Henry S. (Henry Smith) Carhart.

Physics for university students (Volume 2) online

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Copyright) i8gd,


THE present volume has been written in pursuance of
the plan outlined in Part I. ; it is from the same point
of view, and the same method has been followed as far as

The favor with which the first part of the book has been
received by teachers of experience leads the author to hope
that this second part may be found to furnish a satisfactory
completion of the elementary course in Physics which the
two were designed to furnish.

The author would take this occasion to acknowledge the
courtesy of The Cambridge Press in granting permission
to reproduce a few illustrations from Glazebrook's Heat ;
he would also make acknowledgment of similar indebted-
ness to Professor Barker for illustrations from his Physics ;
and to Assistant Professor G. W. Patterson, Jr., for cordial
assistance in proof-reading.






I. Nature of Heat

II. Temperature and it< Measurement

III. Expansion

IV. Measurement ot tiu> Quantity of Heat .... 42
V. Fusion 54

VI. Vaporization . . . 65

VII. Transmission of Heat . . .

VIII. Radiation and Absorption

IX. Thermodynamics

X. Kinetic Theory of Gaaea 142


XI. Electric Charges

XII. Electrification by Influence 171

XIII. Electrical Potential ... .188

XIV. Capacity and Condensers .
XV. Atmospheric Electricity .

XVI. Primary Cells

XVII. Electrolysis

XVIII. Ohm's Law and its Applications

XIX. Thermal Relations .

XX. Properties of Magnets

XXI. Magnetic Effects of a Current

XXII. Electrodynamics

XXIII. Electromagnetism

XXIV. Electromagnetic Induction ....
XXV. Dynamos and Motors ....

XXVI. Electric Oscillations and \Vav,-s





The letters, enclosed in parentheses accompanying the headings
of articles, refer to the following books, numerals denoting pages :

B., Barker's Physics.

G., Glazebrook's Heat.

J. J. T., J. J. Thomson's Elements of Electricity and Magnetism.

M., Maxwell's Theory of Heat (Tenth Edition).

Max., Maxwell's Treatise on Electricity and Magnetism.

P., Preston's Theory of Heat.

S., Stewart's Elementary Treatise on Heat (Sixth Edition).

T., Tait's Heat.

Th., Thompson's Elementary Lessons in Electricity and Magnetism.

Tyn., Tyndall's Heat as a Mode of Motion.

The numerals enclosed in parentheses in the body of the text
refer to articles. When the reference is to Parti., it is indicated
by the letter I. before the number denoting the article.





1. Heat a Form of Energy. The conclusion to which
many remarkable investigations of the present century
lead is that heat is a form of energy, and that it can be
transformed into mechanical work. We are not at liberty
to regard it as a substance, because it can be produced
from something which is not a substance, and it is inex-
haustible in amount. Heat is not motion, but the energy
of motion. It depends on the confused and incessant
activity of the molecules of matter.

Heat is, moreover, the lowest form of energy, or the
form which all other kinds of energy tend to assume
whenever any transformation occurs. It is the form taken
by unavailable energy when work is spent in friction, and
by the unconverted residue when available energy is em-
ployed to do work, as in the heat-engine. When energy
is transformed in any operation in such a way that it is
not directed by the mechanism of the transformation into
some specialized form, it always manifests itself as heat.
Thus, when a piece of zinc is acted on by sulphuric acid,
the energy of the chemical union appears as heat, unless
the conditions are such as to constitute a voltaic cell, when
most of it appears first as the energy of an electric current.

2* . .' t tt 'c ' HEAT.

The kinetic energy of a bnllet is converted into heat when
it strikes the target; the energy of meteors becomes heat
by friction with the air ; the energy of combustion is heat,
and only a small portion of it can be reconverted into
useful forms. The energy of sound, of winds, and of
waves, of lightning and of falling water, ultimately fritters
down into diffused heat.

