_TRANSMUTATIONS OF ENERGY._
_Energy of Visible Motion._
121. Let us begin our list of transmutations with the energy of
visible motion. This is changed into _energy of position_ when a stone
is projected upwards above the earth, or, to take a case precisely
similar, when a planet or a comet goes from perihelion, or its position
nearest the sun, to aphelion, or its position furthest from the sun.
We thus see why a heavenly body should move fastest at perihelion, and
slowest at aphelion. If, however, a planet were to move round the sun
in an orbit exactly circular, its velocity would be the same at all the
various points of this orbit, because there would be no change in its
distance from the centre of attraction, and therefore no transmutation
of energy.
122. We have already (Arts. 108, 109) said that the energy in an
oscillating or vibrating body is alternately that of actual motion, and
that of position. In this respect, therefore, a pendulum is similar to
a comet or heavenly body with an elliptical orbit. Nevertheless the
change of energy is generally more complete in a pendulum or vibrating
body than it is in a heavenly body; for in a pendulum, when at its
lowest point, the energy is entirely that of actual motion, while at
its upper point it is entirely that of position. Now, in a heavenly
body we have only a lessening, but not an entire destruction, of the
velocity, as the body passes from perihelion to aphelion--that is to
say, we have only a partial conversion of the one kind of energy into
the other.
123. Let us next consider the change of actual visible energy into
_absorbed heat_. This takes place in all cases of friction, percussion,
and resistance. In friction, for instance, we have the conversion of
work or energy into heat, which is here produced through the rubbing
of surfaces against each other; and Davy has shown that two pieces of
ice, both colder than the freezing point, may be melted by friction.
In percussion, again, we have the energy of the blow converted into
heat; while, in the case of a meteor or cannon ball passing through the
air with great velocity, we have the loss of energy of the meteor or
cannon ball through its contact with the air, and at the same time the
production of heat on account of this resistance.
The resistance need not be atmospheric, for we may set the cannon ball
to pierce through wooden planks or through sand, and there will equally
be a production of heat on account of the resistance offered by the
wooden planks or by the sand to the motion of the ball. We may even
generalize still further, and assert that whenever the visible momentum
of a body is transferred to a larger mass, there is at the same time
the conversion of visible energy into heat.
124. A little explanation will be required to make this point clear.
The third law of motion tells us that action and reaction are equal and
opposite, so that when two bodies come into collision the forces at
work generate equal and opposite quantities of momentum. We shall best
see the meaning of this law by a numerical example, bearing in mind
that momentum means the product of mass into velocity.
For instance, let us suppose that an inelastic body of mass 10 and
velocity 20 strikes directly another inelastic body of mass 15 and
velocity 15, the direction of both motions being the same.
Now, it is well known that the united mass will, after impact, be
moving with the velocity 17. What, then, has been the influence of the
forces developed by collision? The body of greater velocity had before
impact a momentum 10 × 20 = 200, while its momentum after impact is
only 10 × 17 = 170; it has therefore suffered a loss of 30 units as
regards momentum, or we may consider that a momentum of 30 units has
been impressed upon it in an opposite direction to its previous motion.
On the other hand, the body of smaller velocity had before impact a
momentum 15 × 15 = 225, while after impact it has 15 × 17 = 255 units,
so that its momentum has been increased by 30 units in its previous
direction.
The force of impact has therefore generated 30 units of momentum in two
opposite directions, so that, taking account of direction, the momentum
of the system is the same before and after impact; for before impact we
had a momentum of 10 × 20 + 15 × 15 = 425, while after it we have the
united mass 25 moving with the velocity 17, giving the momentum 425 as
before.
125. But while the momentum is the same before and after impact, the
visible energy of the moving mass is undoubtedly less after impact
than before it. To see this we have only to turn to the expression
of Art. 28, from which we find that the energy before impact was as
follows:--Energy in kilogrammetres = (_m v_²)/(19 · 6) = (10 × 20² + 15
× 15²)/19·6 = 376 nearly; while that after impact = (25 × 17²)/19·6 =
368 nearly.
126. The loss of energy will be still more manifest if we suppose an
inelastic body in motion to strike against a similar body at rest. Thus
if we have a body of mass 20 and velocity 20 striking against one of
equal mass, but at rest, the velocity of the double mass after impact
will obviously be only 10; but, as regards energy, that before impact
will be (20 × 20²)/19·6 = ⁸⁰⁰⁰⁄₁₉·6 while that after impact will be
(40 × 10²)/19·6 = ⁴⁰⁰⁰⁄₁₉·6 or only half the former.
127. Thus there is in all such cases an apparent loss of visible
energy, while at the same time there is the production of heat on
account of the blow which takes place. If, however, the substances that
come together be perfectly elastic (which no substance is), the visible
energy after impact will be the same as that before, and in this case
there will be no conversion into heat. This, however, is an extreme
supposition, and inasmuch as no substance is perfectly elastic, we
have in all cases of collision a greater or less conversion of visible
motion into heat.
128. We have spoken (Art. 122) about the change of energy in an
oscillating or vibrating body, as if it were entirely one of actual
energy into energy of position, and the reverse.
But even here, in each oscillation or vibration, there is a greater
or less conversion of visible energy into heat. Let us, for instance,
take a pendulum, and, in order to make the circumstances as favourable
as possible, let it swing on a knife edge, and in vacuo; in this case
there will be a slight but constant friction of the knife edge against
the plane on which it rests, and though the pendulum may continue to
swing for hours, yet it will ultimately come to rest.
And, again, it is impossible to make a vacuum so perfect that there is
absolutely no air surrounding the pendulum, so that part of the motion
of the pendulum will always be carried off by the residual air of the
vacuum in which it swings.
129. Now, something similar happens in that vibratory motion which
constitutes sound. Thus, when a bell is in vibration, part of the
energy of the vibration is carried off by the surrounding air, and it
is in virtue of this that we hear the sound of the bell; but, even if
there were no air, the bell would not go on vibrating for ever. For
there is in all bodies a greater or less amount of internal viscosity,
a property which prevents perfect freedom of vibration, and which
ultimately converts vibrations into heat.
