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KinBackup
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
| Tape/disk: | Home » Personal collection » Acorn ADFS disks » Electron » Pixel_map.ADF |
| Filename: | KinBackup |
| Read OK: | ✔ |
| File size: | 603F bytes |
| Load address: | 0000 |
| Exec address: | FFFFFFFF |
File contents
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�CE The Kinetic Theory of Gases
�CEby M.T.Ford, January 1996
All of our present understanding of the behaviour of materials is
based on one important fact: that all matter is composed of a finite
number of microscopic particles. This idea was first put forward by the
Greek philosopher Democritus in about 400 BC, but no experimental evidence
was found for his theory until the early nineteenth century. Until then,
it was assumed that if you took a small drop of sea water, and magnified
it, say, to the volume of the Mediterranean Sea, its properties would be
exactly the same as those of the water in a real sea. That is to say, they
thought the properties of a substance such as water were identical on any
scale. However, it is now known that the water in this experiment would
not appear like an ordinary sea, but would consist of hard rubbery
objects, a few centimetres across. Each of these objects would contain
three overlapping spheres: a large oxygen atom with two smaller hydrogen
atoms attached. These objects, called molecules, would be moving around
rapidly, sometimes squeezing past each other, so any object thrown into
the water would be jostled about randomly at high speed as the molecules
bombarded it.
In 1808, Dalton carried out experiments on the volumes of gases
taking part in chemical reactions and he, together with Avogadro, came to
the conclusion that these molecules must exist. Later, in 1827, the
botanist Robert Brown observed that pollen grains, or fine grains of
quartz would undergo small random movements if placed on the surface of
water. Similarly, if smoke particles are observed through a microscope,
they are also seen to jiggle about in random directions. This is exactly
the motion that we would expect for an object in a "sea" of molecules: the
particle is continually being bombarded by air (or water) molecules on all
sides, but these collisions occur randomly. In a short time interval, the
particle may for example be struck by 100 molecules on one side, and only
97 molecules on the other. If the particle is sufficiently light, this
difference will result in an acceleration. In the next time interval, the
particle may accelerate in a different direction, so the effect we see is
a "jiggling" motion. This provided important evidence that there molecules
in the air or water, which are constantly moving in random directions,
even though the material may seem perfectly still in bulk. Kinetic theory
is a way of explaining the bulk properties of gases in terms of this
motion (the word "Kinetic" is derived from the Greek verb "to move").
It can be difficult to visualise how this motion results in the
effects we see, due to the high speed and minute size of the particles.
For example, an oxygen molecule at room temperature travels at an average
speed of 440 metres per second, or 990 mph. Yet the length of the molecule
is only about one two-millionth of a millimetre. That means that when it
collides with a stationary molecule, it approaches at a rate of about one
million million times is own length every second (compare this with a
tennis ball, travelling at 100 mph, which strikes a wall at a speed of 600
times its own lengh per second - or a bullet, at 100000 times its own
length per second). So even if we could magnify a gas to the extent that
the molecules were no longer microscopically small, they would be
travelling thousands of millions of times too fast to be seen.
The other problem with visualising a gas, is that the molecules
move and bounce off each other in three dimensions, while we are used to
using two-dimensional diagrams. For example, the path of a golf ball, or a
snooker ball is restricted to one plane (assuming there is no wind, in the
case of the golf ball), so we can represent their movement on a piece of
paper, and measure angles easily. In the case of a gas, this is not the
case, so it is best to visualise it using a two-dimensional analogy. We
represent the molecules by balls, moving about on a snooker table (without
pockets!). It is essential that the balls do not slow down when they roll
or hit each other if they are to represent a gas accurately, otherwise the
gas would just fall down to the ground and collapse into a solid.
Therefore we must imagine them as hard rubber balls, which would bounce
forever if they were dropped on to the table. This model is of limited use
for mathematical analysis but the general principles will be the same as
in a real gas.
The easiest phenomenon to explain with this model is pressure. If
all the balls are set in random motion, they will frequently bounce
against each other and the sides of the table. As a ball strikes a cushion
(at any angle), it is reflected, like a beam of light from a mirror.
According to Newton's First Law of Motion, a body cannot change its speed
or direction of motion without a force acting on it, so the cushion must
have exerted some force on the ball. Now the speed (velocity, strictly)
of the ball can be divided into two components, one parallel to the
cushion and one perpendicular to it - i.e. the rate that it is travelling
across the table, and the rate that it is travelling up or down the table.
But the component parallel to the cushion was unaffected by the collision,
so the cushion must have exerted a force on the ball in the direction
perpendicular to itself. According to Newton's Third Law, the cushion must
have experienced an equal force in the opposite direction (also
perpendicular to itself), away from the balls. This force is not in the
direction one might expect intuitively if the ball approaches at an angle.
But there are many of these collisions every second in a real gas - for
example a full stop on this page is struck about two thousand million
million million times by air molecules every second, so it is impossible
for us to see the effect of each collision individually. The result is a
spread out force, like that seen in an inflated balloon, where the air at
each point on the surface of the rubber is pushing at right angles to the
surface. Although the air exerts a pressure on all surfaces around us, of
about 100000 pascals (1 bar, or 15 pounds per square inch), we do not
normally feel it. This is because there is a similar pressure inside us
balancing out the external pressure. In a balloon, the pressure is greater
on the inside than on the outside, as the inside surface is struck by more
molecules every second than the outside surface. So it is really only the
pressure difference that we feel in a balloon.
Returning to the analogy, suppose we double the length of the
table, without altering the number of balls, or the width of the table.
Now there are only half as many balls in each square metre of the table as
there were before. It follows from this that the end cushion of the table
(which is the same length as before) is only struck half as often - i.e.
the average force on each metre of the cushion has halved. This is
equivalent to saying that if you double the volume of a gas, you halve its
pressure (pressure in a gas is defined by the average force acting on a
square metre of its container - this is the three-dimensional equivalent
of the average force per metre of a cushion). This is a statement of
Boyle's Law, which was discovered in 1662.
Temperature can also be represented in this model. The simplest way
to understand the temperature of a gas (other than how hot it is!) is the
speed of its molecules - the faster they move, the higher the
temperatuere. In reality, the molecules do not all move at the same speed
- their speeds form a distribution - so we must measure the temperure by
their average speed, or more strictly, the average of the squares of their
speeds. We have to be careful about the scale we use for measuring
temperature in physics. We are used to measuring temperatures on the
Celsius, or Fahrenheit scales in everyday life, where temperatures both
above and below zero are possible. Of course the speeds of the molecules
can never be below zero, so is sensible to choose a scale where the
molecules are stationary at zero degrees. This scale is called the
absolute or Kelvin scale, and is obtained by simply taking a temperature
on the Celsius scale and adding 273.15 degrees. On this scale, doubling a
temperature actually means doubling the squares of the speeds of the
molecules.
Suppose we start the balls moving again, and then double their
speeds. The squares of their speeds, and hence their temperatures (on the
Kelvin scale) increase by a factor of four. The balls will strike the
cushions moving twice as fast as before, on average, and so the force
exerted on the cushion in each collision will be doubled. But the balls
also strike the cushions twice as often as before (imagine filming the
balls, and then playing the film back at double speed - you will see the
same number of collisions in half the time). So the pressure on the
cushions, which depends on the force and frequency of the collisions, will
increase by a factor of four. Since the temperature also increased by a
factor of four, we can deduce that the pressure of a gas varies in
proportion to its temperature (on the Kelvin scale), provided its volume
is not changed. This, combined mathematically with Boyle's law, leads to
the conclusion that the volume of a gas varies in proportion to its
temperature (i.e. if you double the temperature you will double the
volume), provided the pressure is not changed. This is called Charles's
Law, and was not discovered until over a century later, in 1787. It allows
us to understand the expansion of gases when they are heated at
atmospheric pressure, and the important phenomenon of convection, which
carries air up from a heating element, drawing up cooler air from below.
Now imagine we place a moveable cushion across the middle of the
table, representing a piston in a gas jar. The balls can make the cushion
move when they strike it, but they can never cross to the other side. We
now place an equal number of balls on each side of the cushion, and set
them all in motion. We now double the speeds of the balls in one half
(thus raising their temperature and pressure), and leave the other half
unchanged. The cushion will now experience a greater pressure on one side
than the other, and will move, so the the area of the "hot" side
increases, and that of the "cold" side decreases. Eventually it will reach
a position where the two pressures are equal, and it experiences no net
force either way - this is the equilibrium position. But it is still being
continually bombarded by balls on both sides, so it will undergo small
random motions, like the pollen grains observed by Robert Brown. When one
of the fast "hot" molecules strikes the cushion, it will tend to make the
cushion move fast towards the slow "cold" molecules on the other side. The
fast molecule will be slowed down in this interaction, as it has given
part of its energy to the cushion. The next time a slow molecule strikes
it, it will receive a hard "kick" from the cushion, and will probably move
away faster than it came in. As this process continues, the result on
average is that the fast molecules slow down, and the slow molecules speed
up. Eventually the average speeds on both sides of the cushion will
equalise, and they will be at the same temperature. They are now said to
be in thermal equilibrium, as there is no net transfer of heat either way.
This is a property of temperature which we experience in everyday life: if
we heat the air in a house to, say, 20 XC, when the air outside is at 10 XC,
then switch the heaters off, the heat will gradually escape through the
windows, making the inside colder, and the outside warmer (by a very, very
small amount, as there is a much larger amount of air outside than
inside). The windows are, of course, much more complicated structures than
the cushion used in the analogy, as they contain many molecules between
one side and the other. But if each molecule in the window is treated as
an individual "cushion", it will pass the heat on to the next molecule,
and eventually through to the other side. The heat flow stops when the
house temperature has reached 10 XC, and the house is then in thermal
equilibrium with the air outside, and indeed with anything else that
happens to be at 10 XC. This statement is so obvious that it can easily be
overlooked, and had to be named the Zeroth Law of Thermodynamics, after
the First and Second Laws had already been formulated.
One of the arguments used in this explanation was that each time a
ball strikes the partitiom, it pushes the partition back, and in doing so
cools itself. This principle is used in the internal combustion engine:
fuel gases are compressed inside the cylinder, then a spark causes them to
explode so the temperature and pressure suddenly increase as the chemical
energy is released. The molecules then strike the piston at high speed,
accelerating the piston, and cooling the gases. Thus the energy from the
fuel is converted first into heat, then into motion. But it is important
that this process occurs at very high speed, since while the gases are
hot, there will be a tendency for heat to leak out through the side of the
cylinder into the bodywork and atmosphere, and be wasted. If the expansion
occurs at such high speed that no energy has time to escape, it is called
an adiabatic expansion.
We also make use of expansion in refrigerators. A liquid
refrigerant is pumped into the cold box, and then allowed to expand and
vaporise. As it does so, the molecules are forced to push back the vapour
occupying the pipes, just as the gases in a cylinder push back a piston.
However, in this instance, we actually want heat to leak through the sides
of the pipe, in this case from the outside (i.e. the cold box) to the
inside. So we carry out the expansion quite slowly, to give time for this
to occur. If an expansion occurs so slowly that the temperature doesn't
change at all (because it is continually equalising itself with the
outside temperature), then it is called an isothermal expansion.
Returning to the snooker analogy, suppose we introduce a set of
lighter balls on to the table, in addition to the set that was used
previously (leaving out the cushion across the middle). When the balls are
set in motion, all at the same speed, the heavy balls will collide with
the light ones. In these collisions, Newton's Third Law dictates that the
same force must act on both balls in opposite directions. But this force
will have a greater effect on the light balls than the heavy ones (imagine
a collision between a car and a lorry - the lorry may continue along its
original path almost unimpeded, while the car is thrown violently across
the road). The result is that the light balls move faster on average than
the heavy ones. But eventually the balls must reach thermal equilibrium,
and we know from the Zeroth Law that they must be at the same temperature,
despite the fact that the two sets of balls move at different speeds. This
suggests that in general, temperature is not just a measure of the speeds
of the molecules - or even the squares of the speeds - but involves their
mass as well. In fact it turns out that temperature is a measure of the
energy of the molecules. All motion has a quantity of energy associated
with it, called its kinetic energy, and when two different sets of
molecules are in thermal equilibrium, it is not necessarily their speeds,
but their energies which are equal. This explains why temperature is such
a useful concept in thermodynamics - the study of energy and heat changes.
To illustrate this principle using real gases, consider helium and
radon. In both of these two gases, the molecules all consist of a single
spherical atom, but in radon, the atoms are 56 times heavier than those in
helium. This means that at any particular temperature, the atoms in helium
travel about 7 times faster than those in radon. This can easily be tested
experimentally by measuring the speed of sound in each gas. Sound waves
are carried through a gas by the motion of molecules, so the speed of
sound acts as a good measure of the speeds of the molecules themselves.
Something we have left out of the model is the force of gravity.
The molecules in a gas are all acting as projectiles - when they are
moving upwards they are getting slower, and when they move downwards they
get faster. So why doesn't the air in a room all concentrate at the
bottom, leaving a vacuum at the top? The answer lies in the high speed of
the molecules. If you were to take an evacuated room, with oxygen
molecules held against the floor, then suddenly released them all, they
would simultaneously start rising towards the ceiling. Now all molecules
travelling with an initial speed greater than about 7 metres per second
will reach the ceiling (assuming the room is about 2.5 metres high). The
rest will rise to a certain height then fall back, like a ball thrown
gently into the air. But the average speed of an oxygen molecule is about
440 metres per second, so the vast majority will have speeds much greater
than 7 metres per second, and will reach the ceiling. Hence, nearly every
molecule at the bottom of a room full of air has enough energy to reach
the top, and so there are nearly as many molecules at the top of a room as
there are at the bottom. When we look at the Earth's atmosphere as a
whole, there is a very striking difference in air density at different
heights, because the molecules would then need a much greater energy to
travel from the bottom to the top. But our snooker table is only supposed
to represent a small quantity of gas, so gravity can be neglected. (In
reality, of course, molecules do not travel straight from the bottom to
the top of a room, because they undergo many collisions on the way.
However, collisions are just as likely to reduce the energy of a molecule
as to increase it, so their effects average out to zero, and the above
line of argument is still valid).
Another important effect that we have left out is the attraction
that molecules have for one another. If we were to suddenly stop the
motion of every molecule in a gas, they would not just sit still, like the
balls on a snooker table, even without the influence of gravity. They
would all collapse together and form a solid. If we then gradually
increased the temperature of this solid, thus speeding the molecules up,
they would eventually resist their attractive forces sufficiently to form
a liquid, then a gas again. But in changing from a liquid to a gas, the
average distance between adjacent molecules increases by a factor of 10,
and the attractive forces become so weak that they are almost negligible
(this is like pulling two magnets apart: when they are close together,
they attract each other strongly, but the attraction quickly gets weaker
as they are pulled apart). It is convenient to neglect these forces when
studying gases, because the laws governing their behaviour become very
much simpler. These approximate "laws" are called the laws of "perfect
gases" or "ideal gases", which are defined to be gases with no attractive
forces, and infinitely small molecules. There is no such thing as an ideal
gas in reality, but most gases at atmospheric pressure fit the ideal gas
laws quite closely, so the absence of attractive forces in our model is
not a major problem.
Another important effect we often observe in a gas is viscosity. If
we move rapidly through a gas, by standing in the wind, or by driving
through it in a car, we feel a resisting force. This can partially be
explained by the fact that air is "bunching up" in front of us, and not
catching up behind us as we move. This generates a high pressure region in
front and a low pressure region behind, so the net result is a backward
force.
This explanation seems to solve the problem completely, but
consider the following situation. A solid cylinder is rotated at high
speed by an electric motor, then a hollow cylinder is placed around the
rotating cylinder, with an air space of about one millimetre between them.
The outer cylinder experiences a force, trying to rotate it in the same
direction as the motion of the inner cylinder. One would imagine
intuitively that this would only happen in gases where the molecules are
attracted to one another, but in fact the effect occurs even in ideal
gases. The force cannot be explained in the same way as the air resistance
on a car, since there is no air being "pushed out of the way", and no
regions of high and low pressure. In fact the reason for the gas's
resistance to this motion is as follows:
While the outer cylinder is being held stationary, the air
immediately next to it acts as a stationary air mass. That is to say, the
molecules are moving, but there are as many moving one way as another, so
there is no bulk flow. The air immediately next to the inner cylinder
though, is rotating around at the speed of the cylinder, since each time a
molecule strikes the cylinder, it receives a "kick" to keep it moving
round. Thus the air between the cylinders can be divided into thin
cylindrical layers, each layer moving at a slightly different speed from
the layers next to it. Now imagine two adjacent layers of air as two
trains moving on parallel rails at slightly different speeds. The engines
are both switched off, and the trains coast along on perfectly smooth
rails without losing any speed. Now the trains are both full of people,
representing air molecules within the layers. The people are moving around
blindly inside the trains in completely random directions, and sometimes
one of them will step from one train on to the other. If a person steps
from the slow train to the fast one, the fast train will have to exert a
force on him to bring him up to the right speed. But the train will
experience a force in the opposite direction, slowing itself down
slightly. Similarly, if a person steps from the fast train to the slow
one, the slow train will speed up slightly. As people continue to step
from one train to the other, the slow train speeds up and the fast train
slows down, until they are both travelling at the same speed. So each
layer of air in the cylinder experiment is exerting a force on the next
layer, trying to equalise their speeds. This force is conducted through to
the outer cylinder, which tries to equalise its speed with the inner one.
To stop it moving, we have to push it the other way, so we are effectively
acting as the "engines" of the trains, which keep the fast trains moving
faster than the slow trains.
We have seen that most of the important phenomena occurring in
gases can be explained using simple analogies, which can help by reducing
the number of dimensions involved, and by changing the scales and orders
of magnitude. It is important to realise though, that these analogies do
not provide rigorous proofs of the reasons behind an effect - they just
help us to visualise the possible explanations. It is possible to imagine
the behaviour of solids and liquids by similar methods, but in these cases
it is much more difficult to find a suitable analogy. For example in a
liquid, we must consider gravity, intermolecular forces, and the
liquid-vapour interface at the surface, to explain its behaviour fully. It
is the very simple approximations of the ideal (perfect) gas model that
allow us to reach conclusions so easily.
