amount of evenness over which energy is shared among every possible location that the energy can possibly occupy.

How would that work?  Imagine a box full of bouncy balls.  And in this imaginary experiment, let's pretend that the balls and even the walls of this box are so bouncy that the balls never ever stop bouncing.  Maybe this is a box of hydrogen atoms, or children.

Let's start out with all of the balls in this box not moving, just sitting quietly at their desks.  Now, lets throw a really really fast-moving ball (lots of energy!) into the box.  What happens?  At first, the new ball is the only one moving, but as it ricochets off of other balls that were just sitting there minding their own ball business, they too will begin to move.  Eventually, all of the balls will be bouncing around, but none of them as fast as the new ball had been when we first threw it in.  In fact, all of the energy in the box, if added up, would only equal the energy that the new ball had when we threw it in.

At first, when only one ball was moving, Entropy was almost zero.  The energy was not shared among all the possible places (balls) that the energy could exist.  This was actually the MOST uneven arrangement imaginable.  As the new ball began to share its kinetic energy with other balls, Entropy began to increase.  Eventually, when all the balls were moving, Entropy was as high as it could get.

How likely do you think it would be for all the other balls to somehow bounce off the new ball again at exactly the right angle and at exactly the right time so that they all stop moving and the new ball once again has all of the energy to itself?  Pretty much impossible, isn't it.  Entropy never goes down by itself; only ever up.

"But," you say, "what about the example of the wind-up toy?  We can wind up the toy some more and once again the entropy of that toy will be minimum, allowing it to run some more."  Quite so.  But how much did Entropy increase by you doing that?  Was there heat in your fingers that transferred to the winding key?  That's energy being spread around. Did doing that make any sounds?  That also dispersed energy and therefore increased entropy.  Every time entropy is temporarily reduced in one area, it has to increase by an even larger amount everywhere else.

That's why "perpetual motion of the second kind" - something running indefinitely without a source of energy, even if it's not producing any energy - is just as bogus as fantasy machines that people imagine "produce" energy from nothing.   That's simply not how energy works.

How Energy works is really simple and really easy:

1.  Energy always comes from somewhere and always goes somewhere.
2.  Energy always gets spread out as evenly as it possibly can by any means.

-   *   -   *   -

What about matter?

Getting energy to spread itself out more evenly sometimes results in matter having to arrange itself in complex structures, sometimes in ordered structures, and sometimes in random structures.   So, it turns out that Entropy can accommodate ALL arrangements of matter, and not just the messy ones!

A perfectly ordered crystal is actually entropy in action, since the crystal forms as a direct result of energy trying to get to a stable minimum in one bunch of matter so that any excess can get spread around elsewhere.  Complex organic structures also increase entropy by absorbing concentrated chemical energy or even sunlight and turning it into heat, waste, and motion.

A dog, for example, is an excellent device for turning useless Money into valuable hair, noise and poop.  So in no way does biology violate the law of Entropy.


Entropy is easy.  It's a property of Energy, not matter.  It says nothing directly about how or whether matter is arranged.  Measuring Entropy tells us whether Energy is in a useful form (highly concentrated in one place) or if it's unavailable (highly dispersed).

Other than being indestructible, the most basic fact about Energy is that it always spreads out.  That's Entropy.

More Fun with Science

Science is so much fun that if I could, I'd just sit around all day doing science. Oh, wait...

Here's a video I made on one particularly fun day when I figured out how to do something new using the stuff that was just laying around the Science Cave. Enjoy!

Science is easy, but what about Maths?

For many years I have wrestled with the problem of how to get better at Maths, and how to help others do so as well. It isn't easy! I tried all kinds of ways of explaining Maths to people in plain-English. Eventually I became convinced that teaching Maths was actually not possible: Someone either "gets" it or they don't, and nothing you can say or do seems to make any difference.

While that will certainly be the case most of the time, I have recently modified this theory slightly as a result of several chance conversations. One was with a Maths teacher at a local university, the other a student in Social Work who, to my great surprise, happens to love Maths.

In my own life Maths was not a strong suit, initially. I struggled in primary school with the tasks of adding and multiplying. Long division in particular is what I imagined Hell must be like for someone like me who wants to see the Big Picture, and who only worries about details that haven't been worked out before. Dear old Dad finally caved in and bought me a Calculator in about 1975. LED digits. 9-V battery good for about an hour. Fixed decimal point which made the answers off by powers of 10. It was a God-send! A Miracle!