A vibrating bell is thus very much in the same position as an
oscillating pendulum, for in both part of the energy is given off to
the air, and in both there is unavoidable friction--in the one taking
the shape of internal viscosity, and in the other that of friction of
the knife edge against the plane on which it rests.
130. In both these cases, too, that portion of the energy which goes
into the air takes ultimately the shape of heat. The oscillating
pendulum communicates a motion to the air, and this motion ultimately
heats the air. The vibrating bell, or musical instrument, in like
manner communicates part of its energy to the air. This communicated
energy first of all moves through the air with the well-known velocity
of sound, but during its progress it, too, no doubt becomes partly
converted into heat. Ultimately, it is transmitted by the air to other
bodies, and by means of their internal viscosity is sooner or later
converted into heat. Thus we see that heat is the form of energy, into
which all visible terrestrial motion, whether it be rectilinear, or
oscillatory, or vibratory, is ultimately changed.
131. In the case of a body in visible rectilinear motion on the earth’s
surface, this change takes place very soon--if the motion be rotatory,
such as that of a heavy revolving top, it may, perhaps, continue longer
before it is ultimately stopped, by means of the surrounding air, and
by friction of the pivot; if it be oscillatory, as in the pendulum, or
vibratory, as in a musical instrument, we have seen that the air and
internal friction are at work, in one shape or another, to carry it
off, and will ultimately succeed in converting it into heat.
132. But, it may be said, why consider a body moving on the earth’s
surface? why not consider the motion of the earth itself? Will this
also ultimately take the shape of heat?
No doubt it is more difficult to trace the conversion in such a case,
inasmuch as it is not proceeding at a sensible rate before our eyes. In
other words, the very conditions that make the earth habitable, and a
fit abode for intelligent beings like ourselves, are those which unfit
us to perceive this conversion of energy in the case of the earth. Yet
we are not without indications that it is actually taking place. For
the purpose of exhibiting these, we may divide the earth’s motion into
two--a motion of rotation, and one of revolution.
133. Now, with regard to the earth’s rotation, the conversion of the
visible energy of this motion into heat is already well recognized. To
understand this we have only to study the nature of the moon’s action
upon the fluid portions of our globe. In the following diagram (Fig.
11) we have an exaggerated representation of this, by which we see that
the spherical earth is converted into an elongated oval, of which one
extremity always points to the moon. The solid body of the earth itself
revolves as usual, but, nevertheless, this fluid protuberance remains
always pointing towards the moon, as we see in the figure, and hence
the earth rubs against the protuberance as it revolves. The friction
produced by this action tends evidently to lessen the rotatory energy
of the earth--in other words, it acts like a break--and we have, just
as by a break-wheel, the conversion of visible energy into heat. This
was first recognized by Mayer and J. Thomson.
[Illustration: Fig. 11.]
134. But while there can be no doubt about the fact of such a
conversion going on, the only question is regarding its rate of
progress, and the time required before it can cause a perceptible
impression upon the rotative energy of the earth.
Now, it is believed by astronomers that they have detected evidence of
such a change, for our knowledge of the motions of the sun and moon has
become so exact, that not only can we carry forward our calculations so
as to predict an eclipse, but also carry them backwards, and thus fix
the dates and even the very details of the ancient historical eclipses.
If, however, between those times and the present, the earth has lost a
little rotative energy on account of this peculiar action of the moon,
then it is evident that the calculated circumstances of the ancient
total eclipse will not quite agree with those actually recorded; and by
a comparison of this nature it is believed that we have detected a very
slight falling off in the rotative energy of our earth. If we carry out
the argument, we shall be driven to the conclusion that the rotative
energy of our globe will, on account of the moon’s action, always get
less and less, until things are brought into such a state that the
rotation comes to be performed in the same time as the revolution of
the moon, so that then the same portion of the terrestrial surface
being always presented to the moon, it is evident that there will be no
effort made by the solid substance of the earth, to glide from under
the fluid protuberance, and there will in consequence be no friction,
and no further loss of energy.
135. If the fate of the earth be ultimately to turn the same face
always to the moon, we have abundant evidence that this very fate has
long since overtaken the moon herself. Indeed, the much stronger effect
of our earth upon the moon has produced this result, probably, even in
those remote periods when the moon was chiefly fluid; and it is a fact
well known, not merely to astronomers, but to all of us, that the moon
nowadays turns always the same face to the earth.[4] No doubt this fate
has long since overtaken the satellites of Jupiter, Saturn, and the
other large planets; and there are independent indications that, at
least in the case of Jupiter, the satellites turn always the same face
to their primary.
136. To come now to the energy of revolution of the earth, in her
orbit round the sun, we cannot help believing that there is a material
medium of some kind between the sun and the earth; indeed, the
undulatory theory of light requires this belief. But if we believe in
such a medium, it is difficult to imagine that its presence will not
ultimately diminish the motion of revolution of the earth in her orbit;
indeed, there is a strong scientific probability, if not an absolute
certainty, that such will be the case. There is even some reason to
think that the energy of a comet of small period, called Encke’s
comet, is gradually being stopped from this cause; in fine, there can
be hardly any doubt that the cause is really in operation, and will
ultimately affect the motions of the planets and other heavenly bodies,
even although its rate of action may be so slow that we are not able to
detect it.
We may perhaps generalize by saying, that wherever in the universe
there is a differential motion, that is to say, a motion of one part
of it towards or from another, then, in virtue of the subtle medium,
or cement, that binds the various parts of the universe together, this
motion is not unattended by something like friction, in virtue of which
the differential motion will ultimately disappear, while the loss of
energy caused by its disappearance will assume the form of heat.
137. There are, indeed, obscure intimations that a conversion of this
kind is not improbably taking place in the solar system; for, in the
sun himself, we have the matter near the equator, by virtue of the
rotation of our luminary, carried alternately towards and from the
various planets. Now, it would seem that the sun-spots, or atmospheric
disturbances of the sun, affect particularly his equatorial regions,
and have likewise a tendency to attain their maximum size in that
position, which is as far away as possible from the influential
planets, such as Mercury or Venus;[5] so that if Venus, for instance,
were between the earth and the sun, there would be few sun-spots in the
middle of the sun’s disc, because that would be the part of the sun
nearest Venus.