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That| 00000360 20 69 73 20 74 6f 20 73 61 79 2c 20 74 68 65 79 | is to say, they| 00000370 0d 74 68 6f 75 67 68 74 20 74 68 65 20 70 72 6f |.thought the pro| 00000380 70 65 72 74 69 65 73 20 6f 66 20 61 20 73 75 62 |perties of a sub| 00000390 73 74 61 6e 63 65 20 73 75 63 68 20 61 73 20 77 |stance such as w| 000003a0 61 74 65 72 20 77 65 72 65 1a 20 69 64 65 6e 74 |ater were. ident| 000003b0 69 63 61 6c 20 6f 6e 20 61 6e 79 0d 73 63 61 6c |ical on any.scal| 000003c0 65 2e 1a 20 48 6f 77 65 76 65 72 2c 20 69 74 20 |e.. However, it | 000003d0 69 73 20 6e 6f 77 20 6b 6e 6f 77 6e 20 74 68 61 |is now known tha| 000003e0 74 20 74 68 65 20 77 61 74 65 72 20 69 6e 20 74 |t the water in t| 000003f0 68 69 73 1a 20 65 78 70 65 72 69 6d 65 6e 74 1a |his. experiment.| 00000400 20 77 6f 75 6c 64 0d 6e 6f 74 20 61 70 70 65 61 | would.not appea| 00000410 72 1a 20 6c 69 6b 65 1a 20 61 6e 1a 20 6f 72 64 |r. like. an. ord| 00000420 69 6e 61 72 79 1a 20 73 65 61 2c 1a 20 62 75 74 |inary. sea,. but| 00000430 1a 20 77 6f 75 6c 64 1a 20 63 6f 6e 73 69 73 74 |. would. consist| 00000440 1a 20 6f 66 20 68 61 72 64 20 72 75 62 62 65 72 |. of hard rubber| 00000450 79 0d 6f 62 6a 65 63 74 73 2c 1a 20 61 1a 20 66 |y.objects,. a. f| 00000460 65 77 1a 20 63 65 6e 74 69 6d 65 74 72 65 73 1a |ew. centimetres.| 00000470 20 61 63 72 6f 73 73 2e 20 45 61 63 68 20 6f 66 | across. Each of| 00000480 20 74 68 65 73 65 20 6f 62 6a 65 63 74 73 20 77 | these objects w| 00000490 6f 75 6c 64 20 63 6f 6e 74 61 69 6e 0d 74 68 72 |ould contain.thr| 000004a0 65 65 20 6f 76 65 72 6c 61 70 70 69 6e 67 20 73 |ee overlapping s| 000004b0 70 68 65 72 65 73 3a 20 61 20 6c 61 72 67 65 1a |pheres: a large.| 000004c0 20 6f 78 79 67 65 6e 1a 20 61 74 6f 6d 20 77 69 | oxygen. atom wi| 000004d0 74 68 20 74 77 6f 20 73 6d 61 6c 6c 65 72 20 68 |th two smaller h| 000004e0 79 64 72 6f 67 65 6e 0d 61 74 6f 6d 73 20 61 74 |ydrogen.atoms at| 000004f0 74 61 63 68 65 64 2e 20 54 68 65 73 65 20 6f 62 |tached. These ob| 00000500 6a 65 63 74 73 2c 20 63 61 6c 6c 65 64 20 6d 6f |jects, called mo| 00000510 6c 65 63 75 6c 65 73 2c 20 77 6f 75 6c 64 1a 20 |lecules, would. | 00000520 62 65 1a 20 6d 6f 76 69 6e 67 1a 20 61 72 6f 75 |be. moving. arou| 00000530 6e 64 0d 72 61 70 69 64 6c 79 2c 1a 20 73 6f 6d |nd.rapidly,. som| 00000540 65 74 69 6d 65 73 1a 20 73 71 75 65 65 7a 69 6e |etimes. squeezin| 00000550 67 1a 20 70 61 73 74 20 65 61 63 68 20 6f 74 68 |g. past each oth| 00000560 65 72 2c 20 73 6f 20 61 6e 79 20 6f 62 6a 65 63 |er, so any objec| 00000570 74 20 74 68 72 6f 77 6e 20 69 6e 74 6f 0d 74 68 |t thrown into.th| 00000580 65 20 77 61 74 65 72 20 77 6f 75 6c 64 20 62 65 |e water would be| 00000590 1a 20 6a 6f 73 74 6c 65 64 1a 20 61 62 6f 75 74 |. jostled. about| 000005a0 20 72 61 6e 64 6f 6d 6c 79 20 61 74 20 68 69 67 | randomly at hig| 000005b0 68 20 73 70 65 65 64 20 61 73 20 74 68 65 20 6d |h speed as the m| 000005c0 6f 6c 65 63 75 6c 65 73 0d 62 6f 6d 62 61 72 64 |olecules.bombard| 000005d0 65 64 20 69 74 2e 0d 09 49 6e 20 31 38 30 38 2c |ed it...In 1808,| 000005e0 20 44 61 6c 74 6f 6e 20 63 61 72 72 69 65 64 20 | Dalton carried | 000005f0 6f 75 74 1a 20 65 78 70 65 72 69 6d 65 6e 74 73 |out. experiments| 00000600 1a 20 6f 6e 1a 20 74 68 65 1a 20 76 6f 6c 75 6d |. on. the. volum| 00000610 65 73 20 6f 66 20 67 61 73 65 73 0d 74 61 6b 69 |es of gases.taki| 00000620 6e 67 20 70 61 72 74 20 69 6e 20 63 68 65 6d 69 |ng part in chemi| 00000630 63 61 6c 20 72 65 61 63 74 69 6f 6e 73 20 61 6e |cal reactions an| 00000640 64 20 68 65 2c 20 74 6f 67 65 74 68 65 72 20 77 |d he, together w| 00000650 69 74 68 1a 20 41 76 6f 67 61 64 72 6f 2c 20 63 |ith. Avogadro, c| 00000660 61 6d 65 20 74 6f 0d 74 68 65 1a 20 63 6f 6e 63 |ame to.the. conc| 00000670 6c 75 73 69 6f 6e 1a 20 74 68 61 74 1a 20 74 68 |lusion. that. th| 00000680 65 73 65 1a 20 6d 6f 6c 65 63 75 6c 65 73 1a 20 |ese. molecules. | 00000690 6d 75 73 74 1a 20 65 78 69 73 74 2e 1a 20 4c 61 |must. exist.. La| 000006a0 74 65 72 2c 20 69 6e 20 31 38 32 37 2c 20 74 68 |ter, in 1827, th| 000006b0 65 0d 62 6f 74 61 6e 69 73 74 1a 20 52 6f 62 65 |e.botanist. Robe| 000006c0 72 74 1a 20 42 72 6f 77 6e 1a 20 6f 62 73 65 72 |rt. Brown. obser| 000006d0 76 65 64 20 74 68 61 74 20 70 6f 6c 6c 65 6e 20 |ved that pollen | 000006e0 67 72 61 69 6e 73 2c 20 6f 72 1a 20 66 69 6e 65 |grains, or. fine| 000006f0 1a 20 67 72 61 69 6e 73 1a 20 6f 66 0d 71 75 61 |. grains. of.qua| 00000700 72 74 7a 20 77 6f 75 6c 64 20 75 6e 64 65 72 67 |rtz would underg| 00000710 6f 20 73 6d 61 6c 6c 1a 20 72 61 6e 64 6f 6d 1a |o small. random.| 00000720 20 6d 6f 76 65 6d 65 6e 74 73 1a 20 69 66 20 70 | movements. if p| 00000730 6c 61 63 65 64 20 6f 6e 20 74 68 65 20 73 75 72 |laced on the sur| 00000740 66 61 63 65 20 6f 66 0d 77 61 74 65 72 2e 20 53 |face of.water. S| 00000750 69 6d 69 6c 61 72 6c 79 2c 20 69 66 20 73 6d 6f |imilarly, if smo| 00000760 6b 65 20 70 61 72 74 69 63 6c 65 73 20 61 72 65 |ke particles are| 00000770 20 6f 62 73 65 72 76 65 64 1a 20 74 68 72 6f 75 | observed. throu| 00000780 67 68 1a 20 61 1a 20 6d 69 63 72 6f 73 63 6f 70 |gh. a. microscop| 00000790 65 2c 0d 74 68 65 79 1a 20 61 72 65 1a 20 61 6c |e,.they. are. al| 000007a0 73 6f 20 73 65 65 6e 20 74 6f 20 6a 69 67 67 6c |so seen to jiggl| 000007b0 65 20 61 62 6f 75 74 20 69 6e 20 72 61 6e 64 6f |e about in rando| 000007c0 6d 20 64 69 72 65 63 74 69 6f 6e 73 2e 20 54 68 |m directions. Th| 000007d0 69 73 20 69 73 20 65 78 61 63 74 6c 79 0d 74 68 |is is exactly.th| 000007e0 65 20 6d 6f 74 69 6f 6e 20 74 68 61 74 20 77 65 |e motion that we| 000007f0 20 77 6f 75 6c 64 20 65 78 70 65 63 74 20 66 6f | would expect fo| 00000800 72 20 61 6e 20 6f 62 6a 65 63 74 20 69 6e 20 61 |r an object in a| 00000810 20 22 73 65 61 22 20 6f 66 20 6d 6f 6c 65 63 75 | "sea" of molecu| 00000820 6c 65 73 3a 20 74 68 65 0d 70 61 72 74 69 63 6c |les: the.particl| 00000830 65 20 69 73 20 63 6f 6e 74 69 6e 75 61 6c 6c 79 |e is continually| 00000840 20 62 65 69 6e 67 20 62 6f 6d 62 61 72 64 65 64 | being bombarded| 00000850 20 62 79 20 61 69 72 20 28 6f 72 20 77 61 74 65 | by air (or wate| 00000860 72 29 20 6d 6f 6c 65 63 75 6c 65 73 20 6f 6e 20 |r) molecules on | 00000870 61 6c 6c 0d 73 69 64 65 73 2c 20 62 75 74 20 74 |all.sides, but t| 00000880 68 65 73 65 1a 20 63 6f 6c 6c 69 73 69 6f 6e 73 |hese. collisions| 00000890 20 6f 63 63 75 72 20 72 61 6e 64 6f 6d 6c 79 2e | occur randomly.| 000008a0 20 49 6e 20 61 20 73 68 6f 72 74 20 74 69 6d 65 | In a short time| 000008b0 20 69 6e 74 65 72 76 61 6c 2c 20 74 68 65 0d 70 | interval, the.p| 000008c0 61 72 74 69 63 6c 65 20 6d 61 79 20 66 6f 72 20 |article may for | 000008d0 65 78 61 6d 70 6c 65 1a 20 62 65 20 73 74 72 75 |example. be stru| 000008e0 63 6b 20 62 79 20 31 30 30 20 6d 6f 6c 65 63 75 |ck by 100 molecu| 000008f0 6c 65 73 20 6f 6e 20 6f 6e 65 20 73 69 64 65 2c |les on one side,| 00000900 20 61 6e 64 20 6f 6e 6c 79 0d 39 37 20 6d 6f 6c | and only.97 mol| 00000910 65 63 75 6c 65 73 20 6f 6e 20 74 68 65 20 6f 74 |ecules on the ot| 00000920 68 65 72 2e 1a 20 49 66 1a 20 74 68 65 1a 20 70 |her.. If. the. p| 00000930 61 72 74 69 63 6c 65 1a 20 69 73 20 73 75 66 66 |article. is suff| 00000940 69 63 69 65 6e 74 6c 79 20 6c 69 67 68 74 2c 20 |iciently light, | 00000950 74 68 69 73 0d 64 69 66 66 65 72 65 6e 63 65 20 |this.difference | 00000960 77 69 6c 6c 20 72 65 73 75 6c 74 20 69 6e 20 61 |will result in a| 00000970 6e 20 61 63 63 65 6c 65 72 61 74 69 6f 6e 2e 20 |n acceleration. | 00000980 49 6e 20 74 68 65 20 6e 65 78 74 1a 20 74 69 6d |In the next. tim| 00000990 65 20 69 6e 74 65 72 76 61 6c 2c 20 74 68 65 0d |e interval, the.| 000009a0 70 61 72 74 69 63 6c 65 20 6d 61 79 20 61 63 63 |particle may acc| 000009b0 65 6c 65 72 61 74 65 20 69 6e 20 61 20 64 69 66 |elerate in a dif| 000009c0 66 65 72 65 6e 74 20 64 69 72 65 63 74 69 6f 6e |ferent direction| 000009d0 2c 20 73 6f 20 74 68 65 20 65 66 66 65 63 74 1a |, so the effect.| 000009e0 20 77 65 20 73 65 65 20 69 73 0d 61 20 22 6a 69 | we see is.a "ji| 000009f0 67 67 6c 69 6e 67 22 20 6d 6f 74 69 6f 6e 2e 20 |ggling" motion. | 00000a00 54 68 69 73 20 70 72 6f 76 69 64 65 64 20 69 6d |This provided im| 00000a10 70 6f 72 74 61 6e 74 20 65 76 69 64 65 6e 63 65 |portant evidence| 00000a20 20 74 68 61 74 20 74 68 65 72 65 20 6d 6f 6c 65 | that there mole| 00000a30 63 75 6c 65 73 0d 69 6e 1a 20 74 68 65 1a 20 61 |cules.in. the. a| 00000a40 69 72 1a 20 6f 72 1a 20 77 61 74 65 72 2c 20 77 |ir. or. water, w| 00000a50 68 69 63 68 20 61 72 65 20 63 6f 6e 73 74 61 6e |hich are constan| 00000a60 74 6c 79 20 6d 6f 76 69 6e 67 20 69 6e 20 72 61 |tly moving in ra| 00000a70 6e 64 6f 6d 20 64 69 72 65 63 74 69 6f 6e 73 2c |ndom directions,| 00000a80 0d 65 76 65 6e 20 74 68 6f 75 67 68 20 74 68 65 |.even though the| 00000a90 20 6d 61 74 65 72 69 61 6c 20 6d 61 79 20 73 65 | material may se| 00000aa0 65 6d 20 70 65 72 66 65 63 74 6c 79 20 73 74 69 |em perfectly sti| 00000ab0 6c 6c 20 69 6e 20 62 75 6c 6b 2e 20 20 4b 69 6e |ll in bulk. Kin| 00000ac0 65 74 69 63 20 74 68 65 6f 72 79 0d 69 73 20 61 |etic theory.is a| 00000ad0 20 77 61 79 20 6f 66 20 65 78 70 6c 61 69 6e 69 | way of explaini| 00000ae0 6e 67 1a 20 74 68 65 1a 20 62 75 6c 6b 1a 20 70 |ng. the. bulk. p| 00000af0 72 6f 70 65 72 74 69 65 73 1a 20 6f 66 1a 20 67 |roperties. of. g| 00000b00 61 73 65 73 20 20 69 6e 20 74 65 72 6d 73 20 6f |ases in terms o| 00000b10 66 20 74 68 69 73 0d 6d 6f 74 69 6f 6e 20 28 74 |f this.motion (t| 00000b20 68 65 20 77 6f 72 64 20 22 4b 69 6e 65 74 69 63 |he word "Kinetic| 00000b30 22 20 69 73 20 64 65 72 69 76 65 64 20 66 72 6f |" is derived fro| 00000b40 6d 20 74 68 65 20 47 72 65 65 6b 20 76 65 72 62 |m the Greek verb| 00000b50 20 22 74 6f 20 6d 6f 76 65 22 29 2e 0d 09 49 74 | "to move")...It| 00000b60 20 63 61 6e 20 62 65 20 64 69 66 66 69 63 75 6c | can be difficul| 00000b70 74 20 74 6f 1a 20 76 69 73 75 61 6c 69 73 65 1a |t to. visualise.| 00000b80 20 68 6f 77 1a 20 74 68 69 73 1a 20 6d 6f 74 69 | how. this. moti| 00000b90 6f 6e 20 72 65 73 75 6c 74 73 20 69 6e 20 74 68 |on results in th| 00000ba0 65 0d 65 66 66 65 63 74 73 20 77 65 20 73 65 65 |e.effects we see| 00000bb0 2c 20 64 75 65 20 74 6f 20 74 68 65 20 68 69 67 |, due to the hig| 00000bc0 68 20 73 70 65 65 64 20 61 6e 64 1a 20 6d 69 6e |h speed and. min| 00000bd0 75 74 65 1a 20 73 69 7a 65 1a 20 6f 66 20 74 68 |ute. size. of th| 00000be0 65 20 70 61 72 74 69 63 6c 65 73 2e 0d 46 6f 72 |e particles..For| 00000bf0 1a 20 65 78 61 6d 70 6c 65 2c 20 61 6e 20 6f 78 |. example, an ox| 00000c00 79 67 65 6e 20 6d 6f 6c 65 63 75 6c 65 20 61 74 |ygen molecule at| 00000c10 20 72 6f 6f 6d 20 74 65 6d 70 65 72 61 74 75 72 | room temperatur| 00000c20 65 20 74 72 61 76 65 6c 73 20 61 74 20 61 6e 20 |e travels at an | 00000c30 61 76 65 72 61 67 65 0d 73 70 65 65 64 20 6f 66 |average.speed of| 00000c40 20 34 34 30 20 6d 65 74 72 65 73 20 70 65 72 20 | 440 metres per | 00000c50 73 65 63 6f 6e 64 2c 20 6f 72 20 39 39 30 20 6d |second, or 990 m| 00000c60 70 68 2e 20 59 65 74 20 74 68 65 20 6c 65 6e 67 |ph. Yet the leng| 00000c70 74 68 20 6f 66 20 74 68 65 20 6d 6f 6c 65 63 75 |th of the molecu| 00000c80 6c 65 0d 69 73 20 6f 6e 6c 79 1a 20 61 62 6f 75 |le.is only. abou| 00000c90 74 1a 20 6f 6e 65 20 74 77 6f 2d 6d 69 6c 6c 69 |t. one two-milli| 00000ca0 6f 6e 74 68 20 6f 66 20 61 20 6d 69 6c 6c 69 6d |onth of a millim| 00000cb0 65 74 72 65 2e 20 54 68 61 74 20 6d 65 61 6e 73 |etre. That means| 00000cc0 20 74 68 61 74 20 77 68 65 6e 20 69 74 0d 63 6f | that when it.co| 00000cd0 6c 6c 69 64 65 73 20 77 69 74 68 20 61 20 73 74 |llides with a st| 00000ce0 61 74 69 6f 6e 61 72 79 1a 20 6d 6f 6c 65 63 75 |ationary. molecu| 00000cf0 6c 65 2c 20 69 74 20 61 70 70 72 6f 61 63 68 65 |le, it approache| 00000d00 73 20 61 74 20 61 20 72 61 74 65 20 6f 66 20 61 |s at a rate of a| 00000d10 62 6f 75 74 20 6f 6e 65 0d 6d 69 6c 6c 69 6f 6e |bout one.million| 00000d20 20 6d 69 6c 6c 69 6f 6e 20 74 69 6d 65 73 20 69 | million times i| 00000d30 73 20 6f 77 6e 1a 20 6c 65 6e 67 74 68 1a 20 65 |s own. length. e| 00000d40 76 65 72 79 1a 20 73 65 63 6f 6e 64 1a 20 28 63 |very. second. (c| 00000d50 6f 6d 70 61 72 65 1a 20 74 68 69 73 20 77 69 74 |ompare. this wit| 00000d60 68 20 61 0d 74 65 6e 6e 69 73 20 62 61 6c 6c 2c |h a.tennis ball,| 00000d70 20 74 72 61 76 65 6c 6c 69 6e 67 20 61 74 20 31 | travelling at 1| 00000d80 30 30 20 6d 70 68 2c 20 77 68 69 63 68 20 73 74 |00 mph, which st| 00000d90 72 69 6b 65 73 20 61 20 77 61 6c 6c 20 61 74 20 |rikes a wall at | 00000da0 61 20 73 70 65 65 64 20 6f 66 20 36 30 30 0d 74 |a speed of 600.t| 00000db0 69 6d 65 73 20 69 74 73 20 6f 77 6e 20 6c 65 6e |imes its own len| 00000dc0 67 68 20 70 65 72 20 73 65 63 6f 6e 64 20 2d 20 |gh per second - | 00000dd0 6f 72 20 61 20 62 75 6c 6c 65 74 2c 1a 20 61 74 |or a bullet,. at| 00000de0 1a 20 31 30 30 30 30 30 1a 20 74 69 6d 65 73 1a |. 100000. times.