(I now own dozens of calculators, and none of them are completely adequate in all ways. The best calculator for numerical analysis is actually Matlab, a very good and very expensive piece of software. Perhaps my obsession with calculators will be the subject a future post, if enough Readers vote for it!)

University Maths didn't make life any easier for me. I spent an entire year (and a painful one) studying Differential Equations and Linear Algebra. I got C's in both subjects. How is that possible?

I won't blame the teachers, although I won't thank them either. Aside from their impenetrable foreign accents, they presented themselves with an air of utter boredom which I imagine they thought was "professionalism" or even "cool." As if to say, "Whereas you are all morons, I find maths so incredibly easy I can do it in my sleep. I will now demonstrate this fact by pretending to be in a coma while I lecture."

No, students will either learn because of their teachers or in spite of them. I did neither. Why?

The university Maths teacher I mentioned recently gave his theory of how to teach the subject:

"Strip it of all applications and meanings, and deal only with pure notation first. That will get right to the heart of any conceptual difficulty the student may have, without the distraction of trying to interpret 'word problems'."

I immediately recognized the fallacy of this, and realized what the key to learning Maths must be.

My hypothesis was confirmed when I had a chance conversation a few days later with a student in Social Work. I asked whether she found it frustrating to have to take Maths courses which detract from her core interest in getting out there and doing something to make a difference. She said, "No! quite the opposite. I really like Maths, and have always found it easy."

"What do you like about it?"

"I really enjoy order and logic. I like it when things make sense and fit together. It gives me a feeling of satisfaction and control when I can solve a problem and get The Right Answer. Life makes sense when things work out correctly."

Why will some people enjoy Maths and learn it easily, even in spite of poor teaching? Why will otherwise capable students hate Maths and struggle endlessly with it? And most importantly, how do we make Maths easier to learn and to teach?

The human unconscious mind, in order to save us from Information Overload, filters out 99.99...% of all incoming data (sounds, images, stimuli, information), allowing into our conscious awareness only that which it deems relevant. The decision is made based on an individual's unconscious values, beliefs, fears, and desires. Further, memory is also activated in the same way, and we remember only things that unconsciously are important to us or that we care about emotionally. We already have "bins" or structure in the brain for retaining such information. Information far outside our experience is harder to classify and link to previous experience, with the result that there will be few neural connections created to constitute a memory of it.

Therefore in order for a student to have an activated memory and be open to information, it must be information that has emotional meaning to the student, and which relates to something the student already knows well. In the case of that Social Work student and most other "born mathematicians," the emotional meaning of Maths is built-in: the love of order, the satisfaction of being able to solve puzzles, and the sense of "all's right" when they get the one right answer.

Most other students, however, care about different things. Whether it's sports, music, art, books, friends, cars, fashion, money, animals, or Physics, there is always a way to make Maths relevant and something to which a student can and will attach emotional importance. Additionally, the teacher can generate the emotion in the classroom through enthusiasm, a personal story, and showing caring for the students individually. In other words, exactly the way a very good presenter or salesman "sells" any message.

If we want our kids to do better in Maths, (and it is definitely the one subject essential for success in virtually any field), then we should look at changing the way Maths teachers are trained. Or better yet, recruit teachers from the ranks of Salesmen! You don't have to be an expert in N-Dimensional Topology just to teach first-year Algebra, after all. You only need to be an effective communicator and understand the principles of Influence.

How did I eventually get on top of Maths? A decade after my Physics degree, I entered a Master's Degree program for Engineering. I just couldn't get enough of engines, spacecraft, cars, motorcycles, electronics, and gadgets generally. I loved fixing things, building things, and inventing things. When I took a most fascinating course in Control Systems Theory, for example, I needed to know both Differential Equations AND Linear Algebra. Suddenly these were no longer boring, difficult millstones around my neck, but exciting and useful tools that I couldn't get enough of. I was even teaching the other students the finer points of how to use them.

