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Get a Grip on Physics
By John Gribbin
Dover Publications, Inc.Copyright © 1999 John Gribbin
All rights reserved.
ATOMS AND MOLECULES
* An atom is the smallest unit of an element that can exist. The most appropriate image of it is a tiny hard sphere, like a minute billiard ball. Some substances in the everyday world (such as pure gold) are made of only one kind of atom. A pure-gold ring, for example, simply contains billions and billions of gold atoms.
Austrian physicist Ludwig Boltzmann (1844–1906) played a key role in developing the kinetic theory of gases, thereby helping to establish, albeit indirectly, that atoms are real. He became clinically depressed, partly because the atomic theory came under attack in his native Austria, and killed himself in 1906 - just a year after Einstein's work had, unknown to Boltzmann, proved the existence of atoms.
* In some elements, identical ATOMS join together to form MOLECULES. This happens in the case of hydrogen, where each molecule is made up of two hydrogen atoms and is written as H2. Other substances, such as water, are made of two or more different types of atom combined with one another to form molecules. The symbol for a hydrogen atom is H and the symbol for an oxygen atom is O – so, since two hydrogen atoms combine with one oxygen atom to form a molecule of water, the symbol for a molecule of water is H2O.
* When they are on their own, oxygen atoms also like to link up with one another – so that the most common form of oxygen, including the stuff we all breathe, is O2. For the moment, though, all that matters is that these atoms and molecules can all he pictured as tiny balls, constantly in motion, bouncing off one another.
HOW GASES BEHAVE
* The people who worked out the details of this image of a gas as molecules in motion were James Clerk Maxwell, in Britain, and Ludwig Boltzmann, in Germany, in the mid-19th century. They didn't just speculate about this image of little balls bouncing off one another, but instead they developed a fully worked-out kinetic theory of gases founded upon Newton's laws.
* The word 'kinetic' comes from the Greek for motion, and according to Maxwell and Boltzmann's theory the pressure that a gas applies to the walls of its container is explained in terms of action and reaction (Newton's third law again) – each atom or molecule collides with the wall and bounces off, giving a push to the wall as it does so. This happens time and again, as the atoms rebound off each other and bounce back to hit the walls again.
the smallest unit of a chemical element that can take part in a chemical reaction
two or more atoms of the same element or different elements held together by their chemical attraction
theory describing the behaviour of matter in terms of the movement of its component atoms and molecules
MOLECULES IN MOTION
* A key feature of the kinetic theory is that it explains heat simply in terms of the motion of the molecules involved. If you heat up a container full of gas, the molecules move faster - so they give a bigger kick to the walls of the container each time they hit them, and the pressure increases. All of this was described mathematically, using equations (based on Newton's laws) that made it possible to calculate, for example, how much the temperature of a container full of gas would go up if it was heated by a particular amount.
the branch of physics that deals with heat and motion (especially the way heat is transformed into other forms of energy)
SOLID TO LIQUID
* The kinetic theory also explains the differences between solids, liquids and gases. In a solid, the atoms and molecules are held together – we now know, by electric forces – but jiggle about slightly as if they were running on the spot. This is a bit like a restless theatre audience shifting in their seats during a dull play.
* When the solid is heated, the molecules jiggle about more and more (which is why the solid expands), until they have generated enough kinetic energy (energy arising from motion) to break the bonds that hold them in place and are able to slide past one another relatively freely. The solid has now become a liquid.
LIQUID TO GAS
* In a liquid, the molecules are still more or less in contact with one another, but constantly brush past each other. You might make an analogy with the jostling crowd of theatre-goers streaming out of the auditorium after the show.
* Carry on heating the liquid, and at a critical temperature the molecules will have so much energy that they fly freely past one another and can bounce off each other, ricocheting wildly, like balls in a crazy pinball machine. The liquid has now become a gas.
If you Imagine not a fixed container of gas but a cylinder fitted with a piston, you can see how the flying molecules in the gas will push the piston outwards. If the piston is held in place by a force pushing inwards, the hotter the gas inside the more force you will have to apply to the piston. This classic example of Newton's laws at work relates directly to the branch of science known as THERMODYNAMICS (the study of heat and motion). Thermodynamics was hugely important in the 19th century, because at the heart of the Industrial Revolution were steam engines – which were driven by pistons.