2. Heat in Material Bodies (P., 34). In primitive
times heat was supposed to be a subtle fluid. The excess
of it in a body caused it to be hot ; its deficiency left it
cold. After many controversies it was demonstrated to
be without weight, and was therefore included among the
imponderables. It was assumed that this heat-fluid, or
caloric, was indestructible. The quantity of heat in the
universe was, therefore, considered to be constant.

To explain the physical changes produced by heat, it
was imagined that caloric entered into combination with
material bodies. Thus, water was conceived to be a com-
pound of ice and caloric, and steam was ice with a larger
proportion of caloric. The heat generated by friction,
grinding, or compression was said to be forced out of
bodies or to be due to their lessened capacity for heat.
Such explanations, which now seem to partake of the
grotesque, were regarded by many philosophers as plau-
sible and satisfactory, and the theory persisted down into
the present century. But the burden of proof which it
had to sustain became at length too great, and it was aban-
doned, as the material theory of light had been before it.

The real nature of heat had been foreshadowed in early
times. Bacon expressed the opinion that heat consists in
a " brisk agitation " of the parts of a body, and Robert
Boyle concurred in this opinion. The non-materiality of


heat was demonstrated by Count Rumford (Benjamin
Thompson") and by Sir Humphrey Davy at the beginning
of the present century, but their demonstration was not
accepted till Joule had determined the "mechanical equiv-
alent " of heat, or the work that the quantity of heat con-
stituting the unit of measurement is capable of doing

. This equivalence between heat and work is inde-
pendent of any theory of molecular motion. It is a de-
monstration that heat is a form of energy, because heat
and energy in other forms are reciprocally convertible.

The precise theory of the molecular motions concerned
in heat has not yet been made out. We know that the
ultimate particles or molecules of a body are in a state
of perpetual agitation. In gases this motion is in part
vibrational, in part probably rotational, and in part motion
of translation, the molecules colliding and rebounding, but
having at a given temperature a mean velocity of which
we have a fair knowledge (98). In liquids their move-
ments are much more restricted, but diffusion shows that
they enjoy a good degree of freedom of motion. In solids
the molecules are still more limited in their movements.
Earl i molecule is restricted to a very small space which it
never leaves, and is within the limits of the action taking
place among contiguous molecules. In solids and in
liquids a part of the heat-energy is potential, since each
molecule is acted on by its neighbors. The remainder is
the kinetic energy of molecular motion. The heat-energy

ises is all kinetic, but it is not known how the total
kinetic energy of a molecule is divided between the three
components of motion vibration, rotation, and translation.

3. Rumford' s Experiment. During the operation of
luring hi-ass cannon at the military arsenal in Munich in


1799, Rumford was impressed with the large amount of
heat generated by the abrasion of material with the boring
tool. The calorists ascribed the heat to the diminished
capacity of the abraded metal for heat. Rumford sought
to test this explanation by comparing the amount of heat
contained in equal masses of the solid and the abraded
metal by raising them to the same temperature of boiling
water and observing the rise of temperature of the equal
masses of water in which they were cooled. No difference
could be detected.

In this famous experiment, which disproved the material
theory of heat, a blunt steel borer 3 inches wide was
turned by horse power 32 times a minute inside a brass
cylinder weighing 113 pounds. In two and a half hours
the water surrounding the cylinder and weighing 18 J
pounds was heated from 60 F. to the boiling point. Only
4,145 grains of the metal were abraded. Rumford cor-
rectly concluded that this large amount of heat, which
appeared to be inexhaustible, could not have been derived
from the abraded metal, which at the same time had not
lost any of its capacity for heat. After showing that all
other conceivable explanations were excluded by the con-
ditions, he concludes as folloAvs : " It is hardly necessary to
add that anything which any insulated body, or system of
bodies, can continue to furnish without limitation cannot
possibly be a material substance ; and it appears to me
extremely difficult, if not quite impossible, to form any
distinct idea of anything capable of being excited and com-
municated in the manner heat was excited and communi-
cated in these experiments, except it be MOTION."