Stripped of all application and meaning, these subjects made no sense to me and I could not produce the excitement and discipline necessary to gain competence. But in the context of something I cared a lot about and had high interest in, they made perfect sense. They are now subjects I am very comfortable with. My engineering professors were absolutely dumbfounded that I had previously earned C's in those subjects.

But is it really such a mystery?

A 14 year-old Discusses Relativity and Science

The most recent Making Sense of Science Newsletter (available at http://www.wallingup.com/newsletters.php) sparked an online discussion with a Year 8 student. From it, I learned that there is not necessarily an age barrier to understanding advanced science topics, and that these challenging topics can supply the interest levels prerequisite to student engagement in the topic.

It also highlights the importance of integrating science with the humanities. This student had been reading the classic Ender's Game science fiction series by Orson Scott Card for his middle school English class (we both give it ***** five stars out of five).

I'd like to share the ensuing discussion with you.

Student: Aliens travelling to earth may have spent 1000's of years on a ship but the theory of reletivity would mean that they would not feel the ravages of time.

John: You are completely correct that aliens in a spacecraft moving near the speed of light would experience less time elapsed than on either their home world or destination planet. To them it might seem only a few years or even weeks. But to get going that fast requires such absurd quantities of energy it seems incredible that they would chose to do so.

So the aliens could survive the trip if they wanted to bad enough and had virtually unlimited energy to waste. But it would still take many hundreds of years of earth time for them to get here. They would have left on their journey at a time long before there were any radio signals to indicate that someone interesting lives here. We have only been sending out radio signals strong enough to be picked up in space for about the last 60 or 70 years, meaning that aliens living 70 light years away, if they are listening, would only now be aware of us. We can't expect to hear back from them for another 70 years, and we certainly can't expect them to drop by for many hundreds of years at least.

Student: Faster-than-light travel might be possible someday. Look at mobile phones! A few years ago people would have said they were impossible, too.

John: One thing to notice is that we did not exactly "discover" mobile phones, we invented them. The natural laws that allow them to operate were discovered more than a hundred years before.

But the computer technology that makes them work was invented step by step over the last 40 years. We did not discover any natural law that said "computers can do this" or "computers cannot do that," so we just kept trying new things.

There is a huge difference between technology and nature. Nature is the tree, and technology is the decorations. Technology must always follow Nature's rules, but Nature does not have to obey or allow technology. We do not discover technology, we invent it. Nature can only be discovered, and never re-invented to suit us. Technology only works if it is allowed by Nature.

Student: Just because we've never seen something doesn't mean it doesn't exist.

John: You are right about that. Don't make that mistake! If a guy says, "Dogs do not exist," because he has never seen one, he will be totally unprepared the first time a dog shows up and bites him on the bum.

We are not saying "there is no faster than light travel" merely because we have never seen it. We say there is no superluminous travel because we have discovered a natural law which says, "all speeds are less than the speed of light." Many experiments have proven that this law is true. They also prove that the opposite of this law is false. All experiments attempting to disprove this law have failed, too. It seems Nature is trying to tell us something, and the message is loud and clear.

We are not exactly in a room with the light turned off, speculating on what might be or might not be in it. We are also not like the guy who has never seen a dog before, jumping to a false conclusion. The light has been turned on. We have discovered that the faster you go the heavier you get until at the speed of light, you weigh infinity. It also takes infinity energy for matter to go that fast. By analogy, we have discovered dogs, and found that all dogs bark and poop. (and have sharp teeth). There is no need to speculate on the existence of dogs, or on the speed of light, because we are in possession of the facts.

Student: You cannot be certain that for example every element in existence has been discovered yet. New things might be discovered at any time.

John: I am particularly impressed with the way you think. Good job. And good on your teachers who cultivated your thinking skills. Your question is an important one: how can we be certain of what hasn't been discovered?

I'd like you to examine, if you would, all the whole numbers between 1 and 118. Are there any whole numbers missing? Are there any that we have not "discovered" yet? Are there any whole numbers in that range that are not known and still need to be invented?

If not, then there are also no new elements waiting to be discovered or invented either. We know of all elements as surely as we know about all the whole numbers from 1 to a million and beyond. Every element in the universe is a whole number of individual protons in a nucleus, with the same number of electrons hovering around it. To work out what possible elements might exist, simply write down all possible whole numbers. There aren't any missing.