THE ARROW OF TIME
There's something curious about many of the experiments described so far. Newton's laws of motion do not take any account of the direction of the flow of time. It may seem as if there's an 'arrow of time' involved in Newtonian mechanics, because we can talk about some events occurring 'before' or 'after' others. But think about the simplest Newtonian interaction, when two billiard balls (or two atoms) move towards one another, collide and move apart. If you reversed the whole process, the backwards-in-time collision would still conform to Newton's laws of physics. Indeed, if you made a movie of such a collision and ran it backwards through a cine projector, the audience wouldn't suspect there was anything wrong.
SEQUENCE AND CONSEQUENCE
* Something peculiar happens when you deal with large numbers of atoms and molecules. Although every collision between those individual molecules happens in accordance with Newton's laws, the interactions of all the molecules, taken as a whole, follow what we recognize as chronological time. It doesn't look peculiar, because it is what we are used to in everyday life - but in terms of Newtonian physics it really is very strange indeed.
HALFWAY IN OR HALFWAY OUT?
* Think about that piston with the cylinder full of hot gas. As the gas pushes the piston, it moves it further and further out of the cylinder. This takes energy away from the molecules of the gas, so they move more slowly – they cool down. This is a fundamental feature of the Universe: heat flows naturally from a hot object to a cool one. To restore heat to the gas in the cylinder you would have to push the piston in, using energy to do so.
* If you saw a photograph of the piston pushed deep into the cylinder and another showing it much further out, you would know straight away which photo was taken first. When there are lots of molecules and atoms involved, nature has an inbuilt arrow of time.
Half full or half empty?
Instead of a smoothly sliding piston, imagine a box divided into two halves by a wall, with gas in one side and a vacuum in the other. If you open a trap door in the dividing wall, the gas will spread so that it fills both halves of the box evenly (and it will cool down as it does so). No matter how long you wait, the gas will never, of its own accord, all move back into one half of the box. Again, if you saw a photograph of the box with all the gas in one half, and another photo showing the gas evenly spread through both halves of the box, you would know which photo was taken first.
Nobody fully understands how the arrow of time emerges when interactions that individually take no notice of it are put together, but it is a fundamental feature of the physical world.
In thermodynamics, disorder doesn't just mean a mess, but a lack of pattern. A black-and-white chessboard has order. The same amount of paint making the board a uniform grey is disordered.
A measure of the amount of disorder in a system being studied, or in the entire Universe. The entropy of the Universe always increases.
THE FIRST LAW OF THERMODYNAMICS
This is in effect a preamble to the second law. It states that heat and work are two facets of the same thing, energy, and that the total amount of energy in a closed system stays the same.
* This business about the arrow of time and about heat always flowing from a hotter object to a cooler one is part of a law that is regarded as the most fundamental law in the whole of physics - the second law of thermodynamics.
THE SECOND LAW OF THERMODYNAMICS
* The second law was established by the work of William Thompson, 1st Baron Kelvin (1824–1907), in England, and Rudolf Clausius (1822–88), in Germany, early in the 1850s. It can be summarized in three words: 'things wear out'. Or, to put it in slightly more technical language, the amount of DISORDER in the Universe always increases. And if you want to get more technical still, the scientific term for disorder is ENTROPY – so you can simply say 'entropy increases'. Just these two words sum up the most fundamental law of science.
* The classic example of disorder (or entropy) increasing in this way is when you put an ice cube in a glass of water and watch it melt. The water with the ice floating in it has a kind of structure, a pattern. But when the ice cube melts (an example of heat flowing from the hotter object into the cooler object), there is just a featureless, amorphous, uniform blob of water. And again, the arrow of time appears – you often see ice cubes melting in glasses of water, but you never see a glass of water in which ice cubes appear spontaneously while the rest of the water warms up, even though that would not require any input of energy and so would not violate the first law of thermodynamics.
More or less entropy?
One thing that seems to violate the second law of thermodynamics is life itself. Plants and animals are very complicated ordered structures, built out of simple chemicals, that create order (thereby decreasing entropy) on a local scale. They are only able to do this with the aid of a large input of energy, which comes, ultimately, from sunlight. But the amount of order created by life on Earth in this way is more than compensated for by the amount of disorder (entropy) being created inside the Sun – by the processes that release energy in the form of sunlight. In the Universe at large, entropy always increases.