But if the planets influence sun-spots, the action is no doubt
reciprocal, and we have much reason to believe that sun-spots
influence, not only the magnetism, but also the meteorology of our
earth, so that there are most displays of the Aurora Borealis, as well
as most cyclones, in those years when there are most sun-spots.[6] Is
it not then possible that, in these strange, mysterious phenomena, we
see traces of the machinery by means of which the differential motion
of the solar system is gradually being changed into heat?
138. We have thus seen that visible energy of actual motion is not
unfrequently changed into visible energy of position, and that it is
also very often transformed into absorbed heat. We have now to state
that it may likewise be transformed into _electrical separation_.
Thus, when an ordinary electrical machine is in action, considerable
labour is spent in turning the handle; it is, in truth, harder to turn
than if no electricity were being produced--in other words, part of
the energy which is spent upon the machine goes to the production of
electrical separation. There are other ways of generating electricity
besides the frictional method. If, for instance, we bring an insulated
conducting plate near the prime conductor of the electrical machine,
yet not near enough to cause a spark to pass, and if we then touch the
insulated plate, we shall find it, after contact, to be charged with an
electricity the opposite of that in the machine; we may then remove it
and make use of this electricity.
It requires a little thought to see what labour we have spent in this
process. We must bear in mind that, by touching the plate, we have
carried off the electricity of the same name as that of the machine,
so that, after touching the insulated plate it is more strongly
attracted to the conductor than it was before. When we begin to remove
it, therefore, it will cost us an effort to do so, and the mechanical
energy which we spend in removing it will account for the energy of
electrical separation which we then obtain.
139. We may thus make use of a small nucleus of electricity, to assist
us in procuring an unlimited supply, for in the above process the
electricity of the prime conductor remains unaltered, and we may repeat
the operation as often as we like, and gather together a very large
quantity of electricity, without finally altering the electricity of
the prime conductor, but not, however, without the expenditure of an
equivalent amount of energy, in the shape of actual work.
140. While, as we have seen, there is a tendency in all motion to be
changed into heat, there is one instance where it is, in the first
place at least, changed into _a current of electricity_. We allude
to the case where a conducting substance moves in the presence of an
electric current, or of a magnet.
In Art. 104 we found that if one coil connected with a battery were
quickly moved into the presence of another coil connected with a
galvanometer, an induced current would be generated in the latter coil,
and would affect the galvanometer, its direction being the reverse of
that passing in the other. Now, an electric current implies energy, and
we may therefore conclude that some other form of energy must be spent,
or disappear, in order to produce the current which is generated in the
coil attached to the galvanometer.
Again, we learn from Art. 100 that two currents going in opposite
directions repel one another. The current generated in the coil
attached to the galvanometer or secondary current will, therefore,
repel the primary current, which is moving towards it; this repulsion
will either cause a stoppage of motion, or render necessary the
expenditure of energy, in order to keep up the motion of this moving
coil. We thus find that two phenomena occur simultaneously. In the
first place, there is the production of energy in the secondary coil,
in the shape of a current opposite in direction to that of the primary
coil; in the next case, owing to the repulsion between this induced
current and the primary current, there is a stoppage or disappearance
of the energy of actual motion of the moving coil. We have, in fact,
the creation of one species of energy, and at the same time the
disappearance of another, and thus we see that the law of conservation
is by no means broken.
141. We see also the necessary connection between the two electrical
laws described in Arts. 100 and 104. Indeed, had these laws been other
than what they are, the principle of conservation of energy would have
been broken.
For instance, had the induced current in the case now mentioned been
in the same direction as that of the primary, the two currents would
have attracted each other, and thus there would have been the creation
of a secondary current, implying energy, in the coil attached to the
galvanometer, along with an increase of the visible energy of motion
of the primary current--that is to say, instead of the creation of
one kind of energy, accompanied with the disappearance of another, we
should have had the simultaneous creation of both; and thus the law of
conservation of energy would have been broken.
We thus see that the principle of conservation enables us to deduce
the one electrical law from the other, and this is one of the many
instances which strengthen our belief in the truth of the great
principle for which we are contending.
142. Let us next consider what will take place if we cause the primary
current to move from the secondary coil instead of towards it.
In this case we know, from Art. 104, that the induced current will be
in the same direction as the primary, while we are told by Art. 100
that the two currents will now attract each other. The tendency of this
attraction will be to stop the motion of the primary current from
the secondary one, or, in other words, there will be a disappearance
of the energy of visible motion, while at the same time there is the
production of a current. In both cases, therefore, one form of energy
disappears while another takes its place, and in both there will be a
very perceptible resistance experienced in moving the primary coil,
whether towards the secondary or from it. Work will, in fact, have to
be spent in both operations, and the outcome of this work or energy
will be the production of a current in the first place, and of heat in
the second; for we learn from Art. 98 that when a current passes along
a wire its energy is generally spent in heating the wire.
We have thus two phenomena occurring together. In the first place, in
moving a current of electricity to and from a coil of wire, or any
other conductor, or (which is the same thing, since action and reaction
are equal and opposite) in moving a coil of wire or any other conductor
to and from a current of electricity, a sense of resistance will be
experienced, and energy will have to be spent upon the process; in the
second place, an electrical current will be generated in the conductor,
and the conductor will be heated in consequence.
143. The result will be rendered very prominent if we cause a metallic
top, in rapid rotation, to spin near two iron poles, which, by means
of the battery, we can suddenly convert into the poles of a powerful
electro-magnet. When this change is made, and the poles become
magnetic, the motion of the top is very speedily brought to rest,
just as if it had to encounter a species of invisible friction. This
curious result can easily be explained. We have seen from Art. 101
that a magnet resembles an assemblage of electric currents, and in the
metallic top we have a conductor alternately approaching these currents
and receding from them; and hence, according to what has been said, we
shall have a series of secondary currents produced in the conducting
top which will stop its motion, and which will ultimately take the
shape of heat. In other words, the visible energy of the top will be
changed into heat just as truly as if it were stopped by ordinary
friction.