Rumford's experiment was complete except that he did
not proceed to determine the numerical relation between
the work done and the heat generated ; but it must be


remembered that the law of Conservation of Energy was
not then known.

4. Davy's Experiment. About the time of Rum-
ford's experiment, Sir Humphrey Davy devised another
to test the current explanation of the heat generated by
friction. By means of clock-work he arranged to produce
friction between two blocks of ice, in such a manner that
no heat could be received from external objects ; and he
thus demonstrated that the ice could be melted by the
friction of one block against the other. The fusion took
place only at the surface of contact between the two, and
they were almost completely converted into water, whose ca-
pacity for heat, according to the supposition of the calorists,
was diminished. Davy reasoned that heat must have
been generated, because water by universal concession con-
tains more heat than ice. But this heat could not have
come from the diminution of thermal capacity, because the
thermal capacity of water is much greater than that of ice.
This was Davy's first contribution to science ; and he con-
cluded, though with some apparent lack of confidence, that
friction produces heat, and that there is no such thing as
caloric, or the matter of heat. It was not till 1812 that he
asserted with firm conviction that

u The fundamental cause of the phenomena of heat is
motion, and the laws of its communication are precisely
the same as the laws of the communication of motion."

The first of these propositions should now be amended
in view of the doctrine of the Conservation of Energy.
Heat is not motion, or a mode of motion, but the Energy
of Motion. The second of Davy's statements remains
entirely correct.

These experiments of a public officer in the prosecution


of his official duties, and of a young scientific man, des-
tined later to become famous in both physics and chem-
istry, laid the foundation of the modern dynamical theory
of heat, which was developed later by Joule, Him, Clausius,
and Maxwell.

5. Radiant Heat. One of the ways in which a hot
body loses heat is by radiation. We may feel the warmth
of the sun's rays when the temperature of the air is below
freezing. Approach to a hot stove is readily perceived in
the dark without contact. The air is not the medium by
which the heat is conveyed, for radiant energy is trans-
mitted more readily through the most perfect vacuum than
through air. The process by which heat is transferred from
one body to another without heating the medium through
which it passes is called radiation. It is customary to
speak of the radiant energy, which becomes sensible heat
when absorbed by material bodies, as Radiant Heat. But
while heat is certainly communicated from one body to
another by the vibrational process of radiation, we are not
at liberty to speak of what passes between them as heat,
since it does not warm the air through which it passes ;
for the passage of heat through any medium as heat always
warms the medium. When heat leaves a radiating body,
it is wholly transformed into radiant energy. Energy in
the radiant state or form of transmission is not the heat
which gives rise to our sensation of warmth. It is recon-
verted into heat only when it reaches our bodies or other
absorbing substances. We have no evidence that the
radiant energy from the sun is heat during its passage
through interplanetary space. Heat is converted into
radiant energy at the sun, and it is transmitted as radiant
energy through the intangible ether as a medium. It


becomes heat again only when it is absorbed by material
bodies and becomes the energy of irregular molecular
vibrations. But the term Radiant Heat has come into
scientific use on account of the intimate connection between
heat and radiation ; its use does not imply the existence
of a new kind of heat, but refers to the thermal aspect of

6. Radiant Heat and Light Identical. It was for-
merly supposed that the radiations from the sun, or any other
self-luminous body, consisted of three distinct kinds, having
different distributions in the spectrum ; viz., the luminous,
the heat, and the actinic rays. The last were supposed to
})G the only ones concerned in the process of photography ;
but the progress of physical science has shown that the
differences ascribed to radiations are rather differences in
the receptive apparatus (I., 217). Radiant heat and light
are identical, but are perceived by us through different
avenues of sensation. Radiations of identically the same
wave-length produce the impression of light when received
through the eye, and of radiant heat when detected by the
sense of heat or by a thermometer. All radiations when
stopped by the appropriate absorbing body are transformed
into sensible heat; that is, heat which affects the sense of
heat <>r a thermometer. The limit in their effect upon the
eye is imposed by the receptive mechanism; and their pos-
sibilities in initiating chemical changes are determined by
the sensitizing substances used. The most widely appli-
cable method of exploring the spectrum is by heat effects.
Direct optical methods can be applied to only about three
or four per cent, of the wave-lengths actually measured ;
and as yet photography is much more limited than the
method of exploration developed by Langley, which depends


on changes produced by small variations in temperature due
to absorbed heat. The only difference between heat and
light objectively is not a fundamental one, but at most
only a difference of wave-length.