THOMAS YOUNG (1775–1829)
A child prodigy, Young could read at the age of two, absorbed Latin and Greek as a child, and mastered several Middle Eastern languages before his teens. He had read and understood all Newton's work before he was 17. After qualifying as a doctor (in 1796), he became interested in optics through work on the human eye. As a result, Young carried out a series of experiments involving sound and light, and in 1800 published a book proposing (among other things) that light travels as a wave. He was also fascinated by Egyptology, and was instrumental in deciphering the Rosetta Stone.
NEW LIGHT ON LIGHT
* As we shall see, the new physics offers at least one way of explaining problems such as entropy and where the arrow of time comes from. But before we get to grips with them, there's an important piece of old physics to consider - the physics of light.
A KEY CONCEPT
* The behaviour of light proved to be the key to the two great revolutions that swept through physics in the first decades of the 20th century – the quantum revolution and the relativity revolution. Ironically, though, these two breakthroughs occurred just after the theory of light had been put on what seemed to be a secure footing by the physicists of the 19th century – and by two of them in particular, Michael Faraday and James Clerk Maxwell.
WAVES, NOT CANNONBALLS
* Isaac Newton had had the idea that light is like a stream of tiny cannonballs, flying through space and bouncing off things. This tied in with his laws of motion, so it was a natural model for him to adopt.
* Then at the beginning of the 19th century experiments by Thomas Young in England and Augustin Fresnel in France showed that light actually moves through space (or any transparent medium) in the form of a wave. The clearest proof of this is a famous experiment used by Young, known as 'Young's double-slit experiment' or 'the experiment with two holes'. It will be very important when we come to the new physics, so it is worth spelling out in detail what Young discovered.
Politics and optics
A civil engineer, Augustin Fresnel (1788–1827) became head of the public works department in Paris under Napoleon. He was also interested in optics and invented a special lens for lighthouses. When Napoleon was exiled to Elba, Fresnel supported the restoration of the monarchy, thus showing a good eye for the main chance. Alas for Fresnel, Napoleon came back, and he was placed under house arrest in Normandy, where he developed his wave theory of light. However, Waterloo brought Fresnel back into the open and he went back to engineering.
THE EXPERIMENT WITH TWO HOLES
* If you take a bright light and shine it on a piece of cardboard with a tiny hole in it, the light passes through the hole and spreads out on the other side. Now, you put a second piece of cardboard with two holes (tiny pinholes) in it in the path of the light spreading out from the first hole. The light spreads out from both of the holes in the second card. Finally, you put a third piece of cardboard in the path of the light spreading out from the two holes, and look at the pattern of light and shade that is made on this final screen (of course, you have to do this in a darkened room, in order to see the pattern at all). You get a pattern of alternating bright and dark bands (light and shade) – which can be explained if the light is travelling in the form of a wave, very much like ripples on a pond.
* The waves from each of the two holes in the intermediate piece of cardboard start out in step with one another, because they come from the same single hole in the first piece of cardboard. They spread out like ripples on a pond produced by dropping two stones in at the same time, and they interfere with one another to make a more complicated ripple pattern.
PEAKS AND TROUGHS
* Where the waves overlap, in some places the peaks in the waves from each set of ripples coincide, so you get an extra high peak – a bright stripe on the far screen. In some places, the peak of one wave coincides with the trough of the other wave, so they cancel each other out and there is no light on the far screen – a dark stripe. And if two troughs coincide, that also produces a bright stripe, because the waves are adding together, even though they are adding in the opposite direction.
THE DOUBLE – SLIT EXPERIMENT
Young's original version of the so-called experiment with two holes' used narrow slits, cut with a razor, in the screens – which is how the experiment got its original name. With parallel slits, instead of pinholes, the pattern of light and shade produced on the final screen is simply a set of parallel stripes of light and shade, a distinctive interference pattern. By measuring the distance between the stripes in the pattern of light and dark on the final screen, it is possible to work out the wavelengths of the waves involved.
FARADAY AND ELECTROMAGNETISM
* We all have some idea of the nature of electricity and magnetism from practical experience – but the experiments carried out by Michael Faraday, beginning in the 1820s, demonstrated that electricity and magnetism are actually a single force (electromagnetism) that shows two different facets to the world, depending on which way you look at it.
Excerpted from Get a Grip on Physics by John Gribbin. Copyright © 1999 John Gribbin. Excerpted by permission of Dover Publications, Inc..
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