144. The electricity induced in a metallic conductor, moved in
the presence of a powerful magnet, has received the name of
Magneto-Electricity; and Dr. Joule has made use of it as a convenient
means of enabling him to determine the mechanical equivalent of heat,
for it is into heat that the energy of motion of the conductor is
ultimately transformed. But, besides all this, these currents form,
perhaps, the very best means of obtaining electricity; and recently
very powerful machines have been constructed by Wild and others with
this view.
145. These machines, when large, are worked by a steam-engine, and
their mode of operation is as follows:--The nucleus of the machine
is a system of powerful permanent steel magnets, and a conducting
coil is made to revolve rapidly in presence of these magnets. The
current produced by this moving coil is then used in order to produce
an extremely powerful electro-magnet, and finally a coil is made to
move with great rapidity in presence of this powerful electro-magnet,
thus causing induced currents of vast strength. So powerful are these
currents, that when used to produce the electric light, small print may
be read on a dark night at the distance of two miles from the scene of
operation!
It thus appears that in this machine a double use is made of
magneto-electricity. Starting with a nucleus of permanent magnetism,
the magneto-electric currents are used, in the first instance, to
form a powerful electro-magnet much stronger than the first, and this
powerful electro-magnet is again made use of in the same way as the
first, in order to give, by means of magneto-electricity, an induced
current of very great strength.
146. There is, moreover, a very great likeness between a
magneto-electric machine like that of Wild’s for generating electric
currents, and the one which generates statical electricity by means of
the method already described Art. 139. In both cases advantage is taken
of a nucleus, for in the magneto-electric machine we have the molecular
currents of a set of permanent magnets, which are made the means of
generating enormous electric currents without any permanent alteration
to themselves, yet not without the expenditure of work.
Again, in an induction machine for generating statical electricity,
we have an electric nucleus, such as we have supposed to reside in the
prime conductor of a machine; and advantage may be taken, as we have
seen, of this nucleus in order to generate a vast quantity of statical
electricity, without any permanent alteration of the nucleus, but not
without the expenditure of work.
147. We have now seen under what conditions the visible energy of
actual motion may be changed--1stly, into energy of position; 2ndly,
into the two energies which embrace absorbed heat; 3rdly, into
electrical separation; and finally into electricity in motion. As far
as we know, visible energy cannot directly be transformed into chemical
separation, or into radiant energy.
_Visible Energy of Position._
148. Having thus exhausted the transmutations of the energy of
visible motion, we next turn to that of position, and find that it
is transmuted into motion, but not immediately into any other form
of energy; we may, therefore, dismiss this variety at once from our
consideration.
_Absorbed Heat._
140. Coming now to these two forms of energy which embrace _absorbed
heat_, we find that this may be converted into (A) or _actual visible
energy_ in the case of the steam-engine, the air-engine, and all
varieties of heat engines. In the steam-engine, for instance, part
of the heat which passes through it disappears as heat, utterly and
absolutely, to reappear as mechanical effect. There is, however, one
condition which must be rigidly fulfilled, whenever heat is changed
into mechanical effect--there must be a difference of temperature, and
_heat will only be changed into work, while it passes from a body of
high temperature to one of low_.
Carnot, the celebrated French physicist, has ingeniously likened the
mechanical power of heat to that of water; for just as you can get
no work out of heat unless there be a flow of heat from a higher
temperature level to a lower, so neither can you get work out of water
unless it be falling from a higher level to a lower.
150. If we reflect that heat is essentially distributive in its nature,
we shall soon perceive the reason for this peculiar law; for, in virtue
of its nature, heat is always rushing from a body of high temperature
to one of low, and if left to itself it would distribute itself equally
amongst all bodies, so that they would ultimately become of the same
temperature. Now, if we are to coax work out of heat, we must humour
its nature, for it may be compared to a pack of schoolboys, who are
always ready to run with sufficient violence out of the schoolroom into
the open fields, but who have frequently to be dragged back with a very
considerable expenditure of energy. So heat will not allow itself to be
confined, but will resist any attempt to accumulate it into a limited
space. Work cannot, therefore, be gained by such an operation, but
must, on the contrary, be spent upon the process.
151. Let us now for a moment consider the case of an enclosure in which
everything is of the same temperature. Here we have a dull dead level
of heat, out of which it will be impossible to obtain the faintest
semblance of work. The temperature may even be high, and there may be
immense stores of heat energy in the enclosure, but not a trace of this
is available in the shape of work. Taking up Carnot’s comparison, the
water has already fallen to the same level, and lies there without any
power of doing useful work--dead, in a sense, as far as visible energy
is concerned.
152. We thus perceive that, firstly, we can get work out of heat when
it passes from a higher to a lower temperature, but that, secondly,
we must spend work upon it in order to make it pass from a lower
temperature to a higher one; and that, thirdly and finally, nothing
in the shape of work can be got out of heat which is all at the same
temperature level.
What we have now said enables us to realize the conditions under which
all heat engines work. The essential point about such engines is, not
the possession of a cylinder, or piston, or fly wheels, or valves,
but the possession of two chambers, one of high and the other of low
temperature, while it performs work in the process of carrying heat
from the chamber of high to that of low temperature.
Let us take, for example, the low-pressure engine. Here we have the
boiler or chamber of high, and the condenser or chamber of low,
temperature, and the engine works while heat is being carried from
the boiler to the condenser--never while it is being carried from the
condenser to the boiler.
In like manner in the locomotive we have the steam generated at a high
temperature and pressure, and cooled by injection into the atmosphere.
153. But, leaving formal engines, let us take an ordinary fire, which
plays in truth the part of an engine, as far as energy is concerned.
We have here the cold air streaming in over the floor of the room,
and rushing into the fire, to be there united with carbon, while
the rarefied product is carried up the chimney. Dismissing from our
thoughts at present the process of combustion, except as a means of
supplying heat, we see that there is a continual in-draught of cold
air, which is heated by the fire, and then sent to mingle with the
air above. Heat is, in fact, distributed by this means, or carried
from a body of high temperature, _i.e._ the fire, to a body of low
temperature, _i.e._ the outer air, and in this process of distribution
mechanical effect is obtained in the up-rush of air through the chimney
with considerable velocity.