| 00000df0 20 69 74 73 1a 20 6f 77 6e 0d 6c 65 6e 67 74 68 | its. own.length| 00000e00 1a 20 70 65 72 1a 20 73 65 63 6f 6e 64 29 2e 20 |. per. second). | 00000e10 53 6f 20 65 76 65 6e 20 69 66 20 77 65 20 63 6f |So even if we co| 00000e20 75 6c 64 20 6d 61 67 6e 69 66 79 20 61 20 67 61 |uld magnify a ga| 00000e30 73 20 74 6f 20 74 68 65 20 65 78 74 65 6e 74 20 |s to the extent | 00000e40 74 68 61 74 0d 74 68 65 1a 20 6d 6f 6c 65 63 75 |that.the. molecu| 00000e50 6c 65 73 1a 20 77 65 72 65 1a 20 6e 6f 1a 20 6c |les. were. no. l| 00000e60 6f 6e 67 65 72 1a 20 6d 69 63 72 6f 73 63 6f 70 |onger. microscop| 00000e70 69 63 61 6c 6c 79 1a 20 73 6d 61 6c 6c 2c 1a 20 |ically. small,. | 00000e80 74 68 65 79 1a 20 77 6f 75 6c 64 1a 20 62 65 0d |they. would. be.| 00000e90 74 72 61 76 65 6c 6c 69 6e 67 20 74 68 6f 75 73 |travelling thous| 00000ea0 61 6e 64 73 20 6f 66 20 6d 69 6c 6c 69 6f 6e 73 |ands of millions| 00000eb0 20 6f 66 20 74 69 6d 65 73 20 74 6f 6f 20 66 61 | of times too fa| 00000ec0 73 74 20 74 6f 20 62 65 20 73 65 65 6e 2e 0d 09 |st to be seen...| 00000ed0 54 68 65 20 6f 74 68 65 72 20 70 72 6f 62 6c 65 |The other proble| 00000ee0 6d 20 77 69 74 68 20 76 69 73 75 61 6c 69 73 69 |m with visualisi| 00000ef0 6e 67 1a 20 61 1a 20 67 61 73 2c 1a 20 69 73 1a |ng. a. gas,. is.| 00000f00 20 74 68 61 74 20 74 68 65 20 6d 6f 6c 65 63 75 | that the molecu| 00000f10 6c 65 73 0d 6d 6f 76 65 20 61 6e 64 20 62 6f 75 |les.move and bou| 00000f20 6e 63 65 20 6f 66 66 20 65 61 63 68 20 6f 74 68 |nce off each oth| 00000f30 65 72 20 69 6e 20 74 68 72 65 65 20 64 69 6d 65 |er in three dime| 00000f40 6e 73 69 6f 6e 73 2c 1a 20 77 68 69 6c 65 1a 20 |nsions,. while. | 00000f50 77 65 20 61 72 65 20 75 73 65 64 20 74 6f 0d 75 |we are used to.u| 00000f60 73 69 6e 67 20 74 77 6f 2d 64 69 6d 65 6e 73 69 |sing two-dimensi| 00000f70 6f 6e 61 6c 20 64 69 61 67 72 61 6d 73 2e 20 46 |onal diagrams. F| 00000f80 6f 72 20 65 78 61 6d 70 6c 65 2c 20 74 68 65 20 |or example, the | 00000f90 70 61 74 68 20 6f 66 20 61 20 67 6f 6c 66 20 62 |path of a golf b| 00000fa0 61 6c 6c 2c 20 6f 72 20 61 0d 73 6e 6f 6f 6b 65 |all, or a.snooke| 00000fb0 72 20 62 61 6c 6c 20 69 73 20 72 65 73 74 72 69 |r ball is restri| 00000fc0 63 74 65 64 20 74 6f 20 6f 6e 65 20 70 6c 61 6e |cted to one plan| 00000fd0 65 20 28 61 73 73 75 6d 69 6e 67 20 74 68 65 72 |e (assuming ther| 00000fe0 65 20 69 73 20 6e 6f 20 77 69 6e 64 2c 20 69 6e |e is no wind, in| 00000ff0 20 74 68 65 0d 63 61 73 65 20 6f 66 20 74 68 65 | the.case of the| 00001000 20 67 6f 6c 66 20 62 61 6c 6c 29 2c 20 73 6f 20 | golf ball), so | 00001010 77 65 20 63 61 6e 20 72 65 70 72 65 73 65 6e 74 |we can represent| 00001020 20 74 68 65 69 72 20 6d 6f 76 65 6d 65 6e 74 1a | their movement.| 00001030 20 6f 6e 1a 20 61 20 70 69 65 63 65 20 6f 66 0d | on. a piece of.| 00001040 70 61 70 65 72 2c 1a 20 61 6e 64 20 6d 65 61 73 |paper,. and meas| 00001050 75 72 65 20 61 6e 67 6c 65 73 20 65 61 73 69 6c |ure angles easil| 00001060 79 2e 20 49 6e 20 74 68 65 20 63 61 73 65 20 6f |y. In the case o| 00001070 66 20 61 20 67 61 73 2c 20 74 68 69 73 20 69 73 |f a gas, this is| 00001080 1a 20 6e 6f 74 1a 20 74 68 65 0d 63 61 73 65 2c |. not. the.case,| 00001090 20 73 6f 1a 20 69 74 1a 20 69 73 1a 20 62 65 73 | so. it. is. bes| 000010a0 74 20 74 6f 20 76 69 73 75 61 6c 69 73 65 20 69 |t to visualise i| 000010b0 74 20 75 73 69 6e 67 20 61 20 74 77 6f 2d 64 69 |t using a two-di| 000010c0 6d 65 6e 73 69 6f 6e 61 6c 20 61 6e 61 6c 6f 67 |mensional analog| 000010d0 79 2e 20 57 65 0d 72 65 70 72 65 73 65 6e 74 20 |y. We.represent | 000010e0 74 68 65 20 6d 6f 6c 65 63 75 6c 65 73 20 62 79 |the molecules by| 000010f0 20 62 61 6c 6c 73 2c 20 6d 6f 76 69 6e 67 20 61 | balls, moving a| 00001100 62 6f 75 74 20 6f 6e 20 61 20 73 6e 6f 6f 6b 65 |bout on a snooke| 00001110 72 20 74 61 62 6c 65 20 28 77 69 74 68 6f 75 74 |r table (without| 00001120 0d 70 6f 63 6b 65 74 73 21 29 2e 20 49 74 20 69 |.pockets!). It i| 00001130 73 20 65 73 73 65 6e 74 69 61 6c 20 74 68 61 74 |s essential that| 00001140 1a 20 74 68 65 20 62 61 6c 6c 73 20 64 6f 20 6e |. the balls do n| 00001150 6f 74 20 73 6c 6f 77 20 64 6f 77 6e 20 77 68 65 |ot slow down whe| 00001160 6e 20 74 68 65 79 20 72 6f 6c 6c 0d 6f 72 20 68 |n they roll.or h| 00001170 69 74 20 65 61 63 68 20 6f 74 68 65 72 20 69 66 |it each other if| 00001180 20 74 68 65 79 20 61 72 65 20 74 6f 20 72 65 70 | they are to rep| 00001190 72 65 73 65 6e 74 20 61 20 67 61 73 20 61 63 63 |resent a gas acc| 000011a0 75 72 61 74 65 6c 79 2c 20 6f 74 68 65 72 77 69 |urately, otherwi| 000011b0 73 65 20 74 68 65 0d 67 61 73 1a 20 77 6f 75 6c |se the.gas. woul| 000011c0 64 1a 20 6a 75 73 74 20 66 61 6c 6c 20 64 6f 77 |d. just fall dow| 000011d0 6e 20 74 6f 1a 20 74 68 65 1a 20 67 72 6f 75 6e |n to. the. groun| 000011e0 64 1a 20 61 6e 64 1a 20 63 6f 6c 6c 61 70 73 65 |d. and. collapse| 000011f0 1a 20 69 6e 74 6f 1a 20 61 1a 20 73 6f 6c 69 64 |. into. a. solid| 00001200 2e 0d 54 68 65 72 65 66 6f 72 65 20 77 65 20 6d |..Therefore we m| 00001210 75 73 74 1a 20 69 6d 61 67 69 6e 65 1a 20 74 68 |ust. imagine. th| 00001220 65 6d 1a 20 61 73 20 68 61 72 64 20 72 75 62 62 |em. as hard rubb| 00001230 65 72 20 62 61 6c 6c 73 2c 20 77 68 69 63 68 20 |er balls, which | 00001240 77 6f 75 6c 64 20 62 6f 75 6e 63 65 0d 66 6f 72 |would bounce.for| 00001250 65 76 65 72 20 69 66 20 74 68 65 79 20 77 65 72 |ever if they wer| 00001260 65 20 64 72 6f 70 70 65 64 20 6f 6e 20 74 6f 20 |e dropped on to | 00001270 74 68 65 20 74 61 62 6c 65 2e 20 54 68 69 73 20 |the table. 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If.all. the.| 00001340 20 62 61 6c 6c 73 20 61 72 65 20 73 65 74 20 69 | balls are set i| 00001350 6e 20 72 61 6e 64 6f 6d 1a 20 6d 6f 74 69 6f 6e |n random. motion| 00001360 2c 1a 20 74 68 65 79 1a 20 77 69 6c 6c 1a 20 66 |,. they. will. f| 00001370 72 65 71 75 65 6e 74 6c 79 1a 20 62 6f 75 6e 63 |requently. bounc| 00001380 65 0d 61 67 61 69 6e 73 74 20 65 61 63 68 20 6f |e.against each o| 00001390 74 68 65 72 20 61 6e 64 20 74 68 65 20 73 69 64 |ther and the sid| 000013a0 65 73 20 6f 66 20 74 68 65 20 74 61 62 6c 65 2e |es of the table.| 000013b0 20 41 73 20 61 20 62 61 6c 6c 20 73 74 72 69 6b | As a ball strik| 000013c0 65 73 20 61 20 63 75 73 68 69 6f 6e 0d 28 61 74 |es a cushion.(at| 000013d0 20 61 6e 79 20 61 6e 67 6c 65 29 2c 1a 20 69 74 | any angle),. it| 000013e0 1a 20 69 73 1a 20 72 65 66 6c 65 63 74 65 64 2c |. is. reflected,| 000013f0 1a 20 6c 69 6b 65 1a 20 61 1a 20 62 65 61 6d 20 |. like. a. beam | 00001400 6f 66 20 6c 69 67 68 74 20 66 72 6f 6d 20 61 20 |of light from a | 00001410 6d 69 72 72 6f 72 2e 0d 41 63 63 6f 72 64 69 6e |mirror..Accordin| 00001420 67 20 74 6f 20 4e 65 77 74 6f 6e 27 73 20 46 69 |g to Newton's Fi| 00001430 72 73 74 20 4c 61 77 20 6f 66 20 4d 6f 74 69 6f |rst Law of Motio| 00001440 6e 2c 20 61 20 62 6f 64 79 1a 20 63 61 6e 6e 6f |n, a body. canno| 00001450 74 20 63 68 61 6e 67 65 20 69 74 73 20 73 70 65 |t change its spe| 00001460 65 64 0d 6f 72 20 64 69 72 65 63 74 69 6f 6e 20 |ed.or direction | 00001470 6f 66 20 6d 6f 74 69 6f 6e 20 77 69 74 68 6f 75 |of motion withou| 00001480 74 20 61 20 66 6f 72 63 65 20 61 63 74 69 6e 67 |t a force acting| 00001490 20 6f 6e 20 69 74 2c 1a 20 73 6f 1a 20 74 68 65 | on it,. so. the| 000014a0 20 63 75 73 68 69 6f 6e 20 6d 75 73 74 0d 68 61 | cushion must.ha| 000014b0 76 65 1a 20 65 78 65 72 74 65 64 1a 20 73 6f 6d |ve. exerted. som| 000014c0 65 1a 20 66 6f 72 63 65 20 6f 6e 20 74 68 65 20 |e. force on the | 000014d0 62 61 6c 6c 2e 20 4e 6f 77 20 74 68 65 20 73 70 |ball. 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Accord| 00001690 69 6e 67 20 74 6f 20 4e 65 77 74 6f 6e 27 73 20 |ing to Newton's | 000016a0 54 68 69 72 64 20 4c 61 77 2c 20 74 68 65 20 63 |Third Law, the c| 000016b0 75 73 68 69 6f 6e 20 6d 75 73 74 0d 68 61 76 65 |ushion must.have| 000016c0 1a 20 65 78 70 65 72 69 65 6e 63 65 64 1a 20 61 |. experienced. a| 000016d0 6e 1a 20 65 71 75 61 6c 1a 1a 20 66 6f 72 63 65 |n. equal.. force| 000016e0 1a 1a 20 69 6e 1a 20 74 68 65 1a 20 6f 70 70 6f |.. in. the. oppo| 000016f0 73 69 74 65 1a 20 64 69 72 65 63 74 69 6f 6e 1a |site. direction.| 00001700 20 28 61 6c 73 6f 0d 70 65 72 70 65 6e 64 69 63 | (also.perpendic| 00001710 75 6c 61 72 20 74 6f 20 69 74 73 65 6c 66 29 2c |ular to itself),| 00001720 20 61 77 61 79 1a 20 66 72 6f 6d 1a 20 74 68 65 | away. from. the| 00001730 1a 20 62 61 6c 6c 73 2e 20 54 68 69 73 20 66 6f |. balls. This fo| 00001740 72 63 65 20 69 73 20 6e 6f 74 20 69 6e 20 74 68 |rce is not in th| 00001750 65 0d 64 69 72 65 63 74 69 6f 6e 20 6f 6e 65 20 |e.direction one | 00001760 6d 69 67 68 74 20 65 78 70 65 63 74 20 69 6e 74 |might expect int| 00001770 75 69 74 69 76 65 6c 79 20 69 66 20 74 68 65 20 |uitively if the | 00001780 62 61 6c 6c 20 61 70 70 72 6f 61 63 68 65 73 20 |ball approaches | 00001790 61 74 20 61 6e 20 61 6e 67 6c 65 2e 0d 42 75 74 |at an angle..But| 000017a0 20 74 68 65 72 65 20 61 72 65 20 6d 61 6e 79 20 | there are many | 000017b0 6f 66 20 74 68 65 73 65 20 63 6f 6c 6c 69 73 69 |of these collisi| 000017c0 6f 6e 73 1a 20 65 76 65 72 79 1a 20 73 65 63 6f |ons. every. seco| 000017d0 6e 64 1a 20 69 6e 20 61 20 72 65 61 6c 20 67 61 |nd. in a real ga| 000017e0 73 20 2d 20 66 6f 72 0d 65 78 61 6d 70 6c 65 1a |s - for.example.| 000017f0 20 61 1a 20 66 75 6c 6c 20 73 74 6f 70 20 6f 6e | a. full stop on| 00001800 20 74 68 69 73 20 70 61 67 65 20 69 73 20 73 74 | this page is st| 00001810 72 75 63 6b 20 61 62 6f 75 74 1a 20 74 77 6f 1a |ruck about. two.| 00001820 20 74 68 6f 75 73 61 6e 64 1a 20 6d 69 6c 6c 69 | thousand. milli| 00001830 6f 6e 0d 6d 69 6c 6c 69 6f 6e 20 6d 69 6c 6c 69 |on.million milli| 00001840 6f 6e 20 74 69 6d 65 73 1a 20 62 79 1a 20 61 69 |on times. by. ai| 00001850 72 20 6d 6f 6c 65 63 75 6c 65 73 20 65 76 65 72 |r molecules ever| 00001860 79 20 73 65 63 6f 6e 64 2c 20 73 6f 20 69 74 20 |y second, so it | 00001870 69 73 20 69 6d 70 6f 73 73 69 62 6c 65 0d 66 6f |is impossible.fo| 00001880 72 20 75 73 20 74 6f 20 73 65 65 20 74 68 65 1a |r us to see the.| 00001890 20 65 66 66 65 63 74 1a 20 6f 66 20 65 61 63 68 | effect. of each| 000018a0 20 63 6f 6c 6c 69 73 69 6f 6e 20 69 6e 64 69 76 | collision indiv| 000018b0 69 64 75 61 6c 6c 79 2e 20 54 68 65 20 72 65 73 |idually. The res| 000018c0 75 6c 74 20 69 73 20 61 0d 73 70 72 65 61 64 20 |ult is a.spread | 000018d0 6f 75 74 20 66 6f 72 63 65 2c 20 6c 69 6b 65 20 |out force, like | 000018e0 74 68 61 74 20 73 65 65 6e 20 69 6e 1a 20 61 6e |that seen in. an| 000018f0 20 69 6e 66 6c 61 74 65 64 20 62 61 6c 6c 6f 6f | inflated balloo| 00001900 6e 2c 20 77 68 65 72 65 20 74 68 65 20 61 69 72 |n, where the air| 00001910 20 61 74 0d 65 61 63 68 20 70 6f 69 6e 74 20 6f | at.each point o| 00001920 6e 20 74 68 65 20 73 75 72 66 61 63 65 20 6f 66 |n the surface of| 00001930 20 74 68 65 20 72 75 62 62 65 72 1a 20 69 73 20 | the rubber. is | 00001940 70 75 73 68 69 6e 67 20 61 74 20 72 69 67 68 74 |pushing at right| 00001950 20 61 6e 67 6c 65 73 20 74 6f 20 74 68 65 0d 73 | angles to the.s| 00001960 75 72 66 61 63 65 2e 20 41 6c 74 68 6f 75 67 68 |urface. Although| 00001970 20 74 68 65 20 61 69 72 20 65 78 65 72 74 73 20 | the air exerts | 00001980 61 20 70 72 65 73 73 75 72 65 20 6f 6e 20 61 6c |a pressure on al| 00001990 6c 1a 20 73 75 72 66 61 63 65 73 20 61 72 6f 75 |l. surfaces arou| 000019a0 6e 64 20 75 73 2c 20 6f 66 0d 61 62 6f 75 74 1a |nd us, of.about.| 000019b0 20 31 30 30 30 30 30 20 70 61 73 63 61 6c 73 20 | 100000 pascals | 000019c0 28 31 20 62 61 72 2c 20 6f 72 20 31 35 20 70 6f |(1 bar, or 15 po| 000019d0 75 6e 64 73 20 70 65 72 20 73 71 75 61 72 65 1a |unds per square.| 000019e0 20 69 6e 63 68 29 2c 1a 20 77 65 1a 20 64 6f 1a | inch),. we. do.| 000019f0 20 6e 6f 74 0d 6e 6f 72 6d 61 6c 6c 79 20 66 65 | not.normally fe| 00001a00 65 6c 1a 20 69 74 2e 1a 20 54 68 69 73 1a 20 69 |el. it.. This. i| 00001a10 73 20 62 65 63 61 75 73 65 20 74 68 65 72 65 20 |s because there | 00001a20 69 73 20 61 20 73 69 6d 69 6c 61 72 20 70 72 65 |is a similar pre| 00001a30 73 73 75 72 65 20 69 6e 73 69 64 65 20 75 73 0d |ssure inside us.| 00001a40 62 61 6c 61 6e 63 69 6e 67 20 6f 75 74 20 74 68 |balancing out th| 00001a50 65 20 65 78 74 65 72 6e 61 6c 20 70 72 65 73 73 |e external press| 00001a60 75 72 65 2e 20 49 6e 20 61 20 62 61 6c 6c 6f 6f |ure. In a balloo| 00001a70 6e 2c 20 74 68 65 20 70 72 65 73 73 75 72 65 20 |n, the pressure | 00001a80 69 73 20 67 72 65 61 74 65 72 0d 6f 6e 20 74 68 |is greater.on th| 00001a90 65 20 69 6e 73 69 64 65 20 74 68 61 6e 20 6f 6e |e inside than on| 00001aa0 20 74 68 65 20 6f 75 74 73 69 64 65 2c 20 61 73 | the outside, as| 00001ab0 20 74 68 65 20 69 6e 73 69 64 65 20 73 75 72 66 | the inside surf| 00001ac0 61 63 65 20 69 73 20 73 74 72 75 63 6b 20 62 79 |ace is struck by| 00001ad0 20 6d 6f 72 65 0d 6d 6f 6c 65 63 75 6c 65 73 20 | more.molecules | 00001ae0 65 76 65 72 79 20 73 65 63 6f 6e 64 20 74 68 61 |every second tha| 00001af0 6e 20 74 68 65 1a 20 6f 75 74 73 69 64 65 20 73 |n the. outside s| 00001b00 75 72 66 61 63 65 2e 20 53 6f 20 69 74 20 69 73 |urface. So it is| 00001b10 20 72 65 61 6c 6c 79 20 6f 6e 6c 79 20 74 68 65 | really only the| 00001b20 0d 70 72 65 73 73 75 72 65 20 1c 1c 1c 1c 64 69 |.pressure ....di| 00001b30 66 66 65 72 65 6e 63 65 1c 1c 1c 1c 20 74 68 61 |fference.... tha| 00001b40 74 20 77 65 20 66 65 65 6c 20 69 6e 20 61 20 62 |t we feel in a b| 00001b50 61 6c 6c 6f 6f 6e 2e 20 0d 09 52 65 74 75 72 6e |alloon. ..Return| 00001b60 69 6e 67 20 74 6f 20 74 68 65 20 61 6e 61 6c 6f |ing to the analo| 00001b70 67 79 2c 20 73 75 70 70 6f 73 65 1a 20 77 65 1a |gy, suppose. we.