Up to the present time the changes caused in the temperature of bodies
by motion have been very little studied. This class of phenomena merits,
however, the attention of observers. When bodies are in motion,
especially when that motion disappears, or when it produces motive
power, remarkable changes take place in the distribution of heat, and
perhaps in its quantity.
We will collect a few facts which exhibit this phenomenon most clearly.
1. _The Collision of Bodies._—We know that in the collision of bodies
there is always expenditure of motive power. Perfectly elastic bodies
only form an exception, and none such are found in nature.
We also know that always in the collision of bodies there occurs a
change of temperature, an elevation of temperature. We cannot, as did M.
Berthollet, attribute the heat set free in this case to the reduction of
the volume of the body; for when this reduction has reached its limit
the liberation of heat would cease. Now this does not occur.
It is sufficient that the body change form by percussion, without change
of volume, to produce disengagement of heat.
If, for example, we take a cube of lead and strike it successively on
each of its faces, there will always be heat liberated, without sensible
diminution in this disengagement, so long as the blows are continued
with equal force. This does not occur when medals are struck. In this
case the metal cannot change form after the first blows of the die, and
the effect of the collision is not conveyed to the medal, but to the
threads of the screw which are strained, and to its supports.
It would seem, then, that heat set free should be attributed to the
friction of the molecules of the metal, which change place relatively to
each other, that is, the heat is set free just where the moving force is
expended.
A similar remark will apply in regard to the collision of two bodies of
differing hardness—lead and iron for instance. The first of these metals
becomes very hot, while the second does not vary sensibly in
temperature. But the motive power is almost wholly exhausted in changing
the form of the first of these metals. We may also cite, as a fact of
the same nature, the heat produced by the extension of a metallic rod
just before it breaks. Experiment has proved that, other things being
equal, the greater the elongation before rupture, the more considerable
is the elevation of temperature.
(2) [The remainder is blank.]
When a hypothesis no longer suffices to explain phenomena, it should be
abandoned.
This is the case with the hypothesis which regards caloric as matter, as
a subtile fluid.
The experimental facts tending to destroy this theory are as follows:
(1) The development of heat by percussion or the friction of bodies
(experiments of Rumford, friction of wheels on their spindles, on the
axles, experiments to be made). Here the elevation of temperature takes
place at the same time in the body rubbing and the body rubbed.
Moreover, they do not change perceptibly in form or nature (to be
proved). Thus heat is produced by motion. If it is matter, it must be
admitted that the matter is created by motion.
(2) When an air-pump is worked, and at the same time air is admitted
into the receiver, the temperature remains constant in the receiver. It
remains constant on the outside. Consequently, the air compressed by the
pumps must rise in temperature above the air outside, and it is expelled
at a higher temperature. The air enters then at a temperature of 10°,
for instance, and leaves at another, 10° + 90° or 100°, for example.
Thus heat has been created by motion.
(3) If the air in a reservoir is compressed, and at the same time
allowed to escape through a little opening, there is by the compression
elevation of temperature, by the escape lowering of temperature
(according to Gay-Lussac and Welter). The air then enters at one side at
one temperature and escapes at the other side at a higher temperature,
from which follows the same conclusion as in the preceding case.
(Experiment to be made: To fit to a high-pressure boiler a cock and a
tube leading to it and emptying into the atmosphere; to open the cock a
little way, and present a thermometer to the outlet of the steam; to see
if it remains at 100° or more; to see if steam is liquefied in the pipe;
to see whether it comes out cloudy or transparent.)
(4) The elevation of temperature which takes place at the time of the
entrance of the air into the vacuum, an elevation that cannot be
attributed to the compression of the air remaining (air which may be
replaced by steam), can therefore be attributed only to the friction of
the air against the walls of the opening, or against the interior of the
receiver, or against itself.
(5) M. Gay-Lussac showed (it is said) that if two receivers were put in
communication with each other, the one a vacuum, the other full of air,
the temperature would rise in one as much as it would fall in the other.