154. Our own earth is another instance of such an engine, having
the equatorial regions as its boiler, and the polar regions as its
condensers; for, at the equator, the air is heated by the direct
rays of the sun, and we have there an ascending current of air, up a
chimney as it were, the place of which is supplied by an in-draught of
colder air along the ground or floor of the world, from the poles on
both sides. Thus the heated air makes its way from the equator to the
poles in the upper regions of the atmosphere, while the cold air makes
its way from the poles to the equator along the lower regions. Very
often, too, aqueous vapour as well as air is carried up by means of
the sun’s heat to the upper and colder atmospheric regions, and there
deposited in the shape of rain, or hail, or snow, which ultimately
finds its way back again to the earth, often displaying in its passage
immense mechanical energy. Indeed, the mariner who hoists his sail,
and the miller who grinds his corn (whether he use the force of the
wind or that of running water), are both dependent upon this great
earth-engine, which is constantly at work producing mechanical effect,
but always in the act of carrying heat from its hotter to its colder
regions.
155. Now, if it be essential to an engine to have two chambers, one
hot and one cold, it is equally important that there should be a
considerable temperature difference between the two.
If Nature insists upon a difference before she will give us work, we
shall not be able to pacify her, or to meet her requirements by making
this difference as small as possible. And hence, _cæteris paribus_, we
shall obtain a greater proportion of work out of a certain amount of
heat passing through our engine when the temperature difference between
its boiler and condenser is as great as possible. In a steam-engine
this difference cannot be very great, because if the water of the
boiler were at a very high temperature the pressure of its steam would
become dangerous; but in an air-engine, or engine that heats and
cools air, the temperature difference may be much larger. There are,
however, practical inconveniences in engines for which the temperature
of the boiler is very high, and it is possible that these may prove
so formidable as to turn the scale against such engines, although in
theory they ought to be very economical.
156. The principles now stated have been employed by Professor J.
Thomson, in his suggestion that the application of pressure would be
found to lower the freezing point of water; and the truth of this
suggestion was afterwards proved by Professor Sir W. Thomson. The
following was the reasoning employed by the former:--
Suppose that we have a chamber kept constantly at the temperature 0°
C., or the melting point of ice, and that we have a cylinder, of which
the sectional area is one square metre, filled one metre in height with
water, that is to say, containing one cubic metre of water. Suppose,
next, that a well-fitting piston is placed above the surface of the
water in this cylinder, and that a considerable weight is placed upon
the piston. Let us now take the cylinder, water and all, and carry it
into another room, of which the temperature is just a trifle lower. In
course of time the water will freeze, and, as it expands in freezing,
it will push up the piston and weight about ⁹⁄₁₀₀ths of a metre; and we
may suppose that the piston is kept fastened in this position by means
of a peg. Now carry back the machine into the first room, and in the
course of time the ice will be melted, and we shall have water once
more in the cylinder, but there will now be a void space of ⁹⁄₁₀₀ths
of a metre between the piston and the surface. We have thus acquired
a certain amount of energy of position, and we have only to pull out
the peg, and allow the piston with its weight to fall down through
the vacant space, in order to utilize this energy, after which the
arrangement is ready to start afresh. Again, if the weight be very
great, the energy thus gained will be very great; in fact, the energy
will vary with the weight. In fine, the arrangement now described is
a veritable heat engine, of which the chamber at 0° C. corresponds to
the boiler, and the other chamber a trifle lower in temperature to
the condenser, while the amount of work we get out of the engine--or,
in other words, its efficiency--will depend upon the weight which is
raised through the space of ⁹⁄₁₀₀ths of a metre, so that, by increasing
this weight without limit, we may increase the efficiency of our engine
without limit. It would thus at first sight appear that by this device
of having two chambers, one at 0° C., and the other a trifle lower,
we can get any amount of work out of our water engine; and that,
consequently, we have managed to overcome Nature. But here Thomson’s
law come into operation, showing that we cannot overcome Nature by any
such device, but that if we have a large weight upon our piston, we
must have a proportionally large difference of temperature between our
two chambers--that is to say, the freezing point of water, under great
pressure, will be lower in temperature than its freezing point, if the
pressure upon it be only small.
Before leaving this subject we must call upon our readers to realize
what takes place in all heat engines. It is not merely that heat
produces mechanical effect, but that _a given quantity of heat
absolutely passes out of existence as heat in producing its equivalent
of work_. If, therefore, we could measure the mere heat produced in an
engine by the burning of a ton of coals, we should find it to be less
when the engine was doing work than when it was at rest.
In like manner, when a gas expands suddenly its temperature falls,
because a certain amount of its heat passes out of existence in the act
of producing mechanical effect.
157. We have thus endeavoured to show under what conditions absorbed
heat may be converted into mechanical effect. This absorbed heat
embraces (Art. 110) two varieties of energy, one of these being
molecular motion, and the other molecular energy of position.
Let us now, therefore, endeavour to ascertain under what circumstances
the one of these varieties may be changed into the other. It is well
known that it takes a good deal of heat to convert a kilogramme of ice
into water, and that when the ice is melted the temperature of the
water is not perceptibly higher than that of the ice. It is equally
well known that it takes a great deal of heat to convert a kilogramme
of boiling water into steam, and that when the transformation is
accomplished, the steam produced is not perceptibly hotter than the
boiling water. In such cases the heat is said to become latent.
Now, in both these cases, but more obviously in the last, we may
suppose that the heat has not had its usual office to perform, but
that, instead of increasing the motion of the molecules of water, it
has spent its energy in tearing them asunder from each other, against
the force of cohesion which binds them together.
Indeed, we know as a matter of fact that the force of cohesion which is
perceptible in boiling water is apparently absent from steam, or the
vapour of water, because its molecules are too remote from one another
to allow of this force being appreciable. We may, therefore, suppose
that a large part, at least, of the heat necessary to convert boiling
water into steam is spent in doing work against molecular forces.