This means that often it is specific knowledge of what does exist and how it is put together that enables us to make absolutely certain statements about what else might exist, and also things that cannot exist.

The only way to know the difference between what might yet be discovered and what will definitely never be discovered is to get as much understanding of the laws of Nature as you can. Things that those laws allow are possible at least in theory; things that the laws disallow are never possible no matter how hard we try or how much technology we get.

Student: Yes, but new laws are discovered which prove that the old laws were wrong.

John: Now who told you that? I'm sorry to say this is the first statement that is completely false. This has never happened, and people who say so are simply mistaken.

Newton's laws of physics replaced Aristotle's "laws". But those so-called laws were actually wrong to begin with, as any simple experiment could show. They were not really laws, but actually philosophical beliefs that were never tested in practice before they were written down. Galileo proved them to be wrong in his experiments. Finally, Newton worked out the simple laws of motion, forces, speed, mass and distance.

Einstein's laws of Relativity are sometimes said to prove Newton wrong, but the truth is that Relativity proves Newton was exactly right for all possible earthly speeds we encounter in everyday life. It is only speeds above 20 or 30 million meters per second that more information is needed.

Quantum mechanics is said to prove Newton was wrong, too. This deals with objects smaller than atoms, and it says they don't behave according to Newton's laws. But here too, Newton is proved right. Quantum mechanics tells us that large numbers of particles in a bunch together behave exactly as Newton would predict. Things even as tiny as a grain of sand obey Newton's laws perfectly, for all practical purposes. (How many atoms are in a grain of sand? See an older post in this blog.)

So a law that is proven experimentally does not stop being true, even when more information about totally different situations is uncovered.

Student: So the best way to invent stuff is to learn exactly about the laws of science so you can take advantage of them?

John: Good for you! Now you're on the fast-track! People who don't do what you suggest get bogged down forever basically re-proving the laws of Nature that are already known, and never invent anything useful. Do what Isaac Newton said, and Stand on the Shoulders of Giants to see farther than you would on your own legs. And Happy Newton's Birthday, 25 December!

Watch out for this kid. He's only 14 now, but he's going to make a difference.

What are atoms made of?

Everything you will ever encounter in your entire life, everything you will ever eat, touch, hold, see, feel, hear, taste or smell, every part of the earth you stand on, the air you breathe, the house you live in, your entire body, the clothes you wear, even your wristwatch and jewelery, everything you can see out in space, the stars, planets, comets, galaxies, the telescope you use to view them, the sofa you sit on, the TV you watch while sitting on the sofa, the remote control you clutch in your hand (if you're a guy), and the cheezypoof crumbs that adorn your shirt ...

All these things and more are composed of just three kinds of building blocks. Combinations of these three simple bits comprise everything of any consequence in the physical universe. They are The Electron, The Proton, and The Neutron.

The Electron. It carries a negative electric charge, meaning it repels other electrons and is attracted to positive charges. It is very lightweight. Mysteriously, every electron has exactly the same mass and charge as every other electron. As far as the best instruments are able to detect, the electron has no size, but is a single geometric point.

The Proton. A massive particle with a positive electric charge, exactly equal and opposite to that of an electron. Protons have a diameter of about a trillionth of a millimeter. They repel other protons and attract electrons. They are also slightly sticky. Although they repel each other, if you get them close enough, they will stick together.

The Neutron. This weighs about the same as a proton and is about the same size. It is also sticky, like a proton. But it has no electrical charge and is therefore very hard to control, to hold, to detect, or do much of anything with.

When a bunch of protons are mashed together, they sometimes stick and form a ball called a nucleus. They find it easier to do this when some neutrons are included to add more "stick" and help them overcome their mutual electrical repulsion.

When a nucleus forms, it has a strong positive charge equal to the number of protons. Eventually, an exactly equal number of electrons gets involved because of the strong electrical attraction. Then a funny thing happens: the electrons are unable to get closer than a certain distance to the proton/neutron cluster and they end up hovering around in a kind of layered, structured cloud. That's what we call an atom.

How big is the nucleus? If an atom were the size of a sports stadium, the nucleus would be about the size of a marble laying in the grass at center field. Except there would be no grass. Electrons would be the spectators sitting in the stands, except there would be no stands, just electrons.