If, then, both be compressed one half, the first would return to its
previous temperature and the second to a much higher one. Mixing them,
the whole mass would be heated.
When the air enters a vacuum, its passage through one small opening and
the motion imparted to it in the interior appear to produce elevation of
temperature.
We may be allowed to express here an hypothesis in regard to the nature
of heat.
At present, light is generally regarded as the result of a vibratory
movement of the ethereal fluid. Light produces heat, or at least
accompanies the radiating heat, and moves with the same velocity as
heat. Radiating heat is then a vibratory movement. It would be
ridiculous to suppose that it is an emission of matter while the light
which accompanies it could be only a movement.
Could a motion (that of radiating heat) produce matter (caloric)?
No, undoubtedly; it can only produce a motion. Heat is then the result
of a motion.
Then it is plain that it could be produced by the consumption of motive
power, and that it could produce this power.
All the other phenomena—composition and decomposition of bodies, passage
to the gaseous state, specific heat, equilibrium of heat, its more or
less easy transmission, its constancy in experiments with the
calorimeter—could be explained by this hypothesis. But it would be
difficult to explain why, in the development of motive power by heat, a
cold body is necessary; why, in consuming the heat of a warm body,
motion cannot be produced.
It appears very difficult to penetrate into the real essence of bodies.
To avoid erroneous reasoning, it would be necessary to investigate
carefully the source of our knowledge in regard to the nature of bodies,
their form, their forces; to see what the primitive notions are, to see
from what impressions they are derived; to see how one is raised
successively to the different degrees of abstraction.
Is heat the result of a vibratory motion of molecules? If this is so,
quantity of heat is simply quantity of motive power. As long as motive
power is employed to produce vibratory movements, the quantity of heat
must be unchangeable; which seems to follow from experiments with the
calorimeter; but when it passes into movements of sensible extent, the
quantity of heat can no longer remain constant.
Can examples be found of the production of motive power with actual
consumption of heat? It seems that we may find production of heat with
consumption of motive power (re-entrance of the air into a vacuum, for
example).
What is the cause of the production of heat in combinations of
substances? What is radiant caloric?
Liquefaction of bodies, solidification of liquids, crystallization—are
they not forms of combinations of integrant molecules?
Supposing heat due to a vibratory movement, how can the passage from the
solid or the liquid to the gaseous state be explained?
When motive power is produced by the passage of heat from the body _A_
to the body _B_, is the quantity of this heat which arrives at _B_ (if
it is not the same as that which has been taken from _A_, if a portion
has really been consumed to produce motive power) the same whatever may
be the substance employed to realize the motive power?
Is there any way of using more heat in the production of motive power,
and of causing less to reach the body _B_? Could we even utilize it
entirely, allowing none to go to the body _B_? If this were possible,
motive power could be created without consumption of combustible, and by
mere destruction of the heat of bodies.
Is it absolutely certain that steam after having operated an engine and
produced motive power can raise the temperature of the water of
condensation as if it had been conducted directly into it?
Reasoning shows us that there cannot be loss of living force, or, which
is the same thing, of motive power, if the bodies act upon each other
without directly touching each other, without actual collision. Now
everything leads us to believe that the molecules of bodies are always
separated from each other by some space, that they are never actually in
contact. If they touched each other, they would remain united, and
consequently change form.
If the molecules of bodies are never in close contact with each other
whatever may be the forces which separate or attract them, there can
never be either production or loss of motive power in nature. This power
must be as unchangeable in quantity as matter. Then the direct
re-establishment of equilibrium of the caloric, and its re-establishment
with production of motive power, would be essentially different from
each other.
Heat is simply motive power, or rather motion which has changed form. It
is a movement among the particles of bodies. Wherever there is
destruction of motive power there is, at the same time, production of
heat in quantity exactly proportional to the quantity of motive power
destroyed. Reciprocally, wherever there is destruction of heat, there is
production of motive power.
We can then establish the general proposition that motive power is, in
quantity, invariable in nature; that it is, correctly speaking, never
either produced or destroyed. It is true that it changes form, that is,
it produces sometimes one sort of motion, sometimes another, but it is
never annihilated.