When the steam is once more condensed into hot water, the heat thus
spent reassumes the form of molecular motion, and the consequence
is that we require to take away somehow all the latent heat of a
kilogramme of steam before we can convert it into boiling water. In
fact, if it is difficult and tedious to convert water into steam, it is
difficult and tedious to convert steam into water.
158. Besides the case now mentioned, there are other instances in
which, no doubt, molecular separation becomes gradually changed into
heat motion. Thus, when a piece of glass has been suddenly cooled,
its particles have not had time to acquire their proper position, and
the consequence is that the whole structure is thrown into a state of
constraint. In the course of time such bodies tend to assume a more
stable state, and their particles gradually come closer together.
It is owing to this cause that the bulb of a thermometer recently blown
gradually contracts, and it is no doubt owing to the same cause that a
Prince Rupert’s drop, formed by dropping melted glass into water, when
broken, falls into powder with a kind of explosion. It seems probable
that in all such cases these changes are attended with heat, and that
they denote the conversion of the energy of molecular separation into
that of molecular motion.
159. Having thus examined the transmutations of (C) into (D), and
of (D) back again into (C), let us now proceed with our list, and
see under what circumstances absorbed heat is changed into _chemical
separation_.
It is well known that when certain bodies are heated, they are
decomposed; for instance, if limestone or carbonate of lime be heated,
it is decomposed, the carbonic acid being given out in the shape of
gas, while quick-lime remains behind. Now, heat is consumed in this
process, that is to say, a certain amount of heat energy absolutely
passes out of existence _as heat_ and is changed into the energy of
chemical separation. Again, if the lime so obtained be exposed, under
certain circumstances, to an atmosphere of carbonic acid, it will
gradually become changed into carbonate of lime; and in this change
(which is a gradual one) we may feel assured that the energy of
chemical separation is once more converted into the energy of heat,
although we may not perceive any increment of temperature, on account
of the slow nature of the process.
At very high temperatures it is possible that most compounds are
decomposed, and the temperature at which this takes place, for any
compound, has been termed its _temperature of disassociation_.
160. Heat energy is changed into _electrical separation_ when
tourmalines and certain other crystals are heated.
Let us take, for instance, a crystal of tourmaline and raise its
temperature, and we shall find one end positively, and the other
negatively, electrified. Again, let us take the same crystal, and
suddenly cool it, and we shall find an electrification of the
opposite kind to the former, so that the end of the axis, which
was then positive, will now be negative. Now, this separation of
the electricities denotes energy; and we have, therefore, in such
crystals a case where the energy of heat has been changed into that
of electrical separation. In other words, a certain amount of heat has
passed out of existence _as heat_, while in its place a certain amount
of electrical separation has been obtained.
161. Let us next see under what circumstances heat is changed
into _electricity in motion_. This transmutation takes place in
thermo-electricity.
Suppose, for instance, that we have a bar of copper or antimony, say
copper, soldered to a bar of bismuth, as in Fig. 12. Let us now heat
one of the junctions, while the other remains cool. It will be found
that a current of positive electricity circulates round the bar, in
the direction of the arrow-head, going from the bismuth to the copper
across the heated junction, the existence of which may be detected by
means of a compass needle, as we see in the figure.
[Illustration: Fig. 12.]
Here, then, we have a case in which heat energy goes out of existence,
and is converted into that of an electric current, and we may even
arrange matters so as to make, on this principle, an instrument which
shall be an extremely delicate test of the existence of heat.
By having a number of junctions of bismuth and antimony, as in Fig.
13, and heating the upper set, while the lower remain cool, we get a
strong current going from the bismuth to the antimony across the heated
junctions, and we may pass the current so produced round the wire of
a galvanometer, and thus, by increasing the number of our junctions,
and also by using a very delicate galvanometer, we may get a very
perceptible effect for the smallest heating of the upper junctions.
This arrangement is called the _thermopile_, and, in conjunction with
the reflecting galvanometer, it affords the most delicate means known
for detecting small quantities of heat.
[Illustration: Fig. 13.]
162. The last transmutation on our list with respect to absorbed heat
is that in which this species of energy is transformed into _radiant
light and heat_. This takes place whenever a hot body cools in an open
space--the sun, for instance, parts with a large quantity of his heat
in this way; and it is due, in part at least, to this process that
a hot body cools in air, and wholly to it that such a body cools in
vacuo. It is, moreover, due to the penetration of our eye by radiant
energy that we are able to see hot bodies, and thus the very fact that
we see them implies that they are parting with their heat.
Radiant energy moves through space with the enormous velocity of
188,000 miles in one second. It takes about eight minutes to come
from the sun to our earth, so that if our luminary were to be suddenly
extinguished, we should have eight minutes respite before the
catastrophe overtook us. Besides the rays that affect the eye, there
are others which we cannot see, and which may therefore be termed dark
rays. A body, for instance, may not be hot enough to be self-luminous,
and yet it may be rapidly cooling and changing its heat into radiant
energy, which is given off by the body, even although neither the eye
nor the touch may be competent to detect it. It may nevertheless be
detected by the thermopile, which was described in Art. 161. We thus
see how strong is the likeness between a heated body and a sounding
one. For just as a sounding body gives out part of its sound energy
to the atmosphere around it, so does a heated body give out part of
its heat energy to the ethereal medium around it. When, however, we
consider the rates of motion of these energies through their respective
media, there is a mighty difference between the two, sound travelling
through the air with the velocity of 1100 feet a second, while radiant
energy moves over no less a space than 188,000 miles in the same
portion of time.
_Chemical Separation._
163. We now come to the energy denoted by chemical separation, such
as we possess when we have coal or carbon in one place, and oxygen in
another. Very evidently this form of energy of position is transmuted
into _heat_ when we burn the coal, or cause it to combine with the
oxygen of the air; and generally, whenever chemical combination
takes place, we have the production of heat, even although other
circumstances may interfere to prevent its recognition.
Now, in accordance with the principle of conservation, it may be
expected that, if a definite quantity of carbon or of hydrogen be
burned under given circumstances, there will be a definite production
of heat; that is to say, a ton of coals or of coke, when burned, will
give us so many heat units, and neither more or less. We may, no doubt,
burn our ton in such a way as to economize more or less of the heat
produced; but, as far as the mere production of heat is concerned, if
the quantity and quality of the material burned and the circumstances
of combustion be the same, we expect the same amount of heat.