Carbon, for example, is the kind of atom you get when any 6 protons form a ball. Some neutrons are needed to help them hang together. Zero to two neutrons isn't enough, and results in an unstable ball that almost instantly disintegrates due to the proton's mutual repulsion. Three to five neutrons is almost enough and results in a nucleus that survives for a few hundred milliseconds to a few minutes. The more neutrons, the more stable it is.

With 6 or 7 neutrons, the 6-proton neucleus (Carbon) is stable. 98.9% of Carbon atoms have 6 neutrons, while 1.1% have 7. We call these "isotopes" "Carbon-12" and "Carbon-13."

Carbon-14 is famous for its ability to indicate the age of things that contain carbon. In the atmosphere, carbon is exposed to radiation which "activates" some small percentage of it. The result is Carbon-14 which is unstable but which decays very slowly. About half disappears every 5730 years. That rate of decay can be used as a kind of clock to determine how long a carbon sample has been "out of action" as it were.

Electrons, Protons and Neutrons are all that are needed to create every element on the periodic table, and therefore every chemical compound, and therefore every object or substance you will ever encounter in this physical universe. It is true that protons and neutrons are themselves composed of smaller pieces, but they play no significant role in everyday life.

Only three things to keep track of? Anyone can cope with that. And you thought Science was going to be hard.

How Small is an Atom?

A textbook or encyclopedia will tell you that a typical atom is about 0.0000001 of a millimeter in diameter. Now, how are we supposed to picture that? That information may be helpful for calculating how big a carton you'll need for mailing a given number of atoms to someone, but then again, maybe not. It certainly doesn't help the typical person understand what all the fuss is about.

Here's a way you can visuallize the size of an atom, and the vast number of atoms that comprise the everyday objects in your world. For this experiment, I'd like you to get a pin. Find an ordinary sewing pin, now, before reading any further.

Got one? Good. Look at the head of the pin closely. If you have one, use a magnifying glass or even a microscope to look long and closely at the head of the pin. Just stare at it for a while.

Now close your eyes and imagine yourself shrinking down, almost vanishing, descending down onto on the head of the pin. You have shrunk down so small that the head of the pin is a vast desert on which you are standing, the edges of which you cannot see. You begin walking in one direction.

You continue walking on the head of the pin for many days before coming within sight of the edge. How far have you walked? 50 miles? 100 miles?

For the first time, you look down at the surface you have been walking on. It's fairly smooth, with an occasional ditch to stride over and variations up and down. You recognize this as the results of polishing when the pin was manufactured. You kneel down for a closer look at this shimmering surface and notice that it seems to be made up of small marbles packed closely together, and they are all vibrating slightly. Now you are seeing individual atoms. There are mostly iron, but also nickel, copper, and several other species, distinguishable by their differing sizes.

Open your eyes and look again at the head of the pin. You will now be able to visuallize how small atoms are and how impossibly many there are just on the head of that pin.

Now I'd like you to picture yourself on the beach. Next time you go to the beach, remember this and go through these steps. Stand on the beach and look up and down the shoreline. Picture in your mind how deep the sand might be. Deeper than a house is tall? How much sand?

Reach down and pick up a handful of sand. How many grains of sand do you see? Could you even begin to count the number of grains of sand you are holding in that one handful?

Allow most of the sand to fall through your fingers. Inevitably, a few grains remain clinging to your skin. Look closely at your hands, and try to pick out one single grain of sand.

While looking at that one grain of sand, say the following words: "There are possibly more atoms within that single grain of sand than there are grains of sand on this entire beach."

It is no wonder then that the existence of atoms was completely unknown for so long, and then, debated for so long. By about the start of the 20th century, the indirect evidence of atoms from observations made over the previous few hundred years had finally won over most people to the concept and existence of atoms. Now, we have technology that can directly image the atoms on the surface of a grain of sand or on the head of a pin.

Of course, Mankind has gone far beyond that and has probed the very inner workings of individual atoms and the parts they are made of. That will be the subject of a future post.

Now read What Is A Theory?

What Exactly is Heat?

Energy is nothing more mysterious than motion. Things that are moving have energy, which is another way of saying that they are moving.

Suppose the countless atoms that make up an object are all moving with tiny, random motions in all directions at once. It's matter, and it's moving. So it's also energy. When it's in little pieces comprising a large object, we call it Heat.

