Physics for university students (Volume 2) online

woollen cloth or embedding in sawdust.

6O. The Experiment of Ingenhausz. One of the
earliest methods of comparing the thermal conductivities of



TRANSMISSION OF HEAT. 93

metals was suggested by Franklin and executed by Ingen-
hausz over 100 years ago. A number of rods of the same
length and diameter were fitted into the side of a long
trough (Fig. 26). The external portions were thinly coated
with wax. Hot water or hot oil was then poured into the
trough, and the distances to which the wax was melted on
the several bars was measured after their temperatures had
attained a permanent state. The relative rates at which
the wax is melted at first on the several rods are not the
same as their relative conductivities for heat. The rods on
which the wax melts most rapidly are not necessarily the
ones on which the melting finally
proceeds the farthest. If all the
rods had the same conductivity, or
transmitted the same quantities of
heat in unit time, the temperatures
of the rods would then be inversely
as their densities and specific heats.
On prolonged immersion the rods Fi 26

reach a permanent state, and all

the heat entering them by conduction leaves them by
convection and radiation. The rate of flow must be dis-
tinguished from the rate of rise of temperature. The
wave of temperature travels faster in bismuth than in
iron, but the thermal conductivity of iron is much greater
than that of bismuth. While the density of bismuth is
somewhat greater than that of iron, its specific heat is
only about one-fourth as great ; and though the heat reach-
ing it is smaller, its temperature rises more rapidly.

The thermal conductivities of the several rods will not be
directly proportional to the lengths on which the wax has
been melted after prolonged immersion, but to the squares
of those lengths, if the rods have the same rates of radiation.




HEAT.



61. Coefficient of Thermal Conductivity (M., 253;
P., 509; B., 334; G., 168; S., 271). The precise
meaning of the expression coefficient of thermal conductiv-
ity, or specific thermal conductivity, may be best obtained
by considering the transmission of heat through a homo-
geneous wall with plane parallel faces, one of which is
maintained permanently at a temperature t and the other
at t'. Let AB and CD (Fig. 27) be the two parallel faces
of the wall, and let the line AB represent the temperature
of one side and CD that of the other.
Since the temperatures are maintained,
there will be a permanent state and a uni-
form flow of heat across the wall in the
direction AC. Then if the conducting
power of the wall is independent of its
temperature between t and t', the flow of
heat will be uniform ; and it may be
taken as established by experiment that
the quantity of heat traversing any im-
aginary plane EF in the interior of the
wall is proportional to the temperature
difference t t'. The rate of flow across
any section of unit thickness perpendicular to the faces of the
wall will therefore be inversely as the thickness of the wall.
The rate at which the temperature falls from one side of
the wall to the other, or the temperature gradient, will
then be uniform, and will be represented in the figure by
the slope of the line BD. The total flow of heat through
any area S of the wall of unit thickness in time T will be
proportional to S and to T. Consequently we have for the
quantity H which flows through area S and thickness e in
time T




27.



TRANSMISSION OF HEAT. 95

The coefficient K is the specific thermal conductivity
and depends on the nature of the substance. It may be
defined as numerically equal to the quantity of heat which
flows in a unit of time through unit area of a plate of unit
thickness when unit difference of temperature is main-
tained between its faces. If the temperature is measured
in Centigrade degrees, the dimensions in centimetres,
and the time in seconds, the quantity of heat will be in
calories.

The practical methods of measuring thermal conductivi-
ties are not applied to such a wall, but to the flow of heat
along a bar, one end of which is maintained at a constant
temperature and the other is at the temperature of the
room. The temperature gradient will then be represented
bv the tangents to a curve obtained by measuring the tem-
peratures at equal distances along the bar. The heat
flowing past any cross-section of the bar is all dissipated
from the surface beyond the section. The relative con-
ductivities of two bars can be determined by obtaining
their temperature gradients ; but to measure the absolute
conductivity another experiment is necessary for the
purpose pf finding the rate of cooling, so as to be able to
calculate the total quantity of heat traversing any section
of the bar.

62. Comparison of Thermal and Electrical Con-
ductivities. The order of conductivities for the pure
metals is the same for heat as for electricity, though the
relative values of these conductivities are not the same in
the two cases. Both these facts are clearly displayed
by the following table, in which the electrical conductivi-
ties are those of Lenz and the thermal conductivities those
of Wiedemann and Fran/. :



96 HEAT.

Names of metals. Electrical conductivity. Thermal conductivity.