| 00001b80 20 64 6f 75 62 6c 65 1a 20 74 68 65 1a 20 6c 65 | double. the. le| 00001b90 6e 67 74 68 1a 20 6f 66 1a 20 74 68 65 0d 74 61 |ngth. of. the.ta| 00001ba0 62 6c 65 2c 1a 20 77 69 74 68 6f 75 74 1a 20 61 |ble,. without. a| 00001bb0 6c 74 65 72 69 6e 67 1a 20 74 68 65 20 6e 75 6d |ltering. the num| 00001bc0 62 65 72 20 6f 66 20 62 61 6c 6c 73 2c 20 6f 72 |ber of balls, or| 00001bd0 20 74 68 65 20 77 69 64 74 68 20 6f 66 20 74 68 | the width of th| 00001be0 65 20 74 61 62 6c 65 2e 0d 4e 6f 77 20 74 68 65 |e table..Now the| 00001bf0 72 65 20 61 72 65 20 6f 6e 6c 79 20 68 61 6c 66 |re are only half| 00001c00 20 61 73 20 6d 61 6e 79 20 62 61 6c 6c 73 20 69 | as many balls i| 00001c10 6e 20 65 61 63 68 20 73 71 75 61 72 65 20 6d 65 |n each square me| 00001c20 74 72 65 20 6f 66 20 74 68 65 20 74 61 62 6c 65 |tre of the table| 00001c30 20 61 73 0d 74 68 65 72 65 20 77 65 72 65 20 62 | as.there were b| 00001c40 65 66 6f 72 65 2e 20 49 74 1a 20 66 6f 6c 6c 6f |efore. It. follo| 00001c50 77 73 20 66 72 6f 6d 20 74 68 69 73 20 74 68 61 |ws from this tha| 00001c60 74 20 74 68 65 20 65 6e 64 20 63 75 73 68 69 6f |t the end cushio| 00001c70 6e 20 6f 66 20 74 68 65 20 74 61 62 6c 65 0d 28 |n of the table.(| 00001c80 77 68 69 63 68 20 69 73 20 74 68 65 20 73 61 6d |which is the sam| 00001c90 65 20 6c 65 6e 67 74 68 1a 20 61 73 1a 20 62 65 |e length. as. be| 00001ca0 66 6f 72 65 29 20 69 73 20 6f 6e 6c 79 20 73 74 |fore) is only st| 00001cb0 72 75 63 6b 20 68 61 6c 66 20 61 73 20 6f 66 74 |ruck half as oft| 00001cc0 65 6e 20 2d 20 69 2e 65 2e 0d 74 68 65 1a 20 61 |en - i.e..the. a| 00001cd0 76 65 72 61 67 65 1a 20 66 6f 72 63 65 20 6f 6e |verage. force on| 00001ce0 20 65 61 63 68 20 6d 65 74 72 65 20 6f 66 1a 20 | each metre of. | 00001cf0 74 68 65 1a 20 63 75 73 68 69 6f 6e 1a 20 68 61 |the. cushion. ha| 00001d00 73 1a 20 68 61 6c 76 65 64 2e 1a 20 54 68 69 73 |s. halved.. This| 00001d10 1a 20 69 73 0d 65 71 75 69 76 61 6c 65 6e 74 20 |. is.equivalent | 00001d20 74 6f 20 73 61 79 69 6e 67 20 74 68 61 74 20 69 |to saying that i| 00001d30 66 20 79 6f 75 20 64 6f 75 62 6c 65 20 74 68 65 |f you double the| 00001d40 20 76 6f 6c 75 6d 65 20 6f 66 20 61 20 67 61 73 | volume of a gas| 00001d50 2c 20 79 6f 75 20 68 61 6c 76 65 20 69 74 73 0d |, you halve its.| 00001d60 70 72 65 73 73 75 72 65 20 28 70 72 65 73 73 75 |pressure (pressu| 00001d70 72 65 20 69 6e 1a 20 61 1a 20 67 61 73 1a 20 69 |re in. a. gas. i| 00001d80 73 20 64 65 66 69 6e 65 64 20 62 79 20 74 68 65 |s defined by the| 00001d90 20 61 76 65 72 61 67 65 20 66 6f 72 63 65 20 61 | average force a| 00001da0 63 74 69 6e 67 20 6f 6e 20 61 0d 73 71 75 61 72 |cting on a.squar| 00001db0 65 20 6d 65 74 72 65 20 6f 66 20 69 74 73 20 63 |e metre of its c| 00001dc0 6f 6e 74 61 69 6e 65 72 20 2d 20 74 68 69 73 20 |ontainer - this | 00001dd0 69 73 1a 20 74 68 65 1a 20 74 68 72 65 65 2d 64 |is. the. three-d| 00001de0 69 6d 65 6e 73 69 6f 6e 61 6c 20 65 71 75 69 76 |imensional equiv| 00001df0 61 6c 65 6e 74 0d 6f 66 20 74 68 65 20 61 76 65 |alent.of the ave| 00001e00 72 61 67 65 20 66 6f 72 63 65 20 70 65 72 1a 20 |rage force per. | 00001e10 6d 65 74 72 65 20 6f 66 20 61 1a 20 63 75 73 68 |metre of a. cush| 00001e20 69 6f 6e 29 2e 1a 20 54 68 69 73 1a 20 69 73 1a |ion).. This. is.| 00001e30 20 61 1a 20 73 74 61 74 65 6d 65 6e 74 20 6f 66 | a. statement of| 00001e40 0d 42 6f 79 6c 65 27 73 20 4c 61 77 2c 20 77 68 |.Boyle's Law, wh| 00001e50 69 63 68 20 77 61 73 20 64 69 73 63 6f 76 65 72 |ich was discover| 00001e60 65 64 20 69 6e 20 31 36 36 32 2e 20 0d 09 54 65 |ed in 1662. ..Te| 00001e70 6d 70 65 72 61 74 75 72 65 20 63 61 6e 20 61 6c |mperature can al| 00001e80 73 6f 20 62 65 20 72 65 70 72 65 73 65 6e 74 65 |so be represente| 00001e90 64 20 69 6e 20 74 68 69 73 20 6d 6f 64 65 6c 2e |d in this model.| 00001ea0 20 54 68 65 20 73 69 6d 70 6c 65 73 74 20 77 61 | The simplest wa| 00001eb0 79 0d 74 6f 20 75 6e 64 65 72 73 74 61 6e 64 20 |y.to understand | 00001ec0 74 68 65 20 74 65 6d 70 65 72 61 74 75 72 65 20 |the temperature | 00001ed0 6f 66 1a 20 61 20 67 61 73 20 28 6f 74 68 65 72 |of. a gas (other| 00001ee0 20 74 68 61 6e 20 68 6f 77 20 68 6f 74 20 69 74 | than how hot it| 00001ef0 20 69 73 21 29 20 69 73 20 74 68 65 0d 73 70 65 | is!) is the.spe| 00001f00 65 64 1a 20 6f 66 1a 20 69 74 73 1a 20 6d 6f 6c |ed. of. its. mol| 00001f10 65 63 75 6c 65 73 1a 20 2d 1a 20 74 68 65 1a 1a |ecules. -. the..| 00001f20 20 66 61 73 74 65 72 1a 1a 20 74 68 65 79 1a 20 | faster.. they. | 00001f30 6d 6f 76 65 2c 1a 20 74 68 65 1a 20 68 69 67 68 |move,. the. high| 00001f40 65 72 1a 20 74 68 65 0d 74 65 6d 70 65 72 61 74 |er. the.temperat| 00001f50 75 65 72 65 2e 20 49 6e 20 72 65 61 6c 69 74 79 |uere. In reality| 00001f60 2c 20 74 68 65 20 6d 6f 6c 65 63 75 6c 65 73 20 |, the molecules | 00001f70 64 6f 1a 20 6e 6f 74 20 61 6c 6c 20 6d 6f 76 65 |do. not all move| 00001f80 20 61 74 20 74 68 65 20 73 61 6d 65 20 73 70 65 | at the same spe| 00001f90 65 64 0d 2d 20 74 68 65 69 72 20 73 70 65 65 64 |ed.- their speed| 00001fa0 73 20 66 6f 72 6d 20 61 20 1c 1c 1c 1c 64 69 73 |s form a ....dis| 00001fb0 74 72 69 62 75 74 69 6f 6e 1c 1c 1c 1c 20 2d 1a |tribution.... -.| 00001fc0 20 73 6f 1a 20 77 65 20 6d 75 73 74 20 6d 65 61 | so. we must mea| 00001fd0 73 75 72 65 20 74 68 65 20 74 65 6d 70 65 72 75 |sure the temperu| 00001fe0 72 65 20 62 79 0d 74 68 65 69 72 20 61 76 65 72 |re by.their aver| 00001ff0 61 67 65 20 73 70 65 65 64 2c 20 6f 72 20 6d 6f |age speed, or mo| 00002000 72 65 20 73 74 72 69 63 74 6c 79 2c 20 74 68 65 |re strictly, the| 00002010 20 61 76 65 72 61 67 65 20 6f 66 20 74 68 65 20 | average of the | 00002020 73 71 75 61 72 65 73 20 6f 66 20 74 68 65 69 72 |squares of their| 00002030 0d 73 70 65 65 64 73 2e 1a 20 57 65 1a 20 68 61 |.speeds.. We. ha| 00002040 76 65 1a 20 74 6f 1a 20 62 65 20 63 61 72 65 66 |ve. to. be caref| 00002050 75 6c 20 61 62 6f 75 74 20 74 68 65 20 73 63 61 |ul about the sca| 00002060 6c 65 1a 20 77 65 1a 20 75 73 65 1a 20 66 6f 72 |le. we. use. for| 00002070 1a 20 6d 65 61 73 75 72 69 6e 67 0d 74 65 6d 70 |. measuring.temp| 00002080 65 72 61 74 75 72 65 20 69 6e 20 70 68 79 73 69 |erature in physi| 00002090 63 73 2e 20 57 65 20 61 72 65 1a 20 75 73 65 64 |cs. We are. used| 000020a0 1a 20 74 6f 1a 20 6d 65 61 73 75 72 69 6e 67 1a |. to. measuring.| 000020b0 20 74 65 6d 70 65 72 61 74 75 72 65 73 1a 20 6f | temperatures. o| 000020c0 6e 1a 20 74 68 65 0d 43 65 6c 73 69 75 73 2c 1a |n. the.Celsius,.| 000020d0 20 6f 72 1a 20 46 61 68 72 65 6e 68 65 69 74 1a | or. Fahrenheit.| 000020e0 20 73 63 61 6c 65 73 20 69 6e 20 65 76 65 72 79 | scales in every| 000020f0 64 61 79 20 6c 69 66 65 2c 20 77 68 65 72 65 20 |day life, where | 00002100 74 65 6d 70 65 72 61 74 75 72 65 73 20 62 6f 74 |temperatures bot| 00002110 68 0d 61 62 6f 76 65 20 61 6e 64 20 62 65 6c 6f |h.above and belo| 00002120 77 20 7a 65 72 6f 1a 20 61 72 65 1a 20 70 6f 73 |w zero. are. pos| 00002130 73 69 62 6c 65 2e 20 4f 66 20 63 6f 75 72 73 65 |sible. Of course| 00002140 20 74 68 65 20 73 70 65 65 64 73 20 6f 66 20 74 | the speeds of t| 00002150 68 65 20 6d 6f 6c 65 63 75 6c 65 73 0d 63 61 6e |he molecules.can| 00002160 20 6e 65 76 65 72 20 62 65 20 62 65 6c 6f 77 20 | never be below | 00002170 7a 65 72 6f 2c 20 73 6f 1a 20 69 73 1a 20 73 65 |zero, so. is. se| 00002180 6e 73 69 62 6c 65 1a 20 74 6f 1a 20 63 68 6f 6f |nsible. to. choo| 00002190 73 65 1a 20 61 1a 20 73 63 61 6c 65 1a 20 77 68 |se. a. scale. wh| 000021a0 65 72 65 20 74 68 65 0d 6d 6f 6c 65 63 75 6c 65 |ere the.molecule| 000021b0 73 1a 20 61 72 65 1a 20 73 74 61 74 69 6f 6e 61 |s. are. stationa| 000021c0 72 79 1a 20 61 74 1a 20 7a 65 72 6f 1a 20 64 65 |ry. at. zero. de| 000021d0 67 72 65 65 73 2e 1a 20 54 68 69 73 1a 20 73 63 |grees.. 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On| 00002270 20 74 68 69 73 20 73 63 61 6c 65 2c 1a 20 64 6f | this scale,. do| 00002280 75 62 6c 69 6e 67 20 61 0d 74 65 6d 70 65 72 61 |ubling a.tempera| 00002290 74 75 72 65 1a 20 61 63 74 75 61 6c 6c 79 1a 20 |ture. actually. | 000022a0 6d 65 61 6e 73 1a 20 64 6f 75 62 6c 69 6e 67 1a |means. doubling.| 000022b0 20 74 68 65 1a 20 73 71 75 61 72 65 73 1a 20 6f | the. squares. o| 000022c0 66 20 74 68 65 20 73 70 65 65 64 73 20 6f 66 20 |f the speeds of | 000022d0 74 68 65 0d 6d 6f 6c 65 63 75 6c 65 73 2e 0d 09 |the.molecules...| 000022e0 53 75 70 70 6f 73 65 20 77 65 20 73 74 61 72 74 |Suppose we start| 000022f0 20 74 68 65 20 62 61 6c 6c 73 1a 20 6d 6f 76 69 | the balls. movi| 00002300 6e 67 1a 20 61 67 61 69 6e 2c 1a 20 61 6e 64 1a |ng. again,. and.| 00002310 20 74 68 65 6e 1a 20 64 6f 75 62 6c 65 20 74 68 | then. double th| 00002320 65 69 72 0d 73 70 65 65 64 73 2e 20 54 68 65 20 |eir.speeds. The | 00002330 73 71 75 61 72 65 73 20 6f 66 20 74 68 65 69 72 |squares of their| 00002340 20 73 70 65 65 64 73 2c 20 61 6e 64 20 68 65 6e | speeds, and hen| 00002350 63 65 20 74 68 65 69 72 20 74 65 6d 70 65 72 61 |ce their tempera| 00002360 74 75 72 65 73 1a 20 28 6f 6e 20 74 68 65 0d 4b |tures. (on the.K| 00002370 65 6c 76 69 6e 1a 20 73 63 61 6c 65 29 1a 20 69 |elvin. scale). i| 00002380 6e 63 72 65 61 73 65 1a 20 62 79 20 61 20 66 61 |ncrease. by a fa| 00002390 63 74 6f 72 20 6f 66 20 66 6f 75 72 2e 20 54 68 |ctor of four. Th| 000023a0 65 20 62 61 6c 6c 73 20 77 69 6c 6c 1a 20 73 74 |e balls will. st| 000023b0 72 69 6b 65 1a 20 74 68 65 0d 63 75 73 68 69 6f |rike. the.cushio| 000023c0 6e 73 20 6d 6f 76 69 6e 67 20 74 77 69 63 65 20 |ns moving twice | 000023d0 61 73 1a 20 66 61 73 74 1a 20 61 73 1a 20 62 65 |as. fast. as. be| 000023e0 66 6f 72 65 2c 1a 20 6f 6e 1a 20 61 76 65 72 61 |fore,. on. avera| 000023f0 67 65 2c 20 61 6e 64 20 73 6f 20 74 68 65 20 66 |ge, and so the f| 00002400 6f 72 63 65 0d 65 78 65 72 74 65 64 20 6f 6e 20 |orce.exerted on | 00002410 74 68 65 20 63 75 73 68 69 6f 6e 20 69 6e 20 65 |the cushion in e| 00002420 61 63 68 20 63 6f 6c 6c 69 73 69 6f 6e 20 77 69 |ach collision wi| 00002430 6c 6c 20 62 65 1a 20 64 6f 75 62 6c 65 64 2e 1a |ll be. doubled..| 00002440 20 42 75 74 1a 20 74 68 65 20 62 61 6c 6c 73 0d | But. the balls.| 00002450 61 6c 73 6f 1a 20 73 74 72 69 6b 65 1a 20 74 68 |also. strike. th| 00002460 65 1a 20 63 75 73 68 69 6f 6e 73 1a 20 74 77 69 |e. cushions. twi| 00002470 63 65 20 61 73 20 6f 66 74 65 6e 20 61 73 20 62 |ce as often as b| 00002480 65 66 6f 72 65 20 28 69 6d 61 67 69 6e 65 20 66 |efore (imagine f| 00002490 69 6c 6d 69 6e 67 20 74 68 65 0d 62 61 6c 6c 73 |ilming the.balls| 000024a0 2c 20 61 6e 64 20 74 68 65 6e 20 70 6c 61 79 69 |, and then playi| 000024b0 6e 67 20 74 68 65 1a 20 66 69 6c 6d 1a 20 62 61 |ng the. film. ba| 000024c0 63 6b 20 61 74 20 64 6f 75 62 6c 65 20 73 70 65 |ck at double spe| 000024d0 65 64 20 2d 20 79 6f 75 20 77 69 6c 6c 20 73 65 |ed - you will se| 000024e0 65 20 74 68 65 0d 73 61 6d 65 1a 20 6e 75 6d 62 |e the.same. numb| 000024f0 65 72 20 6f 66 20 63 6f 6c 6c 69 73 69 6f 6e 73 |er of collisions| 00002500 20 69 6e 20 68 61 6c 66 20 74 68 65 1a 20 74 69 | in half the. ti| 00002510 6d 65 29 2e 1a 20 53 6f 1a 20 74 68 65 1a 20 70 |me).. So. the. p| 00002520 72 65 73 73 75 72 65 1a 20 6f 6e 1a 20 74 68 65 |ressure. on. the| 00002530 0d 63 75 73 68 69 6f 6e 73 2c 20 77 68 69 63 68 |.cushions, which| 00002540 20 64 65 70 65 6e 64 73 20 6f 6e 20 74 68 65 20 | depends on the | 00002550 66 6f 72 63 65 20 61 6e 64 20 66 72 65 71 75 65 |force and freque| 00002560 6e 63 79 20 6f 66 20 74 68 65 20 63 6f 6c 6c 69 |ncy of the colli| 00002570 73 69 6f 6e 73 2c 20 77 69 6c 6c 0d 69 6e 63 72 |sions, will.incr| 00002580 65 61 73 65 20 62 79 1a 20 61 1a 20 66 61 63 74 |ease by. a. fact| 00002590 6f 72 1a 20 6f 66 20 66 6f 75 72 2e 20 53 69 6e |or. of four. Sin| 000025a0 63 65 20 74 68 65 20 74 65 6d 70 65 72 61 74 75 |ce the temperatu| 000025b0 72 65 20 61 6c 73 6f 20 69 6e 63 72 65 61 73 65 |re also increase| 000025c0 64 20 62 79 20 61 0d 66 61 63 74 6f 72 20 6f 66 |d by a.factor of| 000025d0 20 66 6f 75 72 2c 20 77 65 20 63 61 6e 1a 20 64 | four, we can. d| 000025e0 65 64 75 63 65 1a 20 74 68 61 74 1a 20 74 68 65 |educe. that. the| 000025f0 1a 20 70 72 65 73 73 75 72 65 1a 20 6f 66 1a 20 |. pressure. of. | 00002600 61 1a 20 67 61 73 1a 20 76 61 72 69 65 73 20 69 |a. gas. varies i| 00002610 6e 0d 70 72 6f 70 6f 72 74 69 6f 6e 1a 20 74 6f |n.proportion. to| 00002620 1a 20 69 74 73 20 74 65 6d 70 65 72 61 74 75 72 |. its temperatur| 00002630 65 20 28 6f 6e 20 74 68 65 20 4b 65 6c 76 69 6e |e (on the Kelvin| 00002640 20 73 63 61 6c 65 29 2c 20 70 72 6f 76 69 64 65 | scale), provide| 00002650 64 20 69 74 73 20 76 6f 6c 75 6d 65 0d 69 73 20 |d its volume.is | 00002660 6e 6f 74 20 63 68 61 6e 67 65 64 2e 1a 20 54 68 |not changed.. Th| 00002670 69 73 2c 1a 20 63 6f 6d 62 69 6e 65 64 20 6d 61 |is,. combined ma| 00002680 74 68 65 6d 61 74 69 63 61 6c 6c 79 20 77 69 74 |thematically wit| 00002690 68 20 42 6f 79 6c 65 27 73 20 6c 61 77 2c 20 6c |h Boyle's law, l| 000026a0 65 61 64 73 20 74 6f 0d 74 68 65 20 63 6f 6e 63 |eads to.the conc| 000026b0 6c 75 73 69 6f 6e 20 74 68 61 74 20 74 68 65 20 |lusion that the | 000026c0 