164. The following table, derived from the researches of Andrews, and
those of Favre and Silbermann, shows us how many units of heat we may
get by burning a kilogramme of various substances.
UNITS _of_ HEAT _developed by_ COMBUSTION _in_ OXYGEN.
Kilogrammes of Water raised 1° C.
Substance by the combustion of one kilogramme
Burned. of each substance.
Hydrogen 34,135
Carbon 7,990
Sulphur 2,263
Phosphorus 5,747
Zinc 1,301
Iron 1,576
Tin 1,233
Olefiant Gas 11,900
Alcohol 7,016
165. There are other methods, besides combustion, by which chemical
combination takes place.
When, for instance, we plunge a piece of metallic iron into a solution
of copper, we find that when we take it out, its surface is covered
with copper. Part of the iron has been dissolved, taking the place of
the copper, which has therefore been thrown, in its metallic state,
upon the surface of the iron. Now, in this operation heat is given
out--we have in fact burned, or oxidized, the iron, and we are thus
furnished with a means of arranging the metals, beginning with that
which gives out most heat, when used to displace the metal at the other
extremity of the series.
166. The following list has been formed, on this principle, by Dr.
Andrews:--
1. Zinc
2. Iron
3. Lead
4. Copper
5. Mercury
6. Silver
7. Platinum
--that is to say, the metal platinum can be displaced by any other
metal of the series, but we shall get most heat if we use zinc to
displace it.
We may therefore assume that if we displace a definite quantity of
platinum by a definite quantity of zinc, we shall get a definite amount
of heat. Suppose, however, that instead of performing the operation
in one step, we make two of it. Let us, for instance, first of all
displace copper by means of zinc, and then platinum by means of copper.
Is it not possible that the one of these processes may be more fruitful
in heat giving than the other? Now, Andrews has shown us that we cannot
gain an advantage over Nature in this way, and that if we use our zinc
first of all to displace iron, or copper, or lead, and then use this
metal to displace platinum, we shall obtain just the very same amount
of heat as if we had used the zinc to displace the platinum at once.
167. It ought here to be mentioned that, very generally, chemical
action is accompanied with a change of molecular condition.
A solid, for instance, may be changed into a liquid, or a gas into
a liquid. Sometimes the one change counteracts the other as far as
apparent heat is concerned; but sometimes, too, they co-operate
together to increase the result. Thus, when a gas is absorbed by water,
much heat is evolved, and we may suppose the result to be due in part
to chemical combination, and in part to the condensation of the gas
into a liquid, by which means its latent heat is rendered sensible. On
the other hand, when a liquid unites with a solid, or when two solids
unite with one another, and the product is a liquid, we have very often
the absorption of heat, the heat rendered latent by the dissolution
of the solid being more than that generated by combination. Freezing
mixtures owe their cooling properties to this cause; thus, if snow and
salt be mixed together, they liquefy each other, and the result is
brine of a temperature much lower than that of either the ingredients.
168. When heterogeneous metals, such as zinc and copper, are soldered
together, we have apparently a conversion of the energy of chemical
separation into that of _electrical separation_. This was first
suggested by Volta as the origin of the electrical separation which
we see in the voltaic current, and recently its existence has been
distinctly proved by Sir W. Thomson.
To render manifest this conversion of energy, let us solder a piece of
zinc and copper together--if we now test the bar by means of a delicate
electrometer we shall find that the zinc is positively, while the
copper is negatively, electrified. We have here, therefore, an instance
of the transmutation of one form of energy of position into another; so
much energy of chemical separation disappearing in order to produce so
much electrical separation. This explains the fact recorded in Art. 93,
where we saw that if a battery be insulated and its poles kept apart,
the one will be charged with positive, and the other with negative,
electricity.
169. But further, when such a voltaic battery is in action, we have a
transmutation of chemical separation into _electricity in motion_. To
see this, let us consider what takes place in such a battery.
Here no doubt the sources of electrical excitement are the points of
contact of the zinc and platinum, where, as we see by our last article,
we have electrical separation produced. But this of itself would not
produce a current, for an electrical current implies very considerable
energy, and must be fed by something. Now, in the voltaic battery we
have two things which accompany each other, and which are manifestly
connected together. In the first place we have the combustion, or
at least the oxidation and dissolution, of the zinc; and we have,
secondly, the production of a powerful current. Now, evidently, the
first of these is that which feeds the second, or, in other words, the
energy of chemical separation of the metallic zinc is transmuted into
that of an electrical current, the zinc being virtually burned in the
process of transmutation.
170. Finally, as far as we are aware, the energy of chemical separation
is not directly transmuted into radiant light and heat.
_Electrical Separation._
171. In the first place the energy of electrical separation is
obviously transmuted into that of _visible motion_, when two oppositely
electrified bodies approach each other.
172. Again, it is transmuted into a _current of electricity_, and
ultimately into heat, when a spark passes between two oppositely
electrified bodies.
It ought, therefore, to be borne in mind that when the flash is seen
there is no longer electricity, what we see being merely air, or some
other material, intensely heated by the discharge. Thus a man might
be rendered insensible by a flash of lightning without his seeing the
flash--for the effect of the discharge upon the man, and its effect in
heating the air, might be phenomena so nearly simultaneous that the man
might become insensible before he could perceive the flash.
_Electricity in Motion._
173. This energy is transmuted into that of _visible motion_ when two
wires conveying electrical currents in the same direction attract each
other. When, for instance, two circular currents float on water, both
going in the direction of the hands of a watch, we have seen from Art.
100 that they will move towards each other. Now, here there is, in
truth, a lessening of the intensity of each current when the motion is
taking place, for we know (Art. 104) that when a circuit is moved into
the presence of another circuit conveying a current, there is produced
by induction a current in the opposite direction; and hence we perceive
that, when two similar currents approach each other, each is diminished
by means of this inductive influence--in fact, a certain amount of
current energy disappears from existence in order that an equivalent
amount of the energy of visible motion may be produced.