According to some ideas that I have formed on the theory of heat, the
production of a unit of motive power necessitates the destruction of
2.70 units of heats.
A machine which would produce 20 units of motive power per kilogram of
coal ought to destroy (20 × 2.70)/(7000) of the heat developed by the
combustion. (20 × 2.70)/(7000) = (8)/(1000) about; that is, less than
(1)/(100).
(Each unit of motive power, or dyname, representing the weight of one
cubic metre of water raised to the height of one metre.)
_Experiments to be made on Heat and Motive Power._
To repeat Rumford’s experiments in the drilling of a metal in water, but
to measure the motive power consumed at the same time as the heat
produced; same experiments on several metals and on wood.
To strike a piece of lead in various ways, to measure the motive power
consumed and the heat produced. Same experiments on other metals.
To strongly agitate water in a small cask or in a double-acting pump
having a piston pierced with a small opening.
Experiment of the same sort on the agitation of mercury, alcohol, air
and other gases. To measure the motive power consumed and heat produced.
To admit air into a vacuum or into air more or less rarefied; _id._ for
other gases or vapors. To examine the elevation of temperature by means
of the manometer and the thermometer of Bréguet. Estimation of the error
of the thermometer in the time required for the air to vary a certain
number of degrees. These experiments would serve to measure the changes
which take place in the temperature of the gas during its changes of
volume. They would also furnish means of comparing these changes with
the quantities of motive power produced or consumed.
Expel the air from a large reservoir in which it is compressed, and
check its velocity in a large pipe in which solid bodies have been
placed; measure the temperature when it has become uniform. See if it is
the same as in the reservoir. Same experiments with other gases and with
vapor formed under different pressures.
To repeat Dalton’s experiments and carry them on to pressures of thirty
or forty atmospheres. To measure the constituent heat of the vapor
within these limits.
_Id._ on the vapor of alcohol, of ether, of essence of turpentine, of
mercury, to prove whether the agent employed makes any difference in the
production of motive power.
_Id._ on water charged with a deliquescent salt, the calcium chloride,
for instance.
Is the law of tensions always the same? To measure the specific heat of
vapor.
_Experiments to be made on the Tension of Vapors._
A graduated capillary tube filled with water, mercury, or with oil and
air. Plunge this tube into a bath of oil, of mercury, or of melted lead.
To measure the temperature by an air-thermometer.
Same experiments with alcohol, ether, sulphide of carbon, muriatic
ether, essence of turpentine, sulphur, phosphorus.
Experiments on the tension of steam with a boiler, and a thermometric
tube full of air. A thermometer will be placed in a tube immersed in the
boiler, open outwards and filled with oil or mercury.
Experiments by means of a simple capillary tube filled with three
successive parts—first of air, second of mercury, third of water or
other liquid of which the tension can be measured (of alcohol, of ether,
of essence of turpentine, of lavender, of sulphide of carbon, of
muriatic ether, etc.). One end of the tube may be immersed in a bath of
mercury or oil, the temperature of which is to be measured. The column
of mercury can be made long enough to allow of the air being previously
compressed or rarefied.
[Illustration:
FIG. 6.
]
The tube will be bent into a spiral at one end, the straight part being
graduated (thus permitting the tension of mercurial vapor to be
measured).
[Illustration:
FIG. 7.
]
Experiments on the tension of vapors at low temperature, with a
thermometric tube bent round, and filled partly with mercury, partly
with water or alcohol. The mercury will operate by its weight. The upper
part of the tube will be empty and sealed, or fully open to the
atmosphere.
The bulb will be immersed in water the temperature of which is to be
measured. If the tube is sealed, the upper part must be cooled.
The bulb might contain water, ether, or essence of turpentine.
If the tube is sealed, the tension of mercurial vapor could be measured.
Experiments on the constituent heat of vapors by means of a barometric
tube having two enlarged bulbs. One of the bulbs may be immersed in cold
water, and the elevation of temperature of this water will indicate the
constituent heat of the vapor.