76 6f 6c 75 6d 65 1a 20 6f 66 1a 20 61 1a 20 67 |volume. of. a. g| 000026d0 61 73 1a 20 76 61 72 69 65 73 1a 20 69 6e 1a 20 |as. varies. in. | 000026e0 70 72 6f 70 6f 72 74 69 6f 6e 1a 20 74 6f 20 69 |proportion. to i| 000026f0 74 73 0d 74 65 6d 70 65 72 61 74 75 72 65 1a 20 |ts.temperature. | 00002700 28 69 2e 65 2e 1a 20 69 66 1a 20 79 6f 75 1a 20 |(i.e.. if. you. | 00002710 64 6f 75 62 6c 65 1a 20 74 68 65 1a 20 74 65 6d |double. the. tem| 00002720 70 65 72 61 74 75 72 65 1a 20 79 6f 75 20 77 69 |perature. you wi| 00002730 6c 6c 20 64 6f 75 62 6c 65 20 74 68 65 0d 76 6f |ll double the.vo| 00002740 6c 75 6d 65 29 2c 20 70 72 6f 76 69 64 65 64 20 |lume), provided | 00002750 74 68 65 20 70 72 65 73 73 75 72 65 20 69 73 20 |the pressure is | 00002760 6e 6f 74 20 63 68 61 6e 67 65 64 2e 20 54 68 69 |not changed. Thi| 00002770 73 1a 20 69 73 1a 20 63 61 6c 6c 65 64 1a 20 43 |s. is. called. C| 00002780 68 61 72 6c 65 73 27 73 0d 4c 61 77 2c 20 61 6e |harles's.Law, an| 00002790 64 20 77 61 73 20 6e 6f 74 20 64 69 73 63 6f 76 |d was not discov| 000027a0 65 72 65 64 20 75 6e 74 69 6c 20 6f 76 65 72 20 |ered until over | 000027b0 61 20 63 65 6e 74 75 72 79 20 6c 61 74 65 72 2c |a century later,| 000027c0 20 69 6e 20 31 37 38 37 2e 20 49 74 20 61 6c 6c | in 1787. It all| 000027d0 6f 77 73 0d 75 73 1a 20 74 6f 1a 20 75 6e 64 65 |ows.us. to. unde| 000027e0 72 73 74 61 6e 64 1a 20 74 68 65 1a 20 65 78 70 |rstand. the. exp| 000027f0 61 6e 73 69 6f 6e 1a 20 6f 66 1a 20 67 61 73 65 |ansion. of. gase| 00002800 73 1a 20 77 68 65 6e 1a 20 74 68 65 79 1a 20 61 |s. when. they. a| 00002810 72 65 1a 20 68 65 61 74 65 64 1a 20 61 74 0d 61 |re. heated. at.a| 00002820 74 6d 6f 73 70 68 65 72 69 63 1a 20 70 72 65 73 |tmospheric. pres| 00002830 73 75 72 65 2c 1a 20 61 6e 64 1a 20 74 68 65 20 |sure,. and. the | 00002840 69 6d 70 6f 72 74 61 6e 74 20 70 68 65 6e 6f 6d |important phenom| 00002850 65 6e 6f 6e 20 6f 66 20 63 6f 6e 76 65 63 74 69 |enon of convecti| 00002860 6f 6e 2c 20 77 68 69 63 68 0d 63 61 72 72 69 65 |on, which.carrie| 00002870 73 20 61 69 72 20 75 70 20 66 72 6f 6d 20 61 20 |s air up from a | 00002880 68 65 61 74 69 6e 67 20 65 6c 65 6d 65 6e 74 2c |heating element,| 00002890 20 64 72 61 77 69 6e 67 20 75 70 20 63 6f 6f 6c | drawing up cool| 000028a0 65 72 20 61 69 72 20 66 72 6f 6d 20 62 65 6c 6f |er air from belo| 000028b0 77 2e 0d 09 4e 6f 77 20 69 6d 61 67 69 6e 65 20 |w...Now imagine | 000028c0 77 65 20 70 6c 61 63 65 20 61 1a 20 6d 6f 76 65 |we place a. move| 000028d0 61 62 6c 65 1a 20 63 75 73 68 69 6f 6e 1a 20 61 |able. cushion. a| 000028e0 63 72 6f 73 73 20 74 68 65 20 6d 69 64 64 6c 65 |cross the middle| 000028f0 20 6f 66 20 74 68 65 0d 74 61 62 6c 65 2c 20 72 | of the.table, r| 00002900 65 70 72 65 73 65 6e 74 69 6e 67 20 61 20 70 69 |epresenting a pi| 00002910 73 74 6f 6e 20 69 6e 20 61 20 67 61 73 20 6a 61 |ston in a gas ja| 00002920 72 2e 1a 20 54 68 65 20 62 61 6c 6c 73 20 63 61 |r.. The balls ca| 00002930 6e 20 6d 61 6b 65 20 74 68 65 20 63 75 73 68 69 |n make the cushi| 00002940 6f 6e 0d 6d 6f 76 65 20 77 68 65 6e 20 74 68 65 |on.move when the| 00002950 79 20 73 74 72 69 6b 65 20 69 74 2c 20 62 75 74 |y strike it, but| 00002960 20 74 68 65 79 20 63 61 6e 20 6e 65 76 65 72 1a | they can never.| 00002970 20 63 72 6f 73 73 1a 20 74 6f 20 74 68 65 20 6f | cross. to the o| 00002980 74 68 65 72 20 73 69 64 65 2e 20 57 65 0d 6e 6f |ther side. We.no| 00002990 77 20 70 6c 61 63 65 20 61 6e 20 65 71 75 61 6c |w place an equal| 000029a0 20 6e 75 6d 62 65 72 20 6f 66 20 62 61 6c 6c 73 | number of balls| 000029b0 20 6f 6e 20 65 61 63 68 20 73 69 64 65 20 6f 66 | on each side of| 000029c0 1a 20 74 68 65 1a 20 63 75 73 68 69 6f 6e 2c 1a |. the. cushion,.| 000029d0 20 61 6e 64 20 73 65 74 0d 74 68 65 6d 1a 20 61 | and set.them. a| 000029e0 6c 6c 1a 20 69 6e 1a 20 6d 6f 74 69 6f 6e 2e 1a |ll. in. motion..| 000029f0 20 57 65 1a 20 6e 6f 77 20 64 6f 75 62 6c 65 20 | We. now double | 00002a00 74 68 65 20 73 70 65 65 64 73 20 6f 66 20 74 68 |the speeds of th| 00002a10 65 20 62 61 6c 6c 73 20 69 6e 20 6f 6e 65 20 68 |e balls in one h| 00002a20 61 6c 66 0d 28 74 68 75 73 20 72 61 69 73 69 6e |alf.(thus raisin| 00002a30 67 20 74 68 65 69 72 20 74 65 6d 70 65 72 61 74 |g their temperat| 00002a40 75 72 65 20 61 6e 64 20 70 72 65 73 73 75 72 65 |ure and pressure| 00002a50 29 2c 1a 20 61 6e 64 1a 20 6c 65 61 76 65 1a 20 |),. and. leave. | 00002a60 74 68 65 20 6f 74 68 65 72 20 68 61 6c 66 0d 75 |the other half.u| 00002a70 6e 63 68 61 6e 67 65 64 2e 20 54 68 65 20 63 75 |nchanged. 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When one.of t| 00002c80 68 65 20 66 61 73 74 20 22 68 6f 74 22 1a 20 6d |he fast "hot". m| 00002c90 6f 6c 65 63 75 6c 65 73 20 73 74 72 69 6b 65 73 |olecules strikes| 00002ca0 20 74 68 65 20 63 75 73 68 69 6f 6e 2c 20 69 74 | the cushion, it| 00002cb0 20 77 69 6c 6c 20 74 65 6e 64 20 74 6f 20 6d 61 | will tend to ma| 00002cc0 6b 65 20 74 68 65 0d 63 75 73 68 69 6f 6e 20 6d |ke the.cushion m| 00002cd0 6f 76 65 20 66 61 73 74 20 74 6f 77 61 72 64 73 |ove fast towards| 00002ce0 20 74 68 65 20 73 6c 6f 77 20 22 63 6f 6c 64 22 | the slow "cold"| 00002cf0 20 6d 6f 6c 65 63 75 6c 65 73 20 6f 6e 20 74 68 | molecules on th| 00002d00 65 20 6f 74 68 65 72 20 73 69 64 65 2e 20 54 68 |e other side. 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As this proce| 00002e20 73 73 20 63 6f 6e 74 69 6e 75 65 73 2c 20 74 68 |ss continues, th| 00002e30 65 1a 20 72 65 73 75 6c 74 1a 20 6f 6e 0d 61 76 |e. result. on.av| 00002e40 65 72 61 67 65 20 69 73 20 74 68 61 74 20 74 68 |erage is that th| 00002e50 65 20 66 61 73 74 20 6d 6f 6c 65 63 75 6c 65 73 |e fast molecules| 00002e60 20 73 6c 6f 77 20 64 6f 77 6e 2c 20 61 6e 64 20 | slow down, and | 00002e70 74 68 65 20 73 6c 6f 77 20 6d 6f 6c 65 63 75 6c |the slow molecul| 00002e80 65 73 20 73 70 65 65 64 0d 75 70 2e 20 45 76 65 |es speed.up. 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On| 000033d0 65 20 6f 66 20 74 68 65 20 61 72 67 75 6d 65 6e |e of the argumen| 000033e0 74 73 20 75 73 65 64 1a 20 69 6e 20 74 68 69 73 |ts used. in this| 000033f0 20 65 78 70 6c 61 6e 61 74 69 6f 6e 20 77 61 73 | explanation was| 00003400 20 74 68 61 74 20 65 61 63 68 20 74 69 6d 65 20 | that each time | 00003410 61 0d 62 61 6c 6c 20 73 74 72 69 6b 65 73 20 74 |a.ball strikes t| 00003420 68 65 20 70 61 72 74 69 74 69 6f 6d 2c 20 69 74 |he partitiom, it| 00003430 20 70 75 73 68 65 73 1a 20 74 68 65 20 70 61 72 | pushes. the par| 00003440 74 69 74 69 6f 6e 20 62 61 63 6b 2c 20 61 6e 64 |tition back, and| 00003450 20 69 6e 20 64 6f 69 6e 67 20 73 6f 0d 63 6f 6f | in doing so.coo| 00003460 6c 73 20 69 74 73 65 6c 66 2e 20 54 68 69 73 20 |ls itself. This | 00003470 70 72 69 6e 63 69 70 6c 65 20 69 73 20 75 73 65 |principle is use| 00003480 64 20 69 6e 1a 20 74 68 65 1a 20 69 6e 74 65 72 |d in. the. inter| 00003490 6e 61 6c 1a 20 63 6f 6d 62 75 73 74 69 6f 6e 20 |nal. combustion | 000034a0 65 6e 67 69 6e 65 3a 0d 66 75 65 6c 20 67 61 73 |engine:.fuel gas| 000034b0 65 73 20 61 72 65 20 63 6f 6d 70 72 65 73 73 65 |es are compresse| 000034c0 64 20 69 6e 73 69 64 65 20 74 68 65 20 63 79 6c |d inside the cyl| 000034d0 69 6e 64 65 72 2c 20 74 68 65 6e 20 61 20 73 70 |inder, then a sp| 000034e0 61 72 6b 20 63 61 75 73 65 73 20 74 68 65 6d 20 |ark causes them | 000034f0 74 6f 0d 65 78 70 6c 6f 64 65 1a 20 73 6f 20 74 |to.explode. so t| 00003500 68 65 20 74 65 6d 70 65 72 61 74 75 72 65 20 61 |he temperature a| 00003510 6e 64 20 70 72 65 73 73 75 72 65 20 73 75 64 64 |nd pressure sudd| 00003520 65 6e 6c 79 20 69 6e 63 72 65 61 73 65 20 61 73 |enly increase as| 00003530 20 74 68 65 20 63 68 65 6d 69 63 61 6c 0d 65 6e | the chemical.en| 00003540 65 72 67 79 20 69 73 1a 20 72 65 6c 65 61 73 65 |ergy is. release| 00003550 64 2e 1a 20 54 68 65 1a 20 6d 6f 6c 65 63 75 6c |d.. The. molecul| 00003560 65 73 20 74 68 65 6e 20 73 74 72 69 6b 65 20 74 |es then strike t| 00003570 68 65 20 70 69 73 74 6f 6e 20 61 74 20 68 69 67 |he piston at hig| 00003580 68 20 73 70 65 65 64 2c 0d 61 63 63 65 6c 65 72 |h speed,.acceler| 00003590 61 74 69 6e 67 20 74 68 65 20 70 69 73 74 6f 6e |ating the piston| 000035a0 2c 20 61 6e 64 20 63 6f 6f 6c 69 6e 67 1a 20 74 |, and cooling. t| 000035b0 68 65 1a 20 67 61 73 65 73 2e 20 54 68 75 73 20 |he. gases. Thus | 000035c0 74 68 65 20 65 6e 65 72 67 79 20 66 72 6f 6d 20 |the energy from | 000035d0 74 68 65 0d 66 75 65 6c 20 69 73 20 63 6f 6e 76 |the.fuel is conv| 000035e0 65 72 74 65 64 20 66 69 72 73 74 20 69 6e 74 6f |erted first into| 000035f0 20 68 65 61 74 2c 20 74 68 65 6e 1a 20 69 6e 74 | heat, then. int| 00003600 6f 1a 20 6d 6f 74 69 6f 6e 2e 20 42 75 74 20 69 |o. motion. But i| 00003610 74 20 69 73 20 69 6d 70 6f 72 74 61 6e 74 0d 74 |t is important.t| 00003620 68 61 74 20 74 68 69 73 20 70 72 6f 63 65 73 73 |hat this process| 00003630 20 6f 63 63 75 72 73 20 61 74 20 76 65 72 79 20 | occurs at very | 00003640 68 69 67 68 20 73 70 65 65 64 2c 20 73 69 6e 63 |high speed, sinc| 00003650 65 1a 20 77 68 69 6c 65 1a 20 74 68 65 1a 20 67 |e. while. the. g| 00003660 61 73 65 73 1a 20 61 72 65 0d 68 6f 74 2c 20 74 |ases. are.hot, t| 00003670 68 65 72 65 20 77 69 6c 6c 20 62 65 20 61 20 74 |here will be a t| 00003680 65 6e 64 65 6e 63 79 20 66 6f 72 20 68 65 61 74 |endency for heat| 00003690 20 74 6f 20 6c 65 61 6b 20 6f 75 74 20 74 68 72 | to leak out thr| 000036a0 6f 75 67 68 20 74 68 65 20 73 69 64 65 20 6f 66 |ough the side of| 000036b0 20 74 68 65 0d 63 79 6c 69 6e 64 65 72 20 69 6e | the.cylinder in| 000036c0 74 6f 20 74 68 65 20 62 6f 64 79 77 6f 72 6b 20 |to the bodywork | 000036d0 61 6e 64 20 61 74 6d 6f 73 70 68 65 72 65 2c 20 |and atmosphere, | 000036e0 61 6e 64 20 62 65 20 77 61 73 74 65 64 2e 20 49 |and be wasted. I| 000036f0 66 20 74 68 65 20 65 78 70 61 6e 73 69 6f 6e 0d |f the expansion.| 00003700 6f 63 63 75 72 73 1a 20 61 74 20 73 75 63 68 20 |occurs. at such | 00003710 68 69 67 68 20 73 70 65 65 64 20 74 68 61 74 20 |high speed that | 00003720 6e 6f 20 65 6e 65 72 67 79 20 68 61 73 20 74 69 |no energy has ti| 00003730 6d 65 20 74 6f 20 65 73 63 61 70 65 2c 20 69 74 |me to escape, it| 00003740 20 69 73 20 63 61 6c 6c 65 64 0d 61 6e 20 61 64 | is called.an ad| 00003750 69 61 62 61 74 69 63 20 65 78 70 61 6e 73 69 6f |iabatic expansio| 00003760 6e 2e 0d 09 57 65 1a 20 61 6c 73 6f 1a 20 6d 61 |n...We. also. ma| 00003770 6b 65 1a 20 75 73 65 1a 20 6f 66 1a 1a 20 65 78 |ke. use. of.. ex| 00003780 70 61 6e 73 69 6f 6e 1a 1a 20 69 6e 1a 20 72 65 |pansion.. in. re| 00003790 66 72 69 67 65 72 61 74 6f 72 73 2e 1a 20 41 1a |frigerators.. A.| 000037a0 20 6c 69 71 75 69 64 0d 72 65 66 72 69 67 65 72 | liquid.refriger| 000037b0 61 6e 74 20 69 73 20 70 75 6d 70 65 64 20 69 6e |ant is pumped in| 000037c0 74 6f 20 74 68 65 1a 20 63 6f 6c 64 1a 20 62 6f |to the. cold. bo| 000037d0 78 2c 1a 20 61 6e 64 20 74 68 65 6e 20 61 6c 6c |x,. and then all| 000037e0 6f 77 65 64 20 74 6f 20 65 78 70 61 6e 64 20 61 |owed to expand a| 000037f0 6e 64 0d 76 61 70 6f 72 69 73 65 2e 20 41 73 20 |nd.vaporise. 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This.sugges| 00003e10 74 73 20 74 68 61 74 20 69 6e 1a 20 67 65 6e 65 |ts that in. gene| 00003e20 72 61 6c 2c 20 74 65 6d 70 65 72 61 74 75 72 65 |ral, temperature| 00003e30 20 69 73 20 6e 6f 74 20 6a 75 73 74 20 61 20 6d | is not just a m| 00003e40 65 61 73 75 72 65 20 6f 66 20 74 68 65 20 73 70 |easure of the sp| 00003e50 65 65 64 73 0d 6f 66 20 74 68 65 20 6d 6f 6c 65 |eeds.of the mole| 00003e60 63 75 6c 65 73 20 2d 1a 20 6f 72 20 65 76 65 6e |cules -. or even| 00003e70 20 74 68 65 20 73 71 75 61 72 65 73 20 6f 66 20 | the squares of | 00003e80 74 68 65 20 73 70 65 65 64 73 20 2d 20 62 75 74 |the speeds - but| 00003e90 20 69 6e 76 6f 6c 76 65 73 20 74 68 65 69 72 0d | involves their.| 00003ea0 6d 61 73 73 20 61 73 20 77 65 6c 6c 2e 20 49 6e |mass as well. In| 00003eb0 20 66 61 63 74 1a 20 69 74 1a 20 74 75 72 6e 73 | fact. it. turns| 00003ec0 1a 20 6f 75 74 20 74 68 61 74 20 74 65 6d 70 65 |. out that tempe| 00003ed0 72 61 74 75 72 65 20 69 73 20 61 20 6d 65 61 73 |rature is a meas| 00003ee0 75 72 65 20 6f 66 20 74 68 65 0d 65 6e 65 72 67 |ure of the.energ| 00003ef0 79 20 6f 66 20 74 68 65 20 6d 6f 6c 65 63 75 6c |y of the molecul| 00003f00 65 73 2e 20 41 6c 6c 20 6d 6f 74 69 6f 6e 20 68 |es. All motion h| 00003f10 61 73 20 61 1a 20 71 75 61 6e 74 69 74 79 1a 20 |as a. quantity. | 00003f20 6f 66 1a 20 65 6e 65 72 67 79 20 61 73 73 6f 63 |of. energy assoc| 00003f30 69 61 74 65 64 0d 77 69 74 68 1a 20 69 74 2c 1a |iated.with. it,.