174. Electricity in motion is transmuted into _heat_ during the passage
of a current along a thin wire, or any badly conducting substance--the
wire is heated in consequence, and may even become white hot. Most
frequently the energy of an electric current is spent in heating the
wires and other materials that form the circuit. Now, the energy
of such a current is fed by the burning or oxidation of the metal
(generally zinc) which is used in the circuit, so that the ultimate
effect of this combustion is the heating of the various wires and other
materials through which the current passes.
175. We may, in truth, burn or oxidize zinc in two ways--we may oxidize
it, as we have just seen, in the voltaic battery, and we shall find
that by the combustion of a kilogramme of zinc a definite amount of
heat is produced. Or we may oxidize our zinc by dissolving it in acid
in a single vessel, when, without going through the intermediate
process of a current, we shall get just as much heat out of a
kilogramme of zinc as we did in the former case. In fact, whether we
oxidize our zinc by the battery, or in the ordinary way, the quantity
of heat produced will always bear the same relation to the quantity of
zinc consumed; the only difference being that, in the ordinary way of
oxidizing zinc, the heat is generated in the vessel containing the zinc
and acid, while in the battery it may make its appearance a thousand
miles away, if we have a sufficiently long wire to convey our current.
176. This is, perhaps, the right place for alluding to a discovery
of Peltier, that a current of positive electricity passing across a
junction of bismuth and antimony in the direction from the bismuth to
the antimony appears to produce cold.
[Illustration: Fig. 14.]
To understand the significance of this fact we must consider it in
connection with the thermo-electric current, which we have seen, from
Art. 161, is established in a circuit of bismuth and antimony, of
which one junction is hotter than the other. Suppose we have a circuit
of this kind with both its junctions at the temperature of 100° C.
to begin with. Suppose, next, that while we protect one junction, we
expose the other to the open air--it will, of course, lose heat, so
that the protected junction will now be hotter than the other. The
consequence will be (Art. 161) that a current of positive electricity
will pass along the protected junction from the bismuth to the
antimony.
Now, here we have an apparent anomaly, for the circuit is cooling--that
is to say, it is losing energy--but at the very same time it is
manifesting energy in another shape, namely, in that of an electric
current, which is circulating round it. Clearly, then, some of the heat
of this circuit must be spent in generating this current; in fact,
we should expect the circuit to act as a heat engine, only producing
current energy instead of mechanical energy, and hence (Art. 152)
we should expect to see a conveyance of heat from the hotter to the
colder parts of the circuit. Now, this is precisely what the current
does, for, passing along the hotter junction, in the direction of the
arrow-head, it cools that junction, and heats the colder one at C,--in
other words, it carries heat from the hotter to the colder parts of the
circuit. We should have been very much surprised had such a current
cooled C and heated H, for then we should have had a manifestation of
current energy, accompanied with the conveyance of heat from a colder
to a hotter substance, which is against the principle of Art. 152.
177. Finally, the energy of electricity in motion is converted into
that of _chemical separation_, when a current of electricity is made to
decompose a body. Part of the energy of the current is spent in this
process, and we shall get so much less heat from it in consequence.
Suppose, for instance, that by oxidizing so much zinc in the battery we
get, under ordinary circumstances, 100 units of heat. Let us, however,
set the battery to decompose water, and we shall probably find that by
oxidizing the same amount of zinc we get now only 80 units of heat.
Clearly, then, the deficiency or 20 units have gone to decompose the
water. Now, if we explode the mixed gases which are the result of the
decomposition, we shall get back these 20 units of heat precisely, and
neither more nor less; and thus we see that amid all such changes the
quantity of energy remains the same.
_Radiant Energy._
178. This form of energy is converted into _absorbed heat_ whenever
it falls upon an opaque substance--some of it, however, is generally
conveyed away by reflexion, but the remainder is absorbed by the body,
and consequently heats it.
It is a curious question to ask what becomes of the radiant light from
the sun that is not absorbed either by the planets of our system, or by
any of the stars. We can only reply to such a question, that _as far as
we can judge from our present knowledge_, the radiant energy that is
not absorbed must be conceived to be traversing space at the rate of
188,000 miles a second.
179. There is only one more transmutation of radiant energy that we
know of, and that is when it promotes _chemical separation_. Thus,
certain rays of the sun are known to have the power of decomposing
chloride of silver, and other chemical compounds. Now, in all such
cases there is a transmutation of radiant energy into that of chemical
separation. The sun’s rays, too, decompose carbonic acid in the leaves
of plants, the carbon going to form the woody fibre of the plant, while
the oxygen is set free into the air; and of course a certain proportion
of the energy of the solar rays is consumed in promoting this change,
and we have so much less heating effect in consequence.
But all the solar rays have not this power--for the property of
promoting chemical change is confined to the blue and violet rays,
and some others which are not visible to the eye. Now, these rays are
entirely absent from the radiation of bodies at a comparatively low
temperature, such as an ordinary red heat, so that a photographer would
find it impossible to obtain the picture of a red-hot body, whose only
light was in itself.
180. The actinic, or chemically active, rays of the sun decompose
carbonic acid in the leaves of plants, and they disappear in
consequence, or are absorbed; this may, therefore, be the reason why
very few such rays are either reflected or transmitted from a sun-lit
leaf, in consequence of which the photographer finds it difficult to
obtain an image of such a leaf; in other words, the rays which would
have produced a chemical change on his photographic plate have all been
used up by the leaf for peculiar purposes of its own.
181. And here it is important to bear in mind that while animals in
the act of breathing consume the oxygen of the air, turning it into
carbonic acid, plants, on the other hand, restore the oxygen to the
air; thus the two kingdoms, the animal and the vegetable, work into
each other’s hands, and the purity of the atmosphere is kept up.
FOOTNOTES:
[4] This explanation was first given by Professors Thomson and Tait
in their Natural Philosophy, and by Dr. Frankland in a lecture at the
Royal Institution of London.
[5] _See_ De La Rue, Stewart, and Loewy’s researches on Solar Physics.
[6] _See_ the Magnetic Researches of Sir E. Sabine, also C. Meldrum on
the Periodicity of Cyclones.