[Illustration:
FIG. 8.
]
The other bulb may be warmed either by boiling liquid or by fire.
Water, alcohol, steam, ether, mercury, acetic acid, sulphide of carbon.
The operation may be repeated and add the results.
_Experiments to be made on Gases and Vapors._
To measure the temperature acquired by the air introduced into a vacuum
or space containing previously rarefied air.
[Illustration:
FIG. 9.
]
If the vacuum is made under the glass receiver of an air-pump, and the
cock admitting the outer air be suddenly opened, the introduction of
this air will cause a Bréguet thermometer to rise to 50° or 60°. To
examine the movement of this thermometer when the reintroduction takes
place only by degrees, to compare it with the movement of the manometer.
Construction of a manometer which may give the pressure almost
instantaneously.
Imagine a capillary tube bent into a spiral at one end, and having one
extremity closed, the other open. This tube will be perfectly dry and a
small index of mercury may be introduced into it. The diameter of the
tube will be small enough for the air enclosed in it to take almost
instantly the temperature of the glass. We shall try to ascertain the
time necessary for the establishment of this equilibrium of temperature
by placing the tube under the receiver of the air-pump, making a partial
vacuum, and admitting the air. We shall see whether, some seconds after
the introduction, the index perceptibly moves. The index must be of very
light weight to avoid oscillation as much as possible.
For the same reason, the capillary tube should be also as narrow as
possible. If the straight part of the tube is equal to the bent part and
the index be placed at the beginning of the bent part, for a pressure
equal to atmospheric pressure, it would not be necessary to subject the
instrument to a less pressure than ½ atmosphere. It is between these two
limits that it would serve as a measure.
It might end in an open enlargement to prevent the projection of the
mercury outside the tube. Disposed in this way, it could be used as a
general measure for pressures between _p_ and (½)_p_; _p_ being anything
whatever. The apparatus will be fastened to a board bearing a graduated
scale placed against the straight tube. The scale will be, for instance,
numbered by fives or tens. A corresponding table denoting pressures
would be required.
Placing the instrument under the receiver and forming a partial vacuum,
the index will rise into the enlargement. Then, admitting the air by
degrees and very slowly, we may note the correspondence between the
heights of the ordinary mercury manometer and the point which will be
reached by the lower face of the index of the instrument. This will
answer to form a comparative table of the pressures and the numbers of
the scale. The pressures would be represented by their relations to the
observed pressure at the moment of the passage of the index over zero,
for any other fixed number of the scale.
Thus, for example, suppose that we observed on the manometer 400 or _n_
millimetres of mercury when the index is on _o_, then _n′_ when the
index is on 1, _n″_ when on 2, and so on. This will give the ratios
_n′_/_n_, _n″_/_n_, ... which must be inscribed in the table. Then _n_
could be varied at pleasure, and the table could still be used.
In fact, according to the law of Mariotte, volumes preserving the same
ratios, pressures should also preserve the same ratios to each other.
Let _p_ be the pressure when the index is on _o_, _v_ the volume of air
at the same moment, _p′_ and _v′_ the same pressures and volume at the
moment when the index is on 1. Whether the air be expelled or admitted
the pressures would be instead of _p_ and _p′_, _q_ and _q′_. But there
would follow
_p_ : _p′_ :: _v′_ : _v_ and _q_ : _q′_ :: _v′_ : _v_;
then _p_ : _p′_ :: _q_ : _q′_.
We should moreover work at a uniform temperature and note the
variations.
If the straight part of the tube were perfectly calibrated, the volumes,
and consequently the pressures, would form a geometrical progression,
when the figures of the scale would be found to be in arithmetical
progression, and a table of logarithms would enable one to be found from
the other.
In order to increase as required the mass of air enclosed in the tube
the instrument must be placed on its side or flat, in the air-pump
receivers. The mercury index would be placed in the lateral part of the
enlargement of the tube, and the atmospheric air would enter. The
instrument might also be heated in this position.