| 00003f40 20 63 61 6c 6c 65 64 1a 20 69 74 73 1a 20 6b 69 | called. its. ki| 00003f50 6e 65 74 69 63 1a 20 65 6e 65 72 67 79 2c 1a 20 |netic. energy,. | 00003f60 61 6e 64 1a 20 77 68 65 6e 1a 20 74 77 6f 20 64 |and. when. two d| 00003f70 69 66 66 65 72 65 6e 74 20 73 65 74 73 20 6f 66 |ifferent sets of| 00003f80 0d 6d 6f 6c 65 63 75 6c 65 73 20 61 72 65 20 69 |.molecules are i| 00003f90 6e 20 74 68 65 72 6d 61 6c 20 65 71 75 69 6c 69 |n thermal equili| 00003fa0 62 72 69 75 6d 2c 20 69 74 20 69 73 20 6e 6f 74 |brium, it is not| 00003fb0 20 6e 65 63 65 73 73 61 72 69 6c 79 1a 20 74 68 | necessarily. th| 00003fc0 65 69 72 20 73 70 65 65 64 73 2c 0d 62 75 74 20 |eir speeds,.but | 00003fd0 74 68 65 69 72 20 65 6e 65 72 67 69 65 73 20 77 |their energies w| 00003fe0 68 69 63 68 20 61 72 65 20 65 71 75 61 6c 2e 20 |hich are equal. | 00003ff0 54 68 69 73 20 65 78 70 6c 61 69 6e 73 20 77 68 |This explains wh| 00004000 79 20 74 65 6d 70 65 72 61 74 75 72 65 1a 20 69 |y temperature. i| 00004010 73 20 73 75 63 68 0d 61 20 75 73 65 66 75 6c 20 |s such.a useful | 00004020 63 6f 6e 63 65 70 74 20 69 6e 20 74 68 65 72 6d |concept in therm| 00004030 6f 64 79 6e 61 6d 69 63 73 20 2d 20 74 68 65 20 |odynamics - the | 00004040 73 74 75 64 79 20 6f 66 20 65 6e 65 72 67 79 20 |study of energy | 00004050 61 6e 64 20 68 65 61 74 20 63 68 61 6e 67 65 73 |and heat changes| 00004060 2e 20 20 0d 09 54 6f 20 69 6c 6c 75 73 74 72 61 |. ..To illustra| 00004070 74 65 20 74 68 69 73 20 70 72 69 6e 63 69 70 6c |te this principl| 00004080 65 20 75 73 69 6e 67 1a 20 72 65 61 6c 20 67 61 |e using. real ga| 00004090 73 65 73 2c 20 63 6f 6e 73 69 64 65 72 20 68 65 |ses, consider he| 000040a0 6c 69 75 6d 20 61 6e 64 0d 72 61 64 6f 6e 2e 20 |lium and.radon. | 000040b0 49 6e 20 62 6f 74 68 20 6f 66 20 74 68 65 73 65 |In both of these| 000040c0 20 74 77 6f 1a 20 67 61 73 65 73 2c 1a 20 74 68 | two. gases,. th| 000040d0 65 20 6d 6f 6c 65 63 75 6c 65 73 20 61 6c 6c 20 |e molecules all | 000040e0 63 6f 6e 73 69 73 74 20 6f 66 20 61 20 73 69 6e |consist of a sin| 000040f0 67 6c 65 0d 73 70 68 65 72 69 63 61 6c 20 61 74 |gle.spherical at| 00004100 6f 6d 2c 20 62 75 74 20 69 6e 20 72 61 64 6f 6e |om, but in radon| 00004110 2c 20 74 68 65 20 61 74 6f 6d 73 20 61 72 65 20 |, the atoms are | 00004120 35 36 20 74 69 6d 65 73 20 68 65 61 76 69 65 72 |56 times heavier| 00004130 20 74 68 61 6e 20 74 68 6f 73 65 20 69 6e 0d 68 | than those in.h| 00004140 65 6c 69 75 6d 2e 20 54 68 69 73 20 6d 65 61 6e |elium. This mean| 00004150 73 20 74 68 61 74 20 61 74 20 61 6e 79 20 70 61 |s that at any pa| 00004160 72 74 69 63 75 6c 61 72 20 74 65 6d 70 65 72 61 |rticular tempera| 00004170 74 75 72 65 2c 20 74 68 65 20 61 74 6f 6d 73 20 |ture, the atoms | 00004180 69 6e 20 68 65 6c 69 75 6d 0d 74 72 61 76 65 6c |in helium.travel| 00004190 20 61 62 6f 75 74 20 37 20 74 69 6d 65 73 20 66 | about 7 times f| 000041a0 61 73 74 65 72 20 74 68 61 6e 20 74 68 6f 73 65 |aster than those| 000041b0 20 69 6e 20 72 61 64 6f 6e 2e 20 54 68 69 73 20 | in radon. This | 000041c0 63 61 6e 20 65 61 73 69 6c 79 20 62 65 20 74 65 |can easily be te| 000041d0 73 74 65 64 0d 65 78 70 65 72 69 6d 65 6e 74 61 |sted.experimenta| 000041e0 6c 6c 79 20 62 79 20 6d 65 61 73 75 72 69 6e 67 |lly by measuring| 000041f0 20 74 68 65 20 73 70 65 65 64 20 6f 66 20 73 6f | the speed of so| 00004200 75 6e 64 20 69 6e 1a 20 65 61 63 68 1a 20 67 61 |und in. each. ga| 00004210 73 2e 1a 20 53 6f 75 6e 64 20 77 61 76 65 73 0d |s.. Sound waves.| 00004220 61 72 65 1a 20 63 61 72 72 69 65 64 1a 20 74 68 |are. carried. th| 00004230 72 6f 75 67 68 20 61 20 67 61 73 20 62 79 20 74 |rough a gas by t| 00004240 68 65 20 6d 6f 74 69 6f 6e 20 6f 66 20 6d 6f 6c |he motion of mol| 00004250 65 63 75 6c 65 73 2c 20 73 6f 1a 20 74 68 65 1a |ecules, so. the.| 00004260 20 73 70 65 65 64 1a 20 6f 66 0d 73 6f 75 6e 64 | speed. of.sound| 00004270 20 61 63 74 73 20 61 73 20 61 20 67 6f 6f 64 20 | acts as a good | 00004280 6d 65 61 73 75 72 65 20 6f 66 20 74 68 65 20 73 |measure of the s| 00004290 70 65 65 64 73 20 6f 66 20 74 68 65 20 6d 6f 6c |peeds of the mol| 000042a0 65 63 75 6c 65 73 20 74 68 65 6d 73 65 6c 76 65 |ecules themselve| 000042b0 73 2e 0d 09 53 6f 6d 65 74 68 69 6e 67 20 77 65 |s...Something we| 000042c0 20 68 61 76 65 20 6c 65 66 74 20 6f 75 74 1a 20 | have left out. | 000042d0 6f 66 1a 20 74 68 65 1a 20 6d 6f 64 65 6c 20 69 |of. the. model i| 000042e0 73 20 74 68 65 20 66 6f 72 63 65 20 6f 66 20 67 |s the force of g| 000042f0 72 61 76 69 74 79 2e 0d 54 68 65 20 6d 6f 6c 65 |ravity..The mole| 00004300 63 75 6c 65 73 20 69 6e 20 61 20 67 61 73 20 61 |cules in a gas a| 00004310 72 65 20 61 6c 6c 20 61 63 74 69 6e 67 1a 20 61 |re all acting. a| 00004320 73 1a 20 70 72 6f 6a 65 63 74 69 6c 65 73 1a 20 |s. projectiles. | 00004330 2d 1a 20 77 68 65 6e 1a 20 74 68 65 79 1a 20 61 |-. when. they. a| 00004340 72 65 0d 6d 6f 76 69 6e 67 1a 20 75 70 77 61 72 |re.moving. upwar| 00004350 64 73 20 74 68 65 79 20 61 72 65 20 67 65 74 74 |ds they are gett| 00004360 69 6e 67 20 73 6c 6f 77 65 72 2c 20 61 6e 64 20 |ing slower, and | 00004370 77 68 65 6e 20 74 68 65 79 20 6d 6f 76 65 20 64 |when they move d| 00004380 6f 77 6e 77 61 72 64 73 20 74 68 65 79 0d 67 65 |ownwards they.ge| 00004390 74 20 66 61 73 74 65 72 2e 1a 20 53 6f 1a 20 77 |t faster.. So. w| 000043a0 68 79 1a 20 64 6f 65 73 6e 27 74 1a 20 74 68 65 |hy. doesn't. the| 000043b0 1a 20 61 69 72 1a 20 69 6e 1a 20 61 20 72 6f 6f |. air. in. a roo| 000043c0 6d 20 61 6c 6c 20 63 6f 6e 63 65 6e 74 72 61 74 |m all concentrat| 000043d0 65 20 61 74 20 74 68 65 0d 62 6f 74 74 6f 6d 2c |e at the.bottom,| 000043e0 20 6c 65 61 76 69 6e 67 20 61 20 76 61 63 75 75 | leaving a vacuu| 000043f0 6d 20 61 74 20 74 68 65 20 74 6f 70 3f 20 54 68 |m at the top? Th| 00004400 65 20 61 6e 73 77 65 72 1a 20 6c 69 65 73 20 69 |e answer. lies i| 00004410 6e 20 74 68 65 20 68 69 67 68 20 73 70 65 65 64 |n the high speed| 00004420 20 6f 66 0d 74 68 65 1a 20 6d 6f 6c 65 63 75 6c | of.the. molecul| 00004430 65 73 2e 1a 20 49 66 1a 20 79 6f 75 1a 20 77 65 |es.. If. you. we| 00004440 72 65 1a 20 74 6f 1a 20 74 61 6b 65 1a 20 61 6e |re. to. take. an| 00004450 20 65 76 61 63 75 61 74 65 64 20 72 6f 6f 6d 2c | evacuated room,| 00004460 1a 20 77 69 74 68 1a 20 6f 78 79 67 65 6e 0d 6d |. with. oxygen.m| 00004470 6f 6c 65 63 75 6c 65 73 20 68 65 6c 64 20 61 67 |olecules held ag| 00004480 61 69 6e 73 74 20 74 68 65 20 66 6c 6f 6f 72 2c |ainst the floor,| 00004490 20 74 68 65 6e 20 73 75 64 64 65 6e 6c 79 20 72 | then suddenly r| 000044a0 65 6c 65 61 73 65 64 1a 20 74 68 65 6d 1a 20 61 |eleased. them. a| 000044b0 6c 6c 2c 1a 20 74 68 65 79 0d 77 6f 75 6c 64 1a |ll,. they.would.| 000044c0 20 73 69 6d 75 6c 74 61 6e 65 6f 75 73 6c 79 1a | simultaneously.| 000044d0 20 73 74 61 72 74 20 72 69 73 69 6e 67 20 74 6f | start rising to| 000044e0 77 61 72 64 73 20 74 68 65 20 63 65 69 6c 69 6e |wards the ceilin| 000044f0 67 2e 20 4e 6f 77 20 61 6c 6c 20 6d 6f 6c 65 63 |g. Now all molec| 00004500 75 6c 65 73 0d 74 72 61 76 65 6c 6c 69 6e 67 20 |ules.travelling | 00004510 77 69 74 68 20 61 6e 1a 20 69 6e 69 74 69 61 6c |with an. initial| 00004520 1a 20 73 70 65 65 64 1a 20 67 72 65 61 74 65 72 |. speed. greater| 00004530 20 74 68 61 6e 20 61 62 6f 75 74 20 37 20 6d 65 | than about 7 me| 00004540 74 72 65 73 20 70 65 72 20 73 65 63 6f 6e 64 0d |tres per second.| 00004550 77 69 6c 6c 20 72 65 61 63 68 20 74 68 65 20 63 |will reach the c| 00004560 65 69 6c 69 6e 67 20 28 61 73 73 75 6d 69 6e 67 |eiling (assuming| 00004570 20 74 68 65 1a 20 72 6f 6f 6d 1a 20 69 73 20 61 | the. room. is a| 00004580 62 6f 75 74 20 32 2e 35 20 6d 65 74 72 65 73 20 |bout 2.5 metres | 00004590 68 69 67 68 29 2e 20 54 68 65 0d 72 65 73 74 20 |high). The.rest | 000045a0 77 69 6c 6c 20 72 69 73 65 20 74 6f 20 61 20 63 |will rise to a c| 000045b0 65 72 74 61 69 6e 20 68 65 69 67 68 74 20 74 68 |ertain height th| 000045c0 65 6e 1a 20 66 61 6c 6c 1a 20 62 61 63 6b 2c 1a |en. fall. back,.| 000045d0 20 6c 69 6b 65 1a 20 61 1a 20 62 61 6c 6c 20 74 | like. a. ball t| 000045e0 68 72 6f 77 6e 0d 67 65 6e 74 6c 79 1a 20 69 6e |hrown.gently. in| 000045f0 74 6f 20 74 68 65 20 61 69 72 2e 20 42 75 74 20 |to the air. But | 00004600 74 68 65 20 61 76 65 72 61 67 65 20 73 70 65 65 |the average spee| 00004610 64 20 6f 66 20 61 6e 20 6f 78 79 67 65 6e 20 6d |d of an oxygen m| 00004620 6f 6c 65 63 75 6c 65 20 69 73 20 61 62 6f 75 74 |olecule is about| 00004630 0d 34 34 30 20 6d 65 74 72 65 73 1a 20 70 65 72 |.440 metres. per| 00004640 20 73 65 63 6f 6e 64 2c 20 73 6f 20 74 68 65 20 | second, so the | 00004650 76 61 73 74 20 6d 61 6a 6f 72 69 74 79 20 77 69 |vast majority wi| 00004660 6c 6c 20 68 61 76 65 20 73 70 65 65 64 73 20 6d |ll have speeds m| 00004670 75 63 68 20 67 72 65 61 74 65 72 0d 74 68 61 6e |uch greater.than| 00004680 20 37 20 6d 65 74 72 65 73 1a 20 70 65 72 20 73 | 7 metres. per s| 00004690 65 63 6f 6e 64 2c 20 61 6e 64 20 77 69 6c 6c 20 |econd, and will | 000046a0 72 65 61 63 68 20 74 68 65 20 63 65 69 6c 69 6e |reach the ceilin| 000046b0 67 2e 20 48 65 6e 63 65 2c 20 6e 65 61 72 6c 79 |g. Hence, nearly| 000046c0 20 65 76 65 72 79 0d 6d 6f 6c 65 63 75 6c 65 20 | every.molecule | 000046d0 61 74 20 74 68 65 20 62 6f 74 74 6f 6d 1a 20 6f |at the bottom. o| 000046e0 66 1a 20 61 1a 20 72 6f 6f 6d 20 66 75 6c 6c 20 |f. a. room full | 000046f0 6f 66 20 61 69 72 20 68 61 73 20 65 6e 6f 75 67 |of air has enoug| 00004700 68 20 65 6e 65 72 67 79 20 74 6f 20 72 65 61 63 |h energy to reac| 00004710 68 0d 74 68 65 20 74 6f 70 2c 20 61 6e 64 20 73 |h.the top, and s| 00004720 6f 20 74 68 65 72 65 20 61 72 65 20 6e 65 61 72 |o there are near| 00004730 6c 79 20 61 73 20 6d 61 6e 79 20 6d 6f 6c 65 63 |ly as many molec| 00004740 75 6c 65 73 20 61 74 20 74 68 65 20 74 6f 70 20 |ules at the top | 00004750 6f 66 20 61 20 72 6f 6f 6d 20 61 73 0d 74 68 65 |of a room as.the| 00004760 72 65 20 61 72 65 20 61 74 20 74 68 65 20 62 6f |re are at the bo| 00004770 74 74 6f 6d 2e 20 57 68 65 6e 20 77 65 1a 20 6c |ttom. When we. l| 00004780 6f 6f 6b 1a 20 61 74 1a 20 74 68 65 1a 20 45 61 |ook. at. the. Ea| 00004790 72 74 68 27 73 1a 20 61 74 6d 6f 73 70 68 65 72 |rth's. atmospher| 000047a0 65 1a 20 61 73 20 61 0d 77 68 6f 6c 65 2c 1a 20 |e. as a.whole,. | 000047b0 74 68 65 72 65 1a 20 69 73 1a 20 61 1a 20 76 65 |there. is. a. ve| 000047c0 72 79 20 73 74 72 69 6b 69 6e 67 20 64 69 66 66 |ry striking diff| 000047d0 65 72 65 6e 63 65 20 69 6e 20 61 69 72 20 64 65 |erence in air de| 000047e0 6e 73 69 74 79 20 61 74 20 64 69 66 66 65 72 65 |nsity at differe| 000047f0 6e 74 0d 68 65 69 67 68 74 73 2c 20 62 65 63 61 |nt.heights, beca| 00004800 75 73 65 20 74 68 65 20 6d 6f 6c 65 63 75 6c 65 |use the molecule| 00004810 73 20 77 6f 75 6c 64 1a 20 74 68 65 6e 1a 20 6e |s would. then. n| 00004820 65 65 64 1a 20 61 20 6d 75 63 68 20 67 72 65 61 |eed. a much grea| 00004830 74 65 72 20 65 6e 65 72 67 79 20 74 6f 0d 74 72 |ter energy to.tr| 00004840 61 76 65 6c 20 66 72 6f 6d 20 74 68 65 20 62 6f |avel from the bo| 00004850 74 74 6f 6d 20 74 6f 20 74 68 65 20 74 6f 70 2e |ttom to the top.| 00004860 20 42 75 74 1a 20 6f 75 72 20 73 6e 6f 6f 6b 65 | But. our snooke| 00004870 72 20 74 61 62 6c 65 20 69 73 20 6f 6e 6c 79 20 |r table is only | 00004880 73 75 70 70 6f 73 65 64 0d 74 6f 20 72 65 70 72 |supposed.to repr| 00004890 65 73 65 6e 74 20 61 20 73 6d 61 6c 6c 20 71 75 |esent a small qu| 000048a0 61 6e 74 69 74 79 20 6f 66 20 67 61 73 2c 20 73 |antity of gas, s| 000048b0 6f 20 67 72 61 76 69 74 79 1a 20 63 61 6e 1a 20 |o gravity. can. | 000048c0 62 65 1a 20 6e 65 67 6c 65 63 74 65 64 2e 1a 20 |be. neglected.. | 000048d0 28 49 6e 0d 72 65 61 6c 69 74 79 2c 1a 20 6f 66 |(In.reality,. of| 000048e0 1a 20 63 6f 75 72 73 65 2c 1a 20 6d 6f 6c 65 63 |. course,. molec| 000048f0 75 6c 65 73 20 64 6f 20 6e 6f 74 20 74 72 61 76 |ules do not trav| 00004900 65 6c 20 73 74 72 61 69 67 68 74 20 66 72 6f 6d |el straight from| 00004910 20 74 68 65 20 62 6f 74 74 6f 6d 20 74 6f 0d 74 | the bottom to.t| 00004920 68 65 20 74 6f 70 20 6f 66 20 61 1a 20 72 6f 6f |he top of a. roo| 00004930 6d 2c 1a 20 62 65 63 61 75 73 65 1a 20 74 68 65 |m,. because. the| 00004940 79 1a 20 75 6e 64 65 72 67 6f 1a 20 6d 61 6e 79 |y. undergo. many| 00004950 1a 20 63 6f 6c 6c 69 73 69 6f 6e 73 1a 20 6f 6e |. collisions. on| 00004960 20 74 68 65 20 77 61 79 2e 0d 48 6f 77 65 76 65 | the way..Howeve| 00004970 72 2c 20 63 6f 6c 6c 69 73 69 6f 6e 73 20 61 72 |r, collisions ar| 00004980 65 20 6a 75 73 74 20 61 73 20 6c 69 6b 65 6c 79 |e just as likely| 00004990 20 74 6f 20 72 65 64 75 63 65 20 74 68 65 20 65 | to reduce the e| 000049a0 6e 65 72 67 79 20 6f 66 1a 20 61 20 6d 6f 6c 65 |nergy of. a mole| 000049b0 63 75 6c 65 0d 61 73 1a 20 74 6f 1a 20 69 6e 63 |cule.as. to. inc| 000049c0 72 65 61 73 65 20 69 74 2c 20 73 6f 20 74 68 65 |rease it, so the| 000049d0 69 72 20 65 66 66 65 63 74 73 20 61 76 65 72 61 |ir effects avera| 000049e0 67 65 20 6f 75 74 20 74 6f 20 7a 65 72 6f 2c 20 |ge out to zero, | 000049f0 61 6e 64 1a 20 74 68 65 1a 20 61 62 6f 76 65 0d |and. the. above.