Scientists have technical words they need to use such as "internal thermal energy," but we know that it's really just lots of little motions of lots of little objects in many directions at once. The atoms may be vibrating, spinning, or actually wandering about (if it's a liquid or a gas). It's not really different to the energy of a car whizzing down the street, just a lot smaller and a little trickier to keep track of. Remember, physics is mostly about being a good energy accountant.

Rather than a speedometer, we use a thermometer to keep track of heat energy. The temperature tells us the average speed of the many moving bits. The higher the temperature, the higher the average speed and therefore the more energy is in there. Trust me, it's easier that trying to put a little speedometer on each individual atom.

The temperature is higher when there's more energy. What if all the atoms were to stop at the same time? What would the temperature be then? Answer: -273 C. That's Zero on the absolute temperature scale, or 0 Kelvin.

I have a 1 kg block of ice in front of me that is at a temperature of negative 10 C, or ten below zero. If I add some heat to it, the temperature will go up. If I add 2 kiloJoules of energy (or heat) to it, the temperature will go up by 1 degree. If I add 20 kJ, the temperature goes up by 10 degrees. It's easy to do, but hard to keep track of. How do I add heat? By doing nothing.

Heat always spreads out. It does whatever it can to get away from high temperatures and move to lower temperatures. Just by leaving the block of ice sitting out, heat from the surrounding 20 C room moves towards the -10 C ice in whatever way it can. In this case, mostly through air currents.

Air next to the ice block gets cold. Cold air is heavier, and starts to sink down. Warm air then takes its place next to the ice, and the whole process repeats automatically. As the ice absorbs heat from the air in the room, the ice warms up. One result of that is that the rate of warming slows down. The other result is that the ice eventually starts to melt.

Ice melts at a temperature of 0 C. As we add more heat, more ice melts. But the temperature does not increase until all the ice is melted! Why not?

Water molecules in ice are stuck together and cannot move around. Water molecules automatically stick together when they are not moving very fast, in other words, when the temperature of the water is low (below 0 C, to be exact). If we want them to be unstuck and form a flowing liquid, then we have to give all the water molecules enough motion (meaning energy or heat) to move clear of each other. As we add heat, the temperature stays at 0 C until all the ice is melted. When we have added 335 kJ of heat, then the entire 1 kg block of ice will have melted. Scientists call that "The Latent Heat of Fusion," but we know it's just giving sufficient motion to the molecules to remain free. It's the same energy: motion.

I now no longer have a block of ice on my desk. I now have a litre of water in a pan which I had wisely placed under the ice. I knew what was going to happen, see. The water's temperature is still 0 C, but heat continues to flow towards it from the warmer surroundings. Every time the temperature increases by 1 degree, I know that another 4.2 kJ of heat has gone into the liquid water. Well, that's interesting! It takes more than twice as much energy to warm water as it does to warm ice! Why?

There are more ways for free water molecules to move. Up, down, left, right, forwards, backwards, and spinning in all directions. Previously, they could only wiggle a bit this way and that within the ice crystal structure. Each kind of motion takes a bit of energy to produce. Water molecules have to be doing all of them in order to make the temperature what it is. Therefore, raising the temperature of water requires more heat than it does for ice. Is that why the ice cubes in your drink never cause the entire drink to freeze? It's always the ice that turns to water, and not the other way 'round. How much ice would you have to put in a glass of water to make the entire glass freeze? Come on, accountants, get out your pencil and a calculator. It's not hard.

Eventually, when roughly 84 kJ of heat has entered the water, its temperature will be the same as the surroundings, and the flow of heat will trickle away to a stop. This happens increasingly gradually. Where the trip from 0 to 5 C may take only a few minutes, moving from 15 to 20 C may take hours.

One thing to remember about heat: our hands are not very good thermometers. They tell us when heat is moving into our hand (when we pick up something hot) or out of our hands (when we plunge them into ice water), but try picking up a handful of snow with a gloved hand. The insulation slows the heat flow out of our hand and we do not perceive the temperature as it actually is.

You already know that walking on carpet with bare feet does not feel as "cold" as walking on cement or tiles. But the carpet is exactly the same temperature as the tiles! Just something to think about.

Heat may be endlessly interesting, but never a mystery.