Care must be taken to admit only very dry air, which could be obtained
by placing under the receiver calcium chloride or any other substance
which absorbs moisture greedily.
Instead of bending the tube into a spiral, it might be bent in the
middle in the form of a ᑌ, or it might be better to form three, four or
more parallel branches. Making the tube very long, the index would have
a larger range for the same changes of pressure, and the results
produced could then be measured by a slight variation in density in the
air of the receiver.
_Comparison of the Rapidity with which the Air cools in the Receiver and
in the Tube._
Let us suppose, what I believe to be very near the truth, that the heat
absorbed is proportional to the surface of the bodies in contact. From
this we can infer without difficulty, that the rapidity of the cooling
of the air in two cylindrical tubes would be inversely as their
diameters.
If the receiver is considered as a tube of two decimetres in diameter,
and the manometer as a tube of one millimetre diameter, the rapidity of
the cooling of the air would be in the ratio, very nearly, of 1 to 200.
_Extent of the Movement of the Index._
Suppose the tube turned up on itself five times and having a total
length of 1 metre; a variation of density equal to ⅒ in the air will
give a movement of 1 decimetre; a variation of heat of 1 degree supposed
to be equivalent to a variation of density of ¹⁄₂₆₆ will give ¹⁄₂₆₆ of a
metre, or about 3^{mm}.70, quite an appreciable quantity. As to the time
required to move the mercury index, regard being had to its mass, if we
suppose it 1 centimetre long, and the variation of pressure ¹⁄₁₀₀ of an
atmosphere, it would require about ⅙ of a second to make it pass over
one decimetre.
_Use of the Instrument in Measuring the Variations of the Tensions of
the Air under a Pneumatic Receiver._
At each stroke of the piston which expands the air under the pneumatic
receiver when a vacuum is to be created, a lowering of pressure is
produced, and undoubtedly a change of temperature. It can be determined
approximately, at least, by observing the position of the manometer at
the instant after the dilatation has taken place, and again after a time
long enough for the temperature to have returned to its original point,
that of the surrounding bodies. Comparison of the elastic force in the
two cases will lead to comparison of the temperatures.
The temperature having returned to its original point, we will give a
second stroke of the piston which will rarefy the air more than the
former, and thus we will make two observations of the manometer, before
and after the return to the former temperature. And so on.
APPENDIX B.
CARNOT’S FOOT-NOTES.
NOTE A.—The objection may perhaps be raised here, that perpetual motion,
demonstrated to be impossible by mechanical action alone, may possibly
not be so if the power either of heat or electricity be exerted; but is
it possible to conceive the phenomena of heat and electricity as due to
anything else than some kind of motion of the body, and as such should
they not be subjected to the general laws of mechanics? Do we not know
besides, _à posteriori_, that all the attempts made to produce perpetual
motion by any means whatever have been fruitless?—that we have never
succeeded in producing a motion veritably perpetual, that is, a motion
which will continue forever without alteration in the bodies set to work
to accomplish it? The electromotor apparatus (the pile of Volta) has
sometimes been regarded as capable of producing perpetual motion;
attempts have been made to realize this idea by constructing dry piles
said to be unchangeable; but however it has been done, the apparatus has
always exhibited sensible deteriorations when its action has been
sustained for a time with any energy.
The general and philosophic acceptation of the words _perpetual motion_
should include not only a motion susceptible of indefinitely continuing
itself after a first impulse received, but the action of an apparatus,
of any construction whatever, capable of creating motive power in
unlimited quantity, capable of starting from rest all the bodies of
nature if they should be found in that condition, of overcoming their
inertia; capable, finally, of finding in itself the forces necessary to
move the whole universe, to prolong, to accelerate incessantly, its
motion. Such would be a veritable creation of motive power. If this were
a possibility, it would be useless to seek in currents of air and water
or in combustibles this motive power. We should have at our disposal an
inexhaustible source upon which we could draw at will.