| 00004a00 6c 69 6e 65 20 6f 66 20 61 72 67 75 6d 65 6e 74 |line of argument| 00004a10 20 69 73 20 73 74 69 6c 6c 20 76 61 6c 69 64 29 | is still valid)| 00004a20 2e 20 0d 09 41 6e 6f 74 68 65 72 20 69 6d 70 6f |. ..Another impo| 00004a30 72 74 61 6e 74 20 65 66 66 65 63 74 20 74 68 61 |rtant effect tha| 00004a40 74 20 77 65 1a 20 68 61 76 65 1a 20 6c 65 66 74 |t we. have. left| 00004a50 1a 20 6f 75 74 20 69 73 20 74 68 65 20 61 74 74 |. out is the att| 00004a60 72 61 63 74 69 6f 6e 0d 74 68 61 74 1a 20 6d 6f |raction.that. mo| 00004a70 6c 65 63 75 6c 65 73 20 68 61 76 65 20 66 6f 72 |lecules have for| 00004a80 20 6f 6e 65 20 61 6e 6f 74 68 65 72 2e 20 49 66 | one another. If| 00004a90 20 77 65 1a 20 77 65 72 65 1a 20 74 6f 1a 20 73 | we. were. to. s| 00004aa0 75 64 64 65 6e 6c 79 1a 20 73 74 6f 70 1a 20 74 |uddenly. stop. t| 00004ab0 68 65 0d 6d 6f 74 69 6f 6e 20 6f 66 20 65 76 65 |he.motion of eve| 00004ac0 72 79 20 6d 6f 6c 65 63 75 6c 65 20 69 6e 20 61 |ry molecule in a| 00004ad0 20 67 61 73 2c 20 74 68 65 79 20 77 6f 75 6c 64 | gas, they would| 00004ae0 20 6e 6f 74 20 6a 75 73 74 20 73 69 74 20 73 74 | not just sit st| 00004af0 69 6c 6c 2c 20 6c 69 6b 65 20 74 68 65 0d 62 61 |ill, like the.ba| 00004b00 6c 6c 73 20 6f 6e 1a 20 61 1a 20 73 6e 6f 6f 6b |lls on. a. snook| 00004b10 65 72 1a 20 74 61 62 6c 65 2c 1a 20 65 76 65 6e |er. table,. even| 00004b20 1a 20 77 69 74 68 6f 75 74 20 74 68 65 20 69 6e |. without the in| 00004b30 66 6c 75 65 6e 63 65 20 6f 66 20 67 72 61 76 69 |fluence of gravi| 00004b40 74 79 2e 20 54 68 65 79 0d 77 6f 75 6c 64 1a 20 |ty. They.would. | 00004b50 61 6c 6c 1a 20 63 6f 6c 6c 61 70 73 65 1a 20 74 |all. collapse. t| 00004b60 6f 67 65 74 68 65 72 20 61 6e 64 20 66 6f 72 6d |ogether and form| 00004b70 20 61 1a 20 73 6f 6c 69 64 2e 1a 20 49 66 1a 20 | a. solid.. If. | 00004b80 77 65 1a 20 74 68 65 6e 1a 20 67 72 61 64 75 61 |we. then. gradua| 00004b90 6c 6c 79 0d 69 6e 63 72 65 61 73 65 64 20 74 68 |lly.increased th| 00004ba0 65 20 74 65 6d 70 65 72 61 74 75 72 65 20 6f 66 |e temperature of| 00004bb0 1a 20 74 68 69 73 1a 20 73 6f 6c 69 64 2c 20 74 |. this. solid, t| 00004bc0 68 75 73 20 73 70 65 65 64 69 6e 67 20 74 68 65 |hus speeding the| 00004bd0 20 6d 6f 6c 65 63 75 6c 65 73 20 75 70 2c 0d 74 | molecules up,.t| 00004be0 68 65 79 20 77 6f 75 6c 64 20 65 76 65 6e 74 75 |hey would eventu| 00004bf0 61 6c 6c 79 20 72 65 73 69 73 74 20 74 68 65 69 |ally resist thei| 00004c00 72 20 61 74 74 72 61 63 74 69 76 65 1a 20 66 6f |r attractive. fo| 00004c10 72 63 65 73 20 73 75 66 66 69 63 69 65 6e 74 6c |rces sufficientl| 00004c20 79 20 74 6f 20 66 6f 72 6d 0d 61 20 6c 69 71 75 |y to form.a liqu| 00004c30 69 64 2c 20 74 68 65 6e 20 61 20 67 61 73 20 61 |id, then a gas a| 00004c40 67 61 69 6e 2e 20 42 75 74 1a 20 69 6e 1a 20 63 |gain. But. in. c| 00004c50 68 61 6e 67 69 6e 67 1a 20 66 72 6f 6d 20 61 20 |hanging. from a | 00004c60 6c 69 71 75 69 64 20 74 6f 20 61 20 67 61 73 2c |liquid to a gas,| 00004c70 20 74 68 65 0d 61 76 65 72 61 67 65 1a 20 64 69 | the.average. di| 00004c80 73 74 61 6e 63 65 1a 20 62 65 74 77 65 65 6e 20 |stance. between | 00004c90 61 64 6a 61 63 65 6e 74 20 6d 6f 6c 65 63 75 6c |adjacent molecul| 00004ca0 65 73 20 69 6e 63 72 65 61 73 65 73 20 62 79 20 |es increases by | 00004cb0 61 20 66 61 63 74 6f 72 20 6f 66 20 31 30 2c 0d |a factor of 10,.| 00004cc0 61 6e 64 20 74 68 65 20 61 74 74 72 61 63 74 69 |and the attracti| 00004cd0 76 65 1a 20 66 6f 72 63 65 73 1a 20 62 65 63 6f |ve. forces. beco| 00004ce0 6d 65 20 73 6f 20 77 65 61 6b 20 74 68 61 74 20 |me so weak that | 00004cf0 74 68 65 79 20 61 72 65 20 61 6c 6d 6f 73 74 20 |they are almost | 00004d00 6e 65 67 6c 69 67 69 62 6c 65 0d 28 74 68 69 73 |negligible.(this| 00004d10 20 69 73 20 6c 69 6b 65 20 70 75 6c 6c 69 6e 67 | is like pulling| 00004d20 20 74 77 6f 1a 20 6d 61 67 6e 65 74 73 1a 20 61 | two. magnets. a| 00004d30 70 61 72 74 3a 1a 20 77 68 65 6e 1a 20 74 68 65 |part:. when. the| 00004d40 79 20 61 72 65 20 63 6c 6f 73 65 20 74 6f 67 65 |y are close toge| 00004d50 74 68 65 72 2c 0d 74 68 65 79 20 61 74 74 72 61 |ther,.they attra| 00004d60 63 74 20 65 61 63 68 20 6f 74 68 65 72 20 73 74 |ct each other st| 00004d70 72 6f 6e 67 6c 79 2c 20 62 75 74 20 74 68 65 20 |rongly, but the | 00004d80 61 74 74 72 61 63 74 69 6f 6e 20 71 75 69 63 6b |attraction quick| 00004d90 6c 79 1a 20 67 65 74 73 1a 20 77 65 61 6b 65 72 |ly. gets. weaker| 00004da0 0d 61 73 1a 20 74 68 65 79 1a 20 61 72 65 20 70 |.as. they. are p| 00004db0 75 6c 6c 65 64 20 61 70 61 72 74 29 2e 20 49 74 |ulled apart). It| 00004dc0 20 69 73 20 63 6f 6e 76 65 6e 69 65 6e 74 20 74 | is convenient t| 00004dd0 6f 20 6e 65 67 6c 65 63 74 20 74 68 65 73 65 20 |o neglect these | 00004de0 66 6f 72 63 65 73 20 77 68 65 6e 0d 73 74 75 64 |forces when.stud| 00004df0 79 69 6e 67 20 67 61 73 65 73 2c 20 62 65 63 61 |ying gases, beca| 00004e00 75 73 65 1a 20 74 68 65 1a 20 6c 61 77 73 1a 20 |use. the. laws. | 00004e10 67 6f 76 65 72 6e 69 6e 67 1a 20 74 68 65 69 72 |governing. their| 00004e20 20 62 65 68 61 76 69 6f 75 72 20 62 65 63 6f 6d | behaviour becom| 00004e30 65 20 76 65 72 79 0d 6d 75 63 68 20 73 69 6d 70 |e very.much simp| 00004e40 6c 65 72 2e 20 54 68 65 73 65 20 61 70 70 72 6f |ler. These appro| 00004e50 78 69 6d 61 74 65 20 22 6c 61 77 73 22 20 61 72 |ximate "laws" ar| 00004e60 65 20 63 61 6c 6c 65 64 1a 20 74 68 65 1a 20 6c |e called. the. l| 00004e70 61 77 73 1a 20 6f 66 1a 20 22 70 65 72 66 65 63 |aws. of. "perfec| 00004e80 74 0d 67 61 73 65 73 22 1a 20 6f 72 20 22 69 64 |t.gases". or "id| 00004e90 65 61 6c 20 67 61 73 65 73 22 2c 20 77 68 69 63 |eal gases", whic| 00004ea0 68 20 61 72 65 20 64 65 66 69 6e 65 64 20 74 6f |h are defined to| 00004eb0 20 62 65 20 67 61 73 65 73 20 77 69 74 68 20 6e | be gases with n| 00004ec0 6f 20 61 74 74 72 61 63 74 69 76 65 0d 66 6f 72 |o attractive.for| 00004ed0 63 65 73 2c 20 61 6e 64 20 69 6e 66 69 6e 69 74 |ces, and infinit| 00004ee0 65 6c 79 20 73 6d 61 6c 6c 20 6d 6f 6c 65 63 75 |ely small molecu| 00004ef0 6c 65 73 2e 20 54 68 65 72 65 20 69 73 20 6e 6f |les. There is no| 00004f00 20 73 75 63 68 20 74 68 69 6e 67 20 61 73 20 61 | such thing as a| 00004f10 6e 20 69 64 65 61 6c 0d 67 61 73 20 69 6e 1a 20 |n ideal.gas in. | 00004f20 72 65 61 6c 69 74 79 2c 1a 20 62 75 74 20 6d 6f |reality,. but mo| 00004f30 73 74 20 67 61 73 65 73 20 61 74 20 61 74 6d 6f |st gases at atmo| 00004f40 73 70 68 65 72 69 63 20 70 72 65 73 73 75 72 65 |spheric pressure| 00004f50 20 66 69 74 20 74 68 65 20 69 64 65 61 6c 20 67 | fit the ideal g| 00004f60 61 73 0d 6c 61 77 73 20 71 75 69 74 65 20 63 6c |as.laws quite cl| 00004f70 6f 73 65 6c 79 2c 20 73 6f 1a 20 74 68 65 1a 20 |osely, so. the. | 00004f80 61 62 73 65 6e 63 65 1a 20 6f 66 20 61 74 74 72 |absence. of attr| 00004f90 61 63 74 69 76 65 20 66 6f 72 63 65 73 20 69 6e |active forces in| 00004fa0 20 6f 75 72 20 6d 6f 64 65 6c 20 69 73 0d 6e 6f | our model is.no| 00004fb0 74 20 61 20 6d 61 6a 6f 72 20 70 72 6f 62 6c 65 |t a major proble| 00004fc0 6d 2e 0d 09 41 6e 6f 74 68 65 72 20 69 6d 70 6f |m...Another impo| 00004fd0 72 74 61 6e 74 20 65 66 66 65 63 74 20 77 65 20 |rtant effect we | 00004fe0 6f 66 74 65 6e 20 6f 62 73 65 72 76 65 20 69 6e |often observe in| 00004ff0 20 61 20 67 61 73 20 69 73 20 76 69 73 63 6f 73 | a gas is viscos| 00005000 69 74 79 2e 20 49 66 0d 77 65 20 6d 6f 76 65 20 |ity. If.we move | 00005010 72 61 70 69 64 6c 79 20 74 68 72 6f 75 67 68 20 |rapidly through | 00005020 61 1a 20 67 61 73 2c 1a 20 62 79 1a 20 73 74 61 |a. gas,. by. sta| 00005030 6e 64 69 6e 67 1a 20 69 6e 1a 20 74 68 65 20 77 |nding. in. the w| 00005040 69 6e 64 2c 20 6f 72 20 62 79 20 64 72 69 76 69 |ind, or by drivi| 00005050 6e 67 0d 74 68 72 6f 75 67 68 1a 20 69 74 20 69 |ng.through. it i| 00005060 6e 20 61 20 63 61 72 2c 20 77 65 20 66 65 65 6c |n a car, we feel| 00005070 20 61 20 72 65 73 69 73 74 69 6e 67 20 66 6f 72 | a resisting for| 00005080 63 65 2e 1a 20 54 68 69 73 1a 20 63 61 6e 1a 20 |ce.. This. can. | 00005090 70 61 72 74 69 61 6c 6c 79 1a 20 62 65 0d 65 78 |partially. be.ex| 000050a0 70 6c 61 69 6e 65 64 20 62 79 1a 20 74 68 65 1a |plained by. the.| 000050b0 20 66 61 63 74 1a 20 74 68 61 74 20 61 69 72 20 | fact. that air | 000050c0 69 73 20 22 62 75 6e 63 68 69 6e 67 20 75 70 22 |is "bunching up"| 000050d0 20 69 6e 20 66 72 6f 6e 74 20 6f 66 20 75 73 2c | in front of us,| 000050e0 20 61 6e 64 20 6e 6f 74 0d 63 61 74 63 68 69 6e | and not.catchin| 000050f0 67 20 75 70 20 62 65 68 69 6e 64 20 75 73 20 61 |g up behind us a| 00005100 73 20 77 65 20 6d 6f 76 65 2e 20 54 68 69 73 20 |s we move. This | 00005110 67 65 6e 65 72 61 74 65 73 20 61 20 68 69 67 68 |generates a high| 00005120 20 70 72 65 73 73 75 72 65 20 72 65 67 69 6f 6e | pressure region| 00005130 20 69 6e 0d 66 72 6f 6e 74 20 61 6e 64 20 61 20 | in.front and a | 00005140 6c 6f 77 20 70 72 65 73 73 75 72 65 1a 20 72 65 |low pressure. re| 00005150 67 69 6f 6e 1a 20 62 65 68 69 6e 64 2c 1a 20 73 |gion. behind,. s| 00005160 6f 20 74 68 65 20 6e 65 74 20 72 65 73 75 6c 74 |o the net result| 00005170 20 69 73 20 61 20 62 61 63 6b 77 61 72 64 0d 66 | is a backward.f| 00005180 6f 72 63 65 2e 0d 09 54 68 69 73 1a 20 65 78 70 |orce...This. exp| 00005190 6c 61 6e 61 74 69 6f 6e 1a 20 73 65 65 6d 73 1a |lanation. seems.| 000051a0 20 74 6f 1a 20 73 6f 6c 76 65 1a 20 74 68 65 1a | to. solve. the.| 000051b0 20 70 72 6f 62 6c 65 6d 1a 20 63 6f 6d 70 6c 65 | problem. comple| 000051c0 74 65 6c 79 2c 1a 20 62 75 74 0d 63 6f 6e 73 69 |tely,. but.consi| 000051d0 64 65 72 20 74 68 65 20 66 6f 6c 6c 6f 77 69 6e |der the followin| 000051e0 67 20 73 69 74 75 61 74 69 6f 6e 2e 20 41 1a 20 |g situation. A. | 000051f0 73 6f 6c 69 64 1a 20 63 79 6c 69 6e 64 65 72 1a |solid. cylinder.| 00005200 20 69 73 1a 20 72 6f 74 61 74 65 64 1a 20 61 74 | is. rotated. at| 00005210 20 68 69 67 68 0d 73 70 65 65 64 20 62 79 20 61 | high.speed by a| 00005220 6e 20 65 6c 65 63 74 72 69 63 20 6d 6f 74 6f 72 |n electric motor| 00005230 2c 20 74 68 65 6e 20 61 20 68 6f 6c 6c 6f 77 20 |, then a hollow | 00005240 63 79 6c 69 6e 64 65 72 20 69 73 1a 20 70 6c 61 |cylinder is. pla| 00005250 63 65 64 1a 20 61 72 6f 75 6e 64 1a 20 74 68 65 |ced. around. the| 00005260 0d 72 6f 74 61 74 69 6e 67 20 63 79 6c 69 6e 64 |.rotating cylind| 00005270 65 72 2c 20 77 69 74 68 20 61 6e 20 61 69 72 20 |er, with an air | 00005280 73 70 61 63 65 20 6f 66 20 61 62 6f 75 74 20 6f |space of about o| 00005290 6e 65 20 6d 69 6c 6c 69 6d 65 74 72 65 20 62 65 |ne millimetre be| 000052a0 74 77 65 65 6e 20 74 68 65 6d 2e 0d 54 68 65 1a |tween them..The.| 000052b0 20 6f 75 74 65 72 1a 20 63 79 6c 69 6e 64 65 72 | outer. cylinder| 000052c0 1a 20 65 78 70 65 72 69 65 6e 63 65 73 20 61 20 |. experiences a | 000052d0 66 6f 72 63 65 2c 20 74 72 79 69 6e 67 20 74 6f |force, trying to| 000052e0 20 72 6f 74 61 74 65 20 69 74 20 69 6e 20 74 68 | rotate it in th| 000052f0 65 20 73 61 6d 65 0d 64 69 72 65 63 74 69 6f 6e |e same.direction| 00005300 1a 20 61 73 1a 20 74 68 65 1a 20 6d 6f 74 69 6f |. as. the. motio| 00005310 6e 1a 20 6f 66 1a 20 74 68 65 1a 20 69 6e 6e 65 |n. of. the. inne| 00005320 72 1a 20 63 79 6c 69 6e 64 65 72 2e 1a 20 4f 6e |r. cylinder.. On| 00005330 65 1a 20 77 6f 75 6c 64 1a 20 69 6d 61 67 69 6e |e. would. imagin| 00005340 65 0d 69 6e 74 75 69 74 69 76 65 6c 79 20 74 68 |e.intuitively th| 00005350 61 74 20 74 68 69 73 20 77 6f 75 6c 64 1a 20 6f |at this would. o| 00005360 6e 6c 79 1a 20 68 61 70 70 65 6e 20 69 6e 20 67 |nly. happen in g| 00005370 61 73 65 73 20 77 68 65 72 65 20 74 68 65 20 6d |ases where the m| 00005380 6f 6c 65 63 75 6c 65 73 20 61 72 65 0d 61 74 74 |olecules are.att| 00005390 72 61 63 74 65 64 20 74 6f 20 6f 6e 65 20 61 6e |racted to one an| 000053a0 6f 74 68 65 72 2c 20 62 75 74 20 69 6e 1a 20 66 |other, but in. f| 000053b0 61 63 74 1a 20 74 68 65 1a 20 65 66 66 65 63 74 |act. the. effect| 000053c0 1a 20 6f 63 63 75 72 73 1a 20 65 76 65 6e 20 69 |. occurs. even i| 000053d0 6e 20 69 64 65 61 6c 0d 67 61 73 65 73 2e 20 54 |n ideal.gases. T| 000053e0 68 65 20 66 6f 72 63 65 20 63 61 6e 6e 6f 74 20 |he force cannot | 000053f0 62 65 20 65 78 70 6c 61 69 6e 65 64 20 69 6e 20 |be explained in | 00005400 74 68 65 20 73 61 6d 65 20 77 61 79 20 61 73 20 |the same way as | 00005410 74 68 65 20 61 69 72 20 72 65 73 69 73 74 61 6e |the air resistan| 00005420 63 65 0d 6f 6e 20 61 20 63 61 72 2c 20 73 69 6e |ce.on a car, sin| 00005430 63 65 20 74 68 65 72 65 20 69 73 20 6e 6f 20 61 |ce there is no a| 00005440 69 72 20 62 65 69 6e 67 20 22 70 75 73 68 65 64 |ir being "pushed| 00005450 20 6f 75 74 1a 20 6f 66 1a 20 74 68 65 1a 20 77 | out. of. the. w| 00005460 61 79 22 2c 1a 20 61 6e 64 1a 20 6e 6f 0d 72 65 |ay",. and. no.re| 00005470 67 69 6f 6e 73 1a 20 6f 66 1a 20 68 69 67 68 1a |gions. of. high.| 00005480 20 61 6e 64 1a 20 6c 6f 77 1a 20 70 72 65 73 73 | and. low. press| 00005490 75 72 65 2e 1a 20 49 6e 1a 20 66 61 63 74 1a 20 |ure.. In. fact. | 000054a0 74 68 65 20 72 65 61 73 6f 6e 20 66 6f 72 20 74 |the reason for t| 000054b0 68 65 20 67 61 73 27 73 0d 72 65 73 69 73 74 61 |he gas's.resista| 000054c0 6e 63 65 20 74 6f 20 74 68 69 73 20 6d 6f 74 69 |nce to this moti| 000054d0 6f 6e 20 69 73 20 61 73 20 66 6f 6c 6c 6f 77 73 |on is as follows| 000054e0 3a 0d 09 57 68 69 6c 65 1a 20 74 68 65 1a 20 6f |:..While. the. o| 000054f0 75 74 65 72 1a 20 63 79 6c 69 6e 64 65 72 1a 20 |uter. cylinder. | 00005500 69 73 1a 20 62 65 69 6e 67 1a 20 68 65 6c 64 1a |is. being. held.