Silver 100.0 100.0

Copper 73.3 73.6

Gold 58.5 53.2

Brass 21.5 23.6

Tin ' . . 22.6 14.5

Iron 13.0 11.9

Lead 10.7 8.5

Platinum 10.3 6.4

Bismuth 1.9 1.8

A further question of much interest is the change of
thermal conductivity with increase of temperature. The
electrical conductivity of all the metals diminishes with
increase of temperature. The same law applies to the
thermal conductivity of iron. Matthiessen found that
the electrical conductivity of iron decreased 38.26 per cent
between and 100 C. Forbes found a thermal decre-
ment for iron between the same limits of temperature of
24.5 per cent in one case and 15.9 in another. But Tait
has shown that Forbes overlooked the large change in the
specific heat of iron with change of temperature ; and when
allowance is made for this, the variation in the thermal
conductivity obtained by Forbes is reduced to about -J- of
the original value.

Professor Tait has shown that the thermal conductivity
of iron reaches a minimum somewhere about red-heat;
also that copper and lead show a much smaller change
with change of temperature than iron does, and that this
change is an increment rather than a decrement. Mitchell
has recently repeated the measurements with the same
bars nickel-plated, so as to preserve the surfaces from
oxidation at high temperatures, and he found the tempera-
ture coefficient for iron to be positive, as it is for the other
metals examined.




OF HEAT. 97

63. Conduction in Wood and Crystals (Tyn., 189).
- Tvndall has shown that in thirty-two kinds of wood

investigated heat is conducted much better along the
fibres than across them. Further, the conductivity per-
pendicular to the fibres and to the ligneous layers or rings
is greater in every case than in a direction tangential to
them. The conductivity in the first of these three rectan-
gular directions is from two to four times as great as in
the last.

A similar difference of conductivity
has been found in the case of lami-
nated rocks, conduction being better
along the .planes of cleavage than
across them. The same statement
may be made with regard to bismuth.

If two plates be cut from quartz
crystals, one perpendicular to the rig 28

crystallographic axis or axis of sym-
metry, and the other parallel to it, and if a minute hole be
made through each plate for the admission of a fine wire
which can be heated by an electric current, then a film of
wax on the plate of crystal will be melted in the form of a
circle when the section is at right angles to the axis, but as
an ellipse when the section is parallel to the axis (Fig. 28).
Quartz and calc spar conduct heat best along the axis and
equally in all directions perpendicular to it, while tourma-
line conducts best at right angles to the axis.

64. Conduction by Liquids (P., 557). If a liquid
be heated at the bottom, the expansion by heat diminishes
the density and convection currents are set up. The heat
distributed by convection masks any distribution by con-
duction. This difficulty has been overcome in part by




98



HE A T.



heating at the top. Even then the results are complicated

with diffusion and with conduction by the containing

vessel.

All liquids except molten metals are poor conductors.

The upper strata of water in a test-tube may be boiled for

some time without melting a lump
of ice confined at the bottom of
the tube. If a simple air-thermom-
eter have its bulb surrounded by
water in a funnel (Fig. 29), and
if alcohol be burned in the small
porcelain or platinum crucible at
the top, it will be found that the
thermometer is scarcely affected,
even though its bulb be near the
surface of the water. So feeble
is the flow of heat through liquids
that the result is always open to
the suspicion that the transport is
accomplished by diffusion and con-

J^TEfJ vection.

^7 No very concordant results have
ever been obtained. The best
agreement is perhaps the follow-




Fig. 29.



ing, where
units :



the conductivity is calculated in C.G.S.



Substance. Temperature.

Water 40.8 C.

Salt solution, density 1.178 . . 43.9
Zinc sulphate, " 1.382 . , 45.3



CONDUCTIVITY.
Lundquist. Weber.