It is known that there are waves too short to produce
vision, and these have heat energy, though it is small in
amount and difficult to measure. There are other waves
too long to excite the eye, and they represent more energy
than those lying within the range of vision. But all waves
of ethereal commotion are propagated by the same physical
process. Waves which are too long to excite vision may
yet warm our bodies, or give rise to electromagnetic or
electrical phenomena.

The distinguishing characteristic of radiant heat is that
it travels through any uniform medium in straight lines or
rays like light, for it is intercepted by a screen in the same
manner as light. It is also reflected in accordance with the
same laws as light, for the focus of a mirror for radiant
heat is the same as its focus for light. It is not propagated
instantaneously, but its speed in a vacuum is identical with
that of light. This is demonstrated by the simultaneous
disappearance and reappearance of the light and heat at
the time of a solar eclipse. In fact, since radiant heat and
light are absolutely identical throughout the visible spec-
trum, it follows that all the physical laws which have been
demonstrated to hold for light must also apply to radiant
heat, for none of these laws depend on wave-length.




7. Definition of Temperature. The words hot and
cold are primitive ones, and refer to our impressions
received through the sense of heat. It is now generally
conceded that this sense is independent of the sense of
touch, with which it has often been confused. When we
are warmed by radiation from a fire, or by the rays of the
sun, this change of physical condition is made known to us
as a sensation received through a specialized sense-organ,
which is distinct from the visual sense, but more closely
related to it than to that of touch or smell, since the
impressions of warmth and of light are both excited by the
same radiations from a hot body.

When the surface of our bodies is brought into contact
with other bodies, they may give to us the feeling of either
coldness or hotness, and we may be able to assert that one
body is hotter than another. By means of these sensations
we might arrange a collection of bodies of the same kind in
a series of relative hotness, and should be able to assert
that any one of them is hotter than all others which we
place below it in the series. This order of hotness is scien-
tifically expressed by means of the word temperature. The
body which gives to us the sensation of superior hotness is
said to be of a higher temperature than another of the same
kind which feels cooler.

If now one of two bodies of equal hotness be heated by

10 HEAT.

a flame, we ascribe its rise of temperature to tlie possession
of a larger amount of what we call heat. This simple in-
ference is entirely justifiable, and is independent of any
theory of heat. Imagine, now, this heated body placed in
contact with a cooler one. We can readily determine that
the hotter one becomes cooler and the cooler one hotter ;
and if sufficient time be allowed, the process continues till
both are of the same temperature. Hence we say that in
the attainment of this equilibrium heat has passed from the
hotter body to the cooler one. This inference is justified
by the fact that the application of heat to a body without
change of state makes it feel hotter. Hence, temperature
may be denned by reference to this phenomenon of the
transfer of heat as follows : Temperature is the thermal
condition of a body ivhich determines the transfer of heat
between it and other bodies. If two bodies, A and B, are
placed in thermal communication with each other, one of
three results will 'follow : A will become cooler and B
warmer ; B will become cooler and A warmer ; or neither
will change in relative hotness to the other. In the first
case the temperature of A is said to be higher than that
of B; in the second the temperature of B is higher
than that of A ; and in the third their temperatures are
equal, and the two bodies are said to be in thermal equi-

Temperature is analogous to pressure of gases. If t\vo
vessels in which air has been unequally compressed are
made to communicate with each other, air is forced from
the vessel of higher pressure to the one of lower pressure
till an equilibrium of pressures has been established. The
direction of the flow is determined entirely by pressures
and not in the least by the relative volumes of the two


Temperature may be compared to potential in elec-
tricity, where the flow is from places of higher to places
of lower potential. Similarly heat flows from bodies of
higher to bodies of lower temperature.