| 00005510 20 73 74 61 74 69 6f 6e 61 72 79 2c 1a 20 74 68 | stationary,. th| 00005520 65 1a 20 61 69 72 0d 69 6d 6d 65 64 69 61 74 65 |e. air.immediate| 00005530 6c 79 20 6e 65 78 74 20 74 6f 20 69 74 20 61 63 |ly next to it ac| 00005540 74 73 1a 20 61 73 20 61 20 73 74 61 74 69 6f 6e |ts. as a station| 00005550 61 72 79 20 61 69 72 20 6d 61 73 73 2e 20 54 68 |ary air mass. Th| 00005560 61 74 20 69 73 20 74 6f 20 73 61 79 2c 20 74 68 |at is to say, th| 00005570 65 0d 6d 6f 6c 65 63 75 6c 65 73 20 61 72 65 20 |e.molecules are | 00005580 6d 6f 76 69 6e 67 2c 20 62 75 74 20 74 68 65 72 |moving, but ther| 00005590 65 20 61 72 65 1a 20 61 73 20 6d 61 6e 79 20 6d |e are. as many m| 000055a0 6f 76 69 6e 67 20 6f 6e 65 20 77 61 79 20 61 73 |oving one way as| 000055b0 20 61 6e 6f 74 68 65 72 2c 20 73 6f 0d 74 68 65 | another, so.the| 000055c0 72 65 20 69 73 20 6e 6f 20 62 75 6c 6b 20 66 6c |re is no bulk fl| 000055d0 6f 77 2e 20 54 68 65 20 61 69 72 1a 20 69 6d 6d |ow. The air. imm| 000055e0 65 64 69 61 74 65 6c 79 1a 20 6e 65 78 74 1a 20 |ediately. next. | 000055f0 74 6f 1a 20 74 68 65 1a 20 69 6e 6e 65 72 20 63 |to. the. inner c| 00005600 79 6c 69 6e 64 65 72 0d 74 68 6f 75 67 68 2c 20 |ylinder.though, | 00005610 69 73 20 72 6f 74 61 74 69 6e 67 20 61 72 6f 75 |is rotating arou| 00005620 6e 64 20 61 74 20 74 68 65 20 73 70 65 65 64 20 |nd at the speed | 00005630 6f 66 20 74 68 65 20 63 79 6c 69 6e 64 65 72 2c |of the cylinder,| 00005640 20 73 69 6e 63 65 20 65 61 63 68 20 74 69 6d 65 | since each time| 00005650 20 61 0d 6d 6f 6c 65 63 75 6c 65 1a 20 73 74 72 | a.molecule. str| 00005660 69 6b 65 73 1a 20 74 68 65 1a 20 63 79 6c 69 6e |ikes. the. cylin| 00005670 64 65 72 2c 1a 20 69 74 1a 20 72 65 63 65 69 76 |der,. it. receiv| 00005680 65 73 20 61 20 22 6b 69 63 6b 22 20 74 6f 20 6b |es a "kick" to k| 00005690 65 65 70 20 69 74 20 6d 6f 76 69 6e 67 0d 72 6f |eep it moving.ro| 000056a0 75 6e 64 2e 1a 20 54 68 75 73 1a 20 74 68 65 20 |und.. Thus. the | 000056b0 61 69 72 20 62 65 74 77 65 65 6e 20 74 68 65 1a |air between the.| 000056c0 20 63 79 6c 69 6e 64 65 72 73 1a 20 63 61 6e 1a | cylinders. can.| 000056d0 20 62 65 1a 20 64 69 76 69 64 65 64 1a 20 69 6e | be. divided. in| 000056e0 74 6f 1a 20 74 68 69 6e 0d 63 79 6c 69 6e 64 72 |to. thin.cylindr| 000056f0 69 63 61 6c 20 6c 61 79 65 72 73 2c 20 65 61 63 |ical layers, eac| 00005700 68 1a 20 6c 61 79 65 72 1a 20 6d 6f 76 69 6e 67 |h. layer. moving| 00005710 20 61 74 20 61 20 73 6c 69 67 68 74 6c 79 20 64 | at a slightly d| 00005720 69 66 66 65 72 65 6e 74 20 73 70 65 65 64 20 66 |ifferent speed f| 00005730 72 6f 6d 0d 74 68 65 20 6c 61 79 65 72 73 20 6e |rom.the layers n| 00005740 65 78 74 20 74 6f 20 69 74 2e 1a 20 4e 6f 77 1a |ext to it.. Now.| 00005750 20 69 6d 61 67 69 6e 65 1a 20 74 77 6f 1a 20 61 | imagine. two. a| 00005760 64 6a 61 63 65 6e 74 1a 20 6c 61 79 65 72 73 1a |djacent. layers.| 00005770 20 6f 66 20 61 69 72 20 61 73 20 74 77 6f 0d 74 | of air as two.t| 00005780 72 61 69 6e 73 1a 20 6d 6f 76 69 6e 67 20 6f 6e |rains. moving on| 00005790 20 70 61 72 61 6c 6c 65 6c 20 72 61 69 6c 73 20 | parallel rails | 000057a0 61 74 20 73 6c 69 67 68 74 6c 79 20 64 69 66 66 |at slightly diff| 000057b0 65 72 65 6e 74 20 73 70 65 65 64 73 2e 20 54 68 |erent speeds. Th| 000057c0 65 20 65 6e 67 69 6e 65 73 0d 61 72 65 20 62 6f |e engines.are bo| 000057d0 74 68 1a 20 73 77 69 74 63 68 65 64 1a 20 6f 66 |th. switched. of| 000057e0 66 2c 1a 20 61 6e 64 1a 20 74 68 65 1a 20 74 72 |f,. and. the. tr| 000057f0 61 69 6e 73 20 63 6f 61 73 74 20 61 6c 6f 6e 67 |ains coast along| 00005800 20 6f 6e 20 70 65 72 66 65 63 74 6c 79 20 73 6d | on perfectly sm| 00005810 6f 6f 74 68 0d 72 61 69 6c 73 20 77 69 74 68 6f |ooth.rails witho| 00005820 75 74 20 6c 6f 73 69 6e 67 20 61 6e 79 20 73 70 |ut losing any sp| 00005830 65 65 64 2e 20 4e 6f 77 20 74 68 65 1a 20 74 72 |eed. Now the. tr| 00005840 61 69 6e 73 1a 20 61 72 65 1a 20 62 6f 74 68 20 |ains. are. both | 00005850 66 75 6c 6c 20 6f 66 20 70 65 6f 70 6c 65 2c 0d |full of people,.| 00005860 72 65 70 72 65 73 65 6e 74 69 6e 67 20 61 69 72 |representing air| 00005870 20 6d 6f 6c 65 63 75 6c 65 73 20 77 69 74 68 69 | molecules withi| 00005880 6e 20 74 68 65 20 6c 61 79 65 72 73 2e 20 54 68 |n the layers. Th| 00005890 65 20 70 65 6f 70 6c 65 20 61 72 65 20 6d 6f 76 |e people are mov| 000058a0 69 6e 67 20 61 72 6f 75 6e 64 0d 62 6c 69 6e 64 |ing around.blind| 000058b0 6c 79 20 69 6e 73 69 64 65 20 74 68 65 20 74 72 |ly inside the tr| 000058c0 61 69 6e 73 20 69 6e 1a 20 63 6f 6d 70 6c 65 74 |ains in. complet| 000058d0 65 6c 79 1a 20 72 61 6e 64 6f 6d 20 64 69 72 65 |ely. random dire| 000058e0 63 74 69 6f 6e 73 2c 20 61 6e 64 20 73 6f 6d 65 |ctions, and some| 000058f0 74 69 6d 65 73 0d 6f 6e 65 20 6f 66 20 74 68 65 |times.one of the| 00005900 6d 20 77 69 6c 6c 20 73 74 65 70 20 66 72 6f 6d |m will step from| 00005910 20 6f 6e 65 1a 20 74 72 61 69 6e 1a 20 6f 6e 1a | one. train. on.| 00005920 20 74 6f 20 74 68 65 20 6f 74 68 65 72 2e 20 49 | to the other. I| 00005930 66 20 61 20 70 65 72 73 6f 6e 20 73 74 65 70 73 |f a person steps| 00005940 0d 66 72 6f 6d 20 74 68 65 20 73 6c 6f 77 20 74 |.from the slow t| 00005950 72 61 69 6e 20 74 6f 20 74 68 65 20 66 61 73 74 |rain to the fast| 00005960 20 6f 6e 65 2c 20 74 68 65 20 66 61 73 74 1a 20 | one, the fast. | 00005970 74 72 61 69 6e 1a 20 77 69 6c 6c 20 68 61 76 65 |train. will have| 00005980 20 74 6f 20 65 78 65 72 74 20 61 0d 66 6f 72 63 | to exert a.forc| 00005990 65 1a 20 6f 6e 1a 20 68 69 6d 1a 20 74 6f 1a 20 |e. on. him. to. | 000059a0 62 72 69 6e 67 20 68 69 6d 20 75 70 20 74 6f 20 |bring him up to | 000059b0 74 68 65 20 72 69 67 68 74 20 73 70 65 65 64 2e |the right speed.| 000059c0 20 42 75 74 1a 20 74 68 65 1a 20 74 72 61 69 6e | But. the. train| 000059d0 1a 20 77 69 6c 6c 0d 65 78 70 65 72 69 65 6e 63 |. will.experienc| 000059e0 65 1a 20 61 1a 20 66 6f 72 63 65 1a 20 69 6e 1a |e. a. force. in.| 000059f0 20 74 68 65 1a 20 6f 70 70 6f 73 69 74 65 1a 20 | the. opposite. | 00005a00 64 69 72 65 63 74 69 6f 6e 2c 1a 20 73 6c 6f 77 |direction,. slow| 00005a10 69 6e 67 1a 20 69 74 73 65 6c 66 1a 20 64 6f 77 |ing. itself. dow| 00005a20 6e 0d 73 6c 69 67 68 74 6c 79 2e 20 53 69 6d 69 |n.slightly. Simi| 00005a30 6c 61 72 6c 79 2c 20 69 66 20 61 20 70 65 72 73 |larly, if a pers| 00005a40 6f 6e 1a 20 73 74 65 70 73 1a 20 66 72 6f 6d 1a |on. steps. from.| 00005a50 20 74 68 65 1a 20 66 61 73 74 20 74 72 61 69 6e | the. fast train| 00005a60 20 74 6f 20 74 68 65 20 73 6c 6f 77 0d 6f 6e 65 | to the slow.one| 00005a70 2c 20 74 68 65 20 73 6c 6f 77 20 74 72 61 69 6e |, the slow train| 00005a80 20 77 69 6c 6c 20 73 70 65 65 64 20 75 70 20 73 | will speed up s| 00005a90 6c 69 67 68 74 6c 79 2e 20 41 73 1a 20 70 65 6f |lightly. As. peo| 00005aa0 70 6c 65 1a 20 63 6f 6e 74 69 6e 75 65 1a 20 74 |ple. continue. t| 00005ab0 6f 1a 20 73 74 65 70 0d 66 72 6f 6d 1a 20 6f 6e |o. step.from. on| 00005ac0 65 1a 20 74 72 61 69 6e 20 74 6f 20 74 68 65 20 |e. train to the | 00005ad0 6f 74 68 65 72 2c 20 74 68 65 20 73 6c 6f 77 20 |other, the slow | 00005ae0 74 72 61 69 6e 20 73 70 65 65 64 73 20 75 70 20 |train speeds up | 00005af0 61 6e 64 20 74 68 65 20 66 61 73 74 20 74 72 61 |and the fast tra| 00005b00 69 6e 0d 73 6c 6f 77 73 20 64 6f 77 6e 2c 20 75 |in.slows down, u| 00005b10 6e 74 69 6c 1a 20 74 68 65 79 1a 20 61 72 65 1a |ntil. they. are.| 00005b20 20 62 6f 74 68 1a 20 74 72 61 76 65 6c 6c 69 6e | both. travellin| 00005b30 67 1a 20 61 74 20 74 68 65 20 73 61 6d 65 20 73 |g. at the same s| 00005b40 70 65 65 64 2e 20 53 6f 20 65 61 63 68 0d 6c 61 |peed. So each.la| 00005b50 79 65 72 20 6f 66 20 61 69 72 20 69 6e 20 74 68 |yer of air in th| 00005b60 65 20 63 79 6c 69 6e 64 65 72 20 65 78 70 65 72 |e cylinder exper| 00005b70 69 6d 65 6e 74 20 69 73 1a 20 65 78 65 72 74 69 |iment is. exerti| 00005b80 6e 67 1a 20 61 1a 20 66 6f 72 63 65 20 6f 6e 20 |ng. a. force on | 00005b90 74 68 65 20 6e 65 78 74 0d 6c 61 79 65 72 2c 20 |the next.layer, | 00005ba0 74 72 79 69 6e 67 20 74 6f 20 65 71 75 61 6c 69 |trying to equali| 00005bb0 73 65 20 74 68 65 69 72 20 73 70 65 65 64 73 2e |se their speeds.| 00005bc0 20 54 68 69 73 20 66 6f 72 63 65 20 69 73 20 63 | This force is c| 00005bd0 6f 6e 64 75 63 74 65 64 20 74 68 72 6f 75 67 68 |onducted through| 00005be0 20 74 6f 0d 74 68 65 20 6f 75 74 65 72 20 63 79 | to.the outer cy| 00005bf0 6c 69 6e 64 65 72 2c 20 77 68 69 63 68 20 74 72 |linder, which tr| 00005c00 69 65 73 20 74 6f 20 65 71 75 61 6c 69 73 65 20 |ies to equalise | 00005c10 69 74 73 20 73 70 65 65 64 20 77 69 74 68 20 74 |its speed with t| 00005c20 68 65 1a 20 69 6e 6e 65 72 20 6f 6e 65 2e 0d 54 |he. inner one..T| 00005c30 6f 20 73 74 6f 70 20 69 74 20 6d 6f 76 69 6e 67 |o stop it moving| 00005c40 2c 20 77 65 20 68 61 76 65 20 74 6f 20 70 75 73 |, we have to pus| 00005c50 68 20 69 74 20 74 68 65 20 6f 74 68 65 72 20 77 |h it the other w| 00005c60 61 79 2c 20 73 6f 20 77 65 20 61 72 65 20 65 66 |ay, so we are ef| 00005c70 66 65 63 74 69 76 65 6c 79 0d 61 63 74 69 6e 67 |fectively.acting| 00005c80 1a 20 61 73 1a 20 74 68 65 20 22 65 6e 67 69 6e |. as. the "engin| 00005c90 65 73 22 20 6f 66 20 74 68 65 20 74 72 61 69 6e |es" of the train| 00005ca0 73 2c 20 77 68 69 63 68 20 6b 65 65 70 20 74 68 |s, which keep th| 00005cb0 65 20 66 61 73 74 20 74 72 61 69 6e 73 20 6d 6f |e fast trains mo| 00005cc0 76 69 6e 67 0d 66 61 73 74 65 72 20 74 68 61 6e |ving.faster than| 00005cd0 20 74 68 65 20 73 6c 6f 77 20 74 72 61 69 6e 73 | the slow trains| 00005ce0 2e 0d 09 57 65 20 68 61 76 65 20 73 65 65 6e 20 |...We have seen | 00005cf0 74 68 61 74 20 6d 6f 73 74 1a 20 6f 66 1a 20 74 |that most. of. t| 00005d00 68 65 1a 20 69 6d 70 6f 72 74 61 6e 74 1a 20 70 |he. important. p| 00005d10 68 65 6e 6f 6d 65 6e 61 1a 20 6f 63 63 75 72 72 |henomena. occurr| 00005d20 69 6e 67 20 69 6e 0d 67 61 73 65 73 20 63 61 6e |ing in.gases can| 00005d30 20 62 65 20 65 78 70 6c 61 69 6e 65 64 20 75 73 | be explained us| 00005d40 69 6e 67 20 73 69 6d 70 6c 65 20 61 6e 61 6c 6f |ing simple analo| 00005d50 67 69 65 73 2c 20 77 68 69 63 68 20 63 61 6e 20 |gies, which can | 00005d60 68 65 6c 70 1a 20 62 79 20 72 65 64 75 63 69 6e |help. by reducin| 00005d70 67 0d 74 68 65 1a 20 6e 75 6d 62 65 72 1a 20 6f |g.the. number. o| 00005d80 66 20 64 69 6d 65 6e 73 69 6f 6e 73 20 69 6e 76 |f dimensions inv| 00005d90 6f 6c 76 65 64 2c 20 61 6e 64 20 62 79 20 63 68 |olved, and by ch| 00005da0 61 6e 67 69 6e 67 20 74 68 65 20 73 63 61 6c 65 |anging the scale| 00005db0 73 20 61 6e 64 20 6f 72 64 65 72 73 0d 6f 66 20 |s and orders.of | 00005dc0 6d 61 67 6e 69 74 75 64 65 2e 20 49 74 1a 20 69 |magnitude. It. i| 00005dd0 73 1a 20 69 6d 70 6f 72 74 61 6e 74 20 74 6f 20 |s. important to | 00005de0 72 65 61 6c 69 73 65 20 74 68 6f 75 67 68 2c 20 |realise though, | 00005df0 74 68 61 74 20 74 68 65 73 65 20 61 6e 61 6c 6f |that these analo| 00005e00 67 69 65 73 20 64 6f 0d 6e 6f 74 20 70 72 6f 76 |gies do.not prov| 00005e10 69 64 65 20 72 69 67 6f 72 6f 75 73 20 70 72 6f |ide rigorous pro| 00005e20 6f 66 73 20 6f 66 1a 20 74 68 65 1a 20 72 65 61 |ofs of. the. rea| 00005e30 73 6f 6e 73 1a 20 62 65 68 69 6e 64 20 61 6e 20 |sons. behind an | 00005e40 65 66 66 65 63 74 20 2d 20 74 68 65 79 20 6a 75 |effect - they ju| 00005e50 73 74 0d 68 65 6c 70 20 75 73 20 74 6f 20 76 69 |st.help us to vi| 00005e60 73 75 61 6c 69 73 65 20 74 68 65 20 70 6f 73 73 |sualise the poss| 00005e70 69 62 6c 65 20 65 78 70 6c 61 6e 61 74 69 6f 6e |ible explanation| 00005e80 73 2e 20 49 74 1a 20 69 73 20 70 6f 73 73 69 62 |s. It. is possib| 00005e90 6c 65 20 74 6f 20 69 6d 61 67 69 6e 65 0d 74 68 |le to imagine.th| 00005ea0 65 20 62 65 68 61 76 69 6f 75 72 20 6f 66 20 73 |e behaviour of s| 00005eb0 6f 6c 69 64 73 20 61 6e 64 20 6c 69 71 75 69 64 |olids and liquid| 00005ec0 73 20 62 79 20 73 69 6d 69 6c 61 72 20 6d 65 74 |s by similar met| 00005ed0 68 6f 64 73 2c 20 62 75 74 20 69 6e 20 74 68 65 |hods, but in the| 00005ee0 73 65 20 63 61 73 65 73 0d 69 74 20 69 73 20 6d |se cases.it is m| 00005ef0 75 63 68 20 6d 6f 72 65 20 64 69 66 66 69 63 75 |uch more difficu| 00005f00 6c 74 20 74 6f 20 66 69 6e 64 20 61 20 73 75 69 |lt to find a sui| 00005f10 74 61 62 6c 65 1a 20 61 6e 61 6c 6f 67 79 2e 1a |table. analogy..| 00005f20 20 46 6f 72 1a 20 65 78 61 6d 70 6c 65 1a 20 69 | For. example. i| 00005f30 6e 20 61 0d 6c 69 71 75 69 64 2c 1a 1a 20 77 65 |n a.liquid,.. we| 00005f40 1a 1a 20 6d 75 73 74 1a 20 63 6f 6e 73 69 64 65 |.. must. conside| 00005f50 72 1a 20 67 72 61 76 69 74 79 2c 1a 20 69 6e 74 |r. gravity,. int| 00005f60 65 72 6d 6f 6c 65 63 75 6c 61 72 1a 20 66 6f 72 |ermolecular. for| 00005f70 63 65 73 2c 1a 20 61 6e 64 1a 20 74 68 65 0d 6c |ces,. and. the.l| 00005f80 69 71 75 69 64 2d 76 61 70 6f 75 72 20 69 6e 74 |iquid-vapour int| 00005f90 65 72 66 61 63 65 20 61 74 20 74 68 65 20 73 75 |erface at the su| 00005fa0 72 66 61 63 65 2c 20 74 6f 20 65 78 70 6c 61 69 |rface, to explai| 00005fb0 6e 20 69 74 73 20 62 65 68 61 76 69 6f 75 72 20 |n its behaviour | 00005fc0 66 75 6c 6c 79 2e 20 49 74 0d 69 73 1a 20 74 68 |fully. It.is. th| 00005fd0 65 1a 20 76 65 72 79 1a 20 73 69 6d 70 6c 65 20 |e. very. simple | 00005fe0 61 70 70 72 6f 78 69 6d 61 74 69 6f 6e 73 20 6f |approximations o| 00005ff0 66 20 74 68 65 20 69 64 65 61 6c 20 28 70 65 72 |f the ideal (per| 00006000 66 65 63 74 29 20 67 61 73 20 6d 6f 64 65 6c 20 |fect) gas model | 00006010 74 68 61 74 0d 61 6c 6c 6f 77 20 75 73 20 74 6f |that.allow us to| 00006020 20 72 65 61 63 68 20 63 6f 6e 63 6c 75 73 69 6f | reach conclusio| 00006030 6e 73 20 73 6f 20 65 61 73 69 6c 79 2e 20 0d |ns so easily. .| 0000603f
KinBackup.m0
KinBackup.m1
KinBackup.m2
KinBackup.m4
KinBackup.m5
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