NOTE B.—The experimental facts which best prove the change of
temperature of gases by compression or dilatation are the following:
(1) The fall of the thermometer placed under the receiver of a pneumatic
machine in which a vacuum has been produced. This fall is very sensible
on the Bréguet thermometer: it may exceed 40° or 50°. The mist which
forms in this case seems to be due to the condensation of the watery
vapor caused by the cooling of the air.
(2) The inflammation of German tinder in the so-called pneumatic
tinder-boxes; which are, as we know, little pump-chambers in which the
air is rapidly compressed.
(3) The fall of a thermometer placed in a space where the air has been
first compressed and then allowed to escape by the opening of a cock.
(4) The results of experiments on the velocity of sound. M. de Laplace
has shown that, in order to secure results accurately by theory and
computation, it is necessary to assume the heating of the air by sudden
compression.
The only fact which may be adduced in opposition to the above is an
experiment of MM. Gay-Lussac and Welter, described in the _Annales de
Chimie et de Physique_. A small opening having been made in a large
reservoir of compressed air, and the ball of a thermometer having been
introduced into the current of air which passes out through this
opening, no sensible fall of the temperature denoted by the thermometer
has been observed.
Two explanations of this fact may be given: (1) The striking of the air
against the walls of the opening by which it escapes may develop heat in
observable quantity. (2) The air which has just touched the bowl of the
thermometer possibly takes again by its collision with this bowl, or
rather by the effect of the _détour_ which it is forced to make by its
rencounter, a density equal to that which it had in the receiver,—much
as the water of a current rises against a fixed obstacle, above its
level.
The change of temperature occasioned in the gas by the change of volume
may be regarded as one of the most important facts of Physics, because
of the numerous consequences which it entails, and at the same time as
one of the most difficult to illustrate, and to measure by decisive
experiments. It seems to present in some respects singular anomalies.
Is it not to the cooling of the air by dilatation that the cold of the
higher regions of the atmosphere must be attributed? The reasons given
heretofore as an explanation of this cold are entirely insufficient; it
has been said that the air of the elevated regions receiving little
reflected heat from the earth, and radiating towards celestial space,
would lose caloric, and that this is the cause of its cooling; but this
explanation is refuted by the fact that, at an equal height, cold reigns
with equal and even more intensity on the elevated plains than on the
summit of the mountains, or in those portions of the atmosphere distant
from the sun.
NOTE C.—We see no reason for admitting, _à priori_, the constancy of the
specific heat of bodies at different temperatures, that is, to admit
that equal quantities of heat will produce equal increments of
temperature, when this body changes neither its state nor its density;
when, for example, it is an elastic fluid enclosed in a fixed space.
Direct experiments on solid and liquid bodies have proved that between
zero and 100°, equal increments in the quantities of heat would produce
nearly equal increments of temperature. But the more recent experiments
of MM. Dulong and Petit (see _Annales de Chimie et de Physique_,
February, March, and April, 1818) have shown that this correspondence no
longer continues at temperatures much above 100°, whether these
temperatures be measured on the mercury thermometer or on the
air-thermometer.
Not only do the specific heats not remain the same at different
temperatures, but, also, they do not preserve the same ratios among
themselves, so that no thermometric scale could establish the constancy
of all the specific heats. It would have been interesting to prove
whether the same irregularities exist for gaseous substances, but such
experiments presented almost insurmountable difficulties.
The irregularities of specific heats of solid bodies might have been
attributed, it would seem, to the latent heat employed to produce a
beginning of fusion—a softening which occurs in most bodies long before
complete fusion. We might support this opinion by the following
statement: According to the experiments of MM. Dulong and Petit, the
increase of specific heat with the temperature is more rapid in solids
than in liquids, although the latter possess considerably more
dilatability. The cause of irregularity just referred to, if it is real,
would disappear entirely in gases.
NOTE D.—In order to determine the arbitrary constants _A_, _B_, _A′_,
_B′_, in accordance with the results in M. Dalton’s table, we must begin
by computing the volume of the vapor as determined by its pressure and
temperature,—a result which is easily accomplished by reference to the
laws of Mariotte and Gay-Lussac, the weight of the vapor being fixed.