The sense of heat is, however, a very unreliable means
of determining relative temperatures. It may be totally
misleading when the comparison is made between bodies
of different kinds, having different capacities for heat and
different conductivities. Aside from this source of unrelia-
bility, the sensations cannot be made an accurate measure
of physical properties. In the most favorable cases the
judgment can only be trained by frequent .comparison
with the data furnished by the use of a unit of measure.
It is necessary, therefore, to have recourse to some physical
change produced by heat for the construction of an in-
strument to serve as an accurate measure of temperature.

8. Expansion. One of the most familiar changes due
to the increase of the temperature of a body is its increase
of volume, or expansion by heat. This physical change is
the one commonly employed to measure temperature.

With but few exceptions, an increase in the temperature
of a body is attended by an increase in volume. Thus the
rails of a railway are not laid in contact end to end in cold
weather, but a small space is left for expansion by heat.
The tire of a wagon wheel is put on hot, and it shrinks
and compresses the wheel on cooling. GravesancTs appa-
ratus consists of a metallic ball which closely fits a ring of
the same material when both are at the same temperature.
If now the ball be slightly heated, it will expand to such
an extent that it will no longer pass through the ring.
Clocks and watches, unless carefully compensated, have a
slower rate when warm than when cold. This change in


rate is because the pendulum increases in length with
temperature, or the vibrating parts have their moments of
inertia increased by linear expansion.

A very interesting illustration of expansion is furnished
by the creeping downward of heavy metal roofs. If they
are free when they expand by heat they expand downward
because gravity aids this movement ; but when they con-
tract again in cooling, the upper edge is pulled in. The
result is that the metal sheet has the motion of a common
earthworm, and creeps down the incline by alternately
pushing forward its lower edge and drawing its upper one
after it. In this way the sheet lead covering the choir of
Bristol cathedral is reported by Tyndall to have crept
downward at the rate of nine inches a year.

Liquids and gases expand in volume only. Their appar-
ent dilatation is the difference between that of the gas or
liquid and the containing vessel. If a liquid and its en-
velope expanded at the same rate, the liquid would show
no relative dilatation and could not be employed in the
construction of an instrument for measuring temperature.
Let a large glass bulb, or a small Florence flask with a
long narrow stem, be completely filled with water up to a
convenient point on the stem. On suddenly plunging the
flask into hot water the liquid in the tube will at first de-
scend, but as soon as the heat penetrates into the Ijquid
the index in the stem will stop moving downward and will
then begin to ascend. The envelope first expands by heat,
its increase of volume being indicated by the apparent
shrinkage of the water ; but finally the dilatation of the
water exceeds that of the glass and the index rises. The
movement of the index in the stem indicates then only
the apparent expansion of the liquid, or the excess of its
expansion over that of the glass envelope. This relative



expansion of a liquid contained in a glass envelope is the
phenomenon most commonly employed in the thermometer,
the instrument to measure temperature.

9. The Mercurial Thermometer. - - The mercurial
thermometer consists of a closed capillary glass tube ter-
minating in a bulb or reservoir of a cylin-
drical, spherical, or other form (Fig. 1).
The bulb and a part of the stem are filled
with mercury ; the remainder of the stem
contains only the vapor of mercury. A
cylindrical bulb is preferable to a spherical
one because the mercury then exposes a
larger surface relative to its mass, and so
acquires more promptly the temperature of
surrounding bodies. A small change in
the volume of the mercury in the bulb is
readily indicated by the motion of the end
of the column in the narrow stem.

All such an instrument can do is to in-
dicate its own temperature ; but if it is in
sufficiently intimate contact with another
body, as when it is immersed in a liquid,
it may indicate also the temperature of this
other body with which it is in equilibrium.

Online LibraryHenry S. (Henry Smith) CarhartPhysics for university students (Volume 2) → online text (page 1 of 28)