Physics for university students (Volume 2) online

Small furnaces for fusing, vulcanizing, and enameling
in the operations of dentistry are also in use. For such
purposes electric heating offers a wide field of appli-
cation.

4. Electric Welding. If the abutting ends of two rods
are pressed together while a large current passes through
them, enough heat is generated at the junction where the



THERM A L EEL A TIONS.



291



resistance is greatest to soften and weld them. This
method has been perfected by Elihu Thomson, who em-
ploys several hundred amperes in some
. but under a low electric pressure.
Fig. 118 shows three small welded
joints.

Similar devices are now employed for
the local annealing of armor plates ; the
metal is in this way softened at points
where it is to be drilled.




Fig. 118.



238. The Electric Arc. In 1800
Sir Humph re}' Davy discovered that if
two pieces of charcoal, connected by
suitable conducting wires to a powerful
voltaic battery, be brought into contact
and be then separated a slight dis-
tance, brilliant sparks will pass be-
tween them. But no mention was made of the electric
an- till 1808. In 1810 Davy exhibited the arc light at the
Rnval Institution.

With a battery of 2,000 simple elements, when the car-
bons were drawn apart to a distance of several inches, the
carbon was apparently volatilized, and the current was con-
ducted across in the form of a curved flame or arc. A
brilliant light was emitted at the same time by the white-
hot carbon electrodes, which rapidly burned away, unless
they were enclosed in a vacuum. Foucault surmounted
this difficulty in 1844 by making use of the dense carbon
from a gas retort in place of the wood charcoal pencils.

When the carbon points are separated the heat due to
the current volatilizes some of the carbon, or the volatile
constituents not expelled by previous baking, and this



292



ELECTRICITY AND MAGNETISM.



carbon vapor conducts the current across. The passage of
the current heats the carbons to vivid incandescence. Since
gases are poor radiators, the dazzling light is emitted
chiefly by the carbon electrodes and especially by the posi-
tive one. In it is formed a small cavity by the transport
of carbon across to the negative. According to Violle, the
temperature of this cup-shaped depression, or crater, is
about 3,500 C. It is the temperature at which carbon
volatilizes. The positive carbon wastes away about twice

as fast as the negative. The
appearance of the two carbon
pencils is shown in Fig. 119.

The resistance of the elec-
tric arc may be only a fraction
of an ohm. It is not large
enough to account for all the
heat developed; but the crater
in the positive appears to be
the seat of a counter E.M.F.
of about 39 volts for a quiet
arc. Hence a potential dif-
ference of from 40 to 45 volts
is necessary to maintain a
steady arc without hissing.
The large quantity of heat generated is due to the fact
that the current encounters an opposing E.M.F. at the
arc, and energy is in consequence transformed into heat.

239. The Carbon Filament. In the incandescent
system of electric lighting the heat is due to the simple
resistance of a thin carbon filament. Carbon is the only
substance thus far found to be available, because it does
not fuse and has a high radiating power.




Fig. 119.



Tfl ER MA L E EL A Tin \ 8. 293

The filament is made of a variety of materials, including
certain vegetable fibres, silk, and parchmentized cotton
thread. After preliminary treatment it is carbonized by
raising to a cherry-red heat out of contact with the air. It
is thru surrounded by an atmosphere of rarefied hydro-
carbon vapor, and is raised to a white heat by a current.
The heat decomposes the vapor, and the carbon residue is
deposited in a dense form on the filament. By this treat-
ment it acquires a hard, steel-gray surface and greater
uniformity. Its durability is thereby greatly increased.

The filament is finally mounted in an exhausted glass
globe and provided with convenient external terminals.
The vacuum prevents oxidation and loss of energy by heat
convection.

The temperature to which the carbon filament can be
raised is limited by volatilization, and by a tendency of the
carbon to disintegrate at high temperatures. This disin-
tegration rapidly reduces the thickness of the filament and
blackens the glass bulb.

A 100-volt. 16-candle-power lamp has a resistance hot of
about '200 ohms. The current is then half an ampere, and
each lamp transforms into heat 50 watts, or three and one-
eighth watts per candle. A 50-volt lamp of the same candle
power has only one-quarter of the resistance and takes
double the current for the same candle power.

*- V

240. Thermal Electricity. AVhen heat is applied to
the junction of two dissimilar substances an E.M.F. is pro-
duced, which will cause a current to flow across the junction
from the substance of lower potential to the one of higher
if there is a closed circuit. This phenomenon is the con-
verse of the generation of heat by a current. It was
discovered by Seebeck in 1821 or 1822. If a circuit be



294 ELECTRICITY AND MAGNETISM.

formed of an iron and a copper wire, and if the tempera-
ture of one of the junctions be raised above that of the
other, a current will flow across the warmer junction from
copper to iron.

The heated junction is the seat of an E.M.F. of such
direction that the iron is at a higher potential than the
copper. A current therefore flows around through the cir-
cuit from the warmer iron across the cooler junction and
back to the warmer copper. Across the warmer junction
the current flows from lower to higher potential.

The dissimilar substances composing a thermo-electric
pair may be either two metals, a. metal and a liquid, two
liquids, or even two pieces of the same metal at different
temperatures or in different physical states.

241. Neutral Temperature. The E.M.F. of a thermal
element is small, and depends not only on the temperature-
difference of the two contacts, but on the absolute values
of their temperatures. Every combination of two metals
appears to have what is called a neutral temperature. It
is the mean of the temperatures of the two junctions when
the electromotive forces at the two are equal and in oppo-
site directions round the circuit. For this neutral tem-
perature there is therefore no current. For silver and iron
the neutral temperature is 223.5 C. ; for copper and
iron it is 274. 5 C. When the mean temperature is above
the neutral temperature for the two substances, the current
is reversed. If ^ and t, are the temperatures of the two
junctions, there is no current when ^ equals ,, and none
when J (1 + Q equals the neutral temperature.

If an iron and a copper wire be twisted together and
their free ends connected to a galvanometer, moderate
heating of the twisted junction will cause a current to flow



Til EH .V. I L /,' EL . 1 770 .V 8.



across it from copper to iron ; but if the junction be heated
to a dull red, the galvanometer will indicate a reversal of

the current.

242. Variation of Thermal Electromotive Force with
Temperature. If one junction of a thermal couple, such
as iron and copper, be kept at a fixed temperature, while
that of the other is gradually raised, tin- E.M.F. increases
to a maximum, then diminishes,
at length vanishes, and is finally
reversed. AVith most pairs of
metals, if the temperatures be
plotted as abscissas and the
electromotive forces as ordi-
natrs, the result will be a para-
bola with its axis vertical (Fig.
120). If. therefore, e denotes
the E.M.F. and t' the tempera-

Fig. 120.

ture, and if E and T denote

the E.M.F. and temperature corresponding to the vertex

of the parabola, we obtain




where k is a