0.00156 0.00159
0.00149 0.00150
0.00144 0.00145



65. Conduction by Gases. - The difficulties encoun-
tered in measuring the conductivity of liquids are exagger-



TKAXS.VTSSIOX OF If EAT. 99

atecl in the case of gases, so that they become almost
insuperable. Many familiar facts, however, go to show
that heat is conveyed very imperfectly by gases, except
under conditions favorable to convection. The interstices
filled with air in bodies made of wool, hair, feathers, fur,
and some vegetable fibres, render them poorer conductors
than when they have been compressed so as to diminish
the air spaces. So some solids which conduct fairly well
are very poor conductors when reduced to a powder,
because of the interstices containing air.

The dynamical theory of heat leads to the conclusion
that the coefficient of conductivity for air is 0.000055, or
about sinjoT) that f copper ; also that the coefficient for
hydrogen is 7.1 times as great as for air. These conclu-
sions have been approximately verified. But this theory
does not demonstrate that gases conduct heat in the same
sense as do solids, for it is based on molecular convection,
or the energy transferred by the exchange of motion
among molecules when they collide.

66. Convection in Liquids. The distribution of heat
by currents of warm water may be illustrated by heating
a large beaker filled with water and containing some bits
of cochineal. A stream of warm water will be observed
ascending along the axis above the burner, and currents
of cooler water descending along the sides. Faraday's
apparatus to illustrate convection currents is shown in
Fig. 30. If the flask and connecting tubes are completely
filled with water above the open end of the tube AB, the
water will begin to circulate up AB and down CD as soon
as heat is applied to the flask by means of a Bunsen
burner. To make the circulation visible, the liquid in the
flask mav be colored red with some aniline dye, and that



100



HEAT.



in the large open tube at the top may be colored bine.
The red liquid will ascend and the blue one descend.

This experiment illustrates the method of heating by
hot water. A pipe rises from the top of the boiler to an
expansion tank in the upper part of the
building. From this tank the water is
distributed through the several radiators,
and finally again enters the boiler at the
bottom. The water loses heat in the
radiators and so becomes denser. The
heat of the boiler and the loss by radiation
and convection at the radiators produce
unequal hydrostatic pressures, which give
rise to continuous currents so long as the
heat is applied.

The Gulf Stream, even though it may
be largely produced by wind, is a convec-
tion current on a gigantic scale, and it
transports enormous quantities of heat
from the equatorial regions and distributes it over the
British Islands and the western part of the continent of
Europe. A stream of cold water flows south from Green-
land and washes the Atlantic coast of America. Hence
the contrast between the climate along the Hudson and
the Tiber.

67. Convection in Gases. Since the mobility of
gases is greater than that of liquids, convection currents
are all the more easily set up in them. The heated air
over a gas flame or a fire rises rapidly, and its place is
supplied by the inrush of cold air from the sides. The
same action goes on near the sea-coast on a large scale.
The ground is heated by the sun, and it in turn heats the




Fig. 30.



TRANSMISSION OF



101



air in contact with it. The heated air rises and the cooler
air from the sea flows landward to take its place, giving
rise to the sea-breeze. As soon as the sun sets the ground
cools rapidly by nncompensated radiation and the air
above it becomes cooler than that over the sea. Hence
the pressure is outward from the land, and the land-breeze
sets in.

Under the vertical rays of a tropical sun the earth and
the atmosphere are highly heated; the latter expands,
rises, and overflows toward either
hemisphere. The denser air flows
in from north and south to replace
the ascending mass. This inflow
has the velocity toward the east of
those parts of the earth's surface
from which it comes. This is less
than the velocity at the equator.
Hence, the currents of air approach-
ing the equatorial belt lag behind the
rotating sphere and arrive as north-
east and southeast Trade Winds.

A belt of calms advances a few
degrees toward the north in summer,
while in winter it recedes somewhat toward the south, fol-
lowing the declination of the sun. The overflow north and
south veers toward the east by reason of its greater eastern
velocity than the successive points at which it arrives. It
therefore constitutes the southwest and the northwest
upper trades, which gradually sink toward the earth.

The principle of convection explains ventilation. The
heated air in a chimney rises because it is warmer than
the air without. The external pressure is therefore only
partly counterbalanced by that of the air in the flue. If




31.



102



TIE A T.



the chimney happens to be colder than the external air,
there is a downdraft, or the chimney smokes.

Place a lighted candle at the bottom of a lamp chimney.
Ingress of air at the bottom may be prevented by pouring
a little water in the outer dish (Fig. 31). The flame soon
goes out for lack of air. If the T-shaped partition be now
inserted in the chimney and the candle be relighted, it
will continue to burn ; and if a piece of smouldering brown
paper be held over the tube, the smoke will descend on
one side of the partition and ascend on the
other, a true convection current supplying
oxygen to the candle and carrying off the
products of combustion.

68. Convection by Hydrogen. The rapid
distribution of heat by hydrogen was the sub-
ject of a celebrated experiment by Dr.
Andrews. A thin platinum wire, which
could be heated by an electric current, was
stretched along the axis of a tube. The corks
at the ends were provided with an inlet and
an outlet tube (Fig. 32.) When the tube
was exhausted of air, the current was ad-
justed so as to heat the wire to vivid bright-
ness without fusing it. The introduction of
I n air diminished the brightness of the wire

somewhat ; but when the tube was filled with
hydrogen the wire was scarcely red hot. In
a vacuum the wire loses heat almost entirely
by radiation, but in an atmosphere of hydro-
gen, even though it be very attenuated, the
light and rapidly moving molecules carry

frequent cargoes of heat from the wire to the cooler walls

of the tube.



Fig. 32.



JV OF HEAT. 103



The slow rate of cooling of a heated platinum wire in
an exhausted globe, as compared with its rate in the open
air, illustrates the loss of heat by convection currents.
The wire remains visible for a sensibly longer time in a
vacuum than in the air after the heating current of elec-
tricity is cut off.

The incandescent lamp is ordinarily made with a high
vacuum to avoid the loss of heat by the convective pro-
cess. For this reason an inert gas like nitrogen cannot be
used in the bulb, because the energy is then rapidly con-
veyed from the filament to the envelope, and heats it at
the expense of the brightness of the filament. The glass
globe heats to a still higher temperature when the carbon
filament is enclosed in an atmosphere of hydrogen. Hydro-
carbon gases have sometimes been used in glow lamps
because of their reparative function when decomposed by
heat, since they deposit carbon on the filament as an offset
to the waste going on in the normal operation of the
lamp.

PROBLEMS.

1. How many calories of heat will be conducted in one hour
through an iron plate one metre square and 0.3 cm. thick if the two
sides are kept at the temperatures and 60 C., the coefficient of
conductivity of iron being 0.175?

2. One side of a brass plate 1 cm. thick and 100 sq. cms. in
area is kept in contact with boiling water on one side and with melt-
ing ice on the other; it was found that 22.9 kilos, of ice were melted
in. 10 minutes. Find the coefficient of conductivity of brass in C.G.S.
units.

3. How much water will be evaporated per hour at 100 C. from
a boiler 0.5 cms. thick and with a heating surface of 1,000 sq. cms.,
its outer surface being kept at 150 C. ?

4. A plate of glass 2 cms. thick and 3X4 metres in area sepa-
rates two rooms which are kept at 15 and 50 C. respectively. If
the coefficient of conductivity of the glass is 0.015, find the quantity
of heat given oft* per minute by the glass.



104 HEAT.



CHAPTER VIII.

RADIATION AND ABSORPTION.

69. Appliances for the Study of Radiation. - The
physical identity of radiant heat and light has already been
dwelt upon in an earlier chapter (6). The transmission of
heat-energy through a medium without affecting it is an
operation identical with that of the transmission of light ;
but since radiations of longer wave-length than about 7,600
tenth-metres (I., 217) do not excite vision, the study of
radiations of long wave-length falls within the domain of
Heat ; for to produce any effect these radiations must first
be absorbed, and by this process energy is imparted to the
substance on which they fall. The most general effect of
this absorption is heat.

In light the effects are directly visible, but we need some
means of recognizing the presence of those radiations which
do not excite vision.

Since most substances exhibit the same selective prefer-
ence in the absorption of radiation generally, as they do for
those wave-lengths which lie within the visible spectrum
and give rise to color, it becomes of prime importance in
studying heat effects to find some substance which will
absorb all radiations alike. Such a substance is lampblack.

A thermometer with a blackened bulb is sufficient for
many purposes in the study of radiant heat. A still more
sensitive receiving apparatus is the thermopile, which will




JlADIATIOy A.\l> ABSORPTION. 105

be fully described later. It will be sufficient to explain
here that if a junction of two dissimilar metals, such as
antimony and bismuth, be heated, an electromotive force
will be generated, which will give rise to a current through
a closed circuit. If a number of thin bars of the two
metals, alternating with each other, be joined together and
arranged so that the alternate junctions all fall on one side
of a cube, as in Fig. 33, then when this
face is heated a current will flow through
the circuit and it will be indicated by an
appropriate galvanometer. If the same
face be cooled, a current will flow in the
reverse direction.

Boys' radiomicrometer consists of a single Fi 33

thermal junction and a galvanometer com-
bined in one instrument. 1 It has been made so sensitive
as to indicate readily the heat radiated from a candle on
the opposite side of a large hall. In both instruments the
receptive portion must be covered with lampblack.

7O. Invisible Radiation reflected like Light. The
essential identity of radiant heat and light becomes evident
when it is demonstrated that the various phenomena of
optics may be reproduced by those radiations which do not
directly affect the eye. Aside from the simplest observa-
tion that radiant heat like light travels in straight lines
through a uniform medium, the most obvious analogy
between the two is found in their common obedience to
the law of reflection.

Let two large concave mirrors, usually of brass or
copper, be placed several metres apart and facing each

1 Preston's Theory of Heat, p. 497.



106 HEAT.

other, as in Fig. 34. If a caudle be placed at the principal
focus of one mirror, the two may be adjusted in position,
and the image of the candle may be found at the focus of
the second one by means of a small piece of white paper.
Then if the candle be replaced by a heated iron ball, and
the blackened face of the thermopile be placed where the
image was found, the galvanometer will at once show that
the thermopile is heated. The largest effect Avill be
obtained when the face of the pile is exactly at the focus
previously found. The reflection of the non-luminous
rays from the two mirrors takes place in the same manner





Fig. 34.

as that of the luminous rays, for they converge to the
same point. If the ball be heated to a dull red, the con-
vergence of the heat at the focus of the mirror may be
readily ascertained by the hand. The thermopile will
detect it when the ball has cooled to such an extent that
it may be held in the fingers.

In connection with this apparatus, attention may be
called to the fact that if the ball be replaced by a piece j
of ice the current through the galvanometer will show
that the thermopile is cooled. The significance of this \
fact will appear later.

It lias been demonstrated by experiment that
(1) Radiant heat is reflected copiously from metals in *
the same manner as light.



UM)IAT10\ AXD ABSORPTION.



107



(2) When radiant heat is reflected, either from glass or
polished metals, the variation of the intensity with the
angle of incidence follows the same law as that applying
to light ; that is, the percentage of the incident radiation
which is reflected increases with the angle of incidence.
Thus glass, which at normal incidence reflects only 4.3 per
cent, at 88 reflects 81.9 per cent of the incident radiation.

(3) Heat is diffusely reflected in the same manner as
light. Just as diffusion is selective for light, red flannel
for example appearing brilliantly red in the less refrangible
end of the spectrum and black in the green (I., 219), so,
as Melloni showed, diffusion is selective also for, the non-
luminous radiations.

71. The Law of Inverse Squares. Melloni was the
first to perform an ingenious experiment to demonstrate
that the thermal radiation received by any small area
varies inversely
as the square
of its distance
from the source.
BC (Fig. 35)
is a shallow box
filled with hot
water and hav-
ing its anterior
face covered
with lampblack.
A is a thermopile with a converging cone to concentrate
the radiations on its blackened face. Let it be placed
in the position A, and let the resulting deflection of
the galvanometer be noted ; then let the thermopile be
moved tu double the distance from the box at A. The




Fig. 35.



108 HEAT.

galvanometer will indicate the same current as before.
The radiating surfaces in the two cases are the bases of
the dotted cones. Their linear dimensions are as one to
two and their areas as one to four. Since the radiation
from a four-fold area produces the same effect at twice
the distance, the intensity of the radiation received from
any small area must vary inversely as the square of the
distance. Since the radiating surface increases as the
square of the distance, the intensity of the radiation must
diminish as the inverse square of the distance. In the
same way a uniformly red-hot surface, viewed by the eye
through a tube, appears equally bright at all distances, so
long as the surface fills the field of view through the tube.

72. Refraction of Radiant Heat (S., 196). Herschel
made the observation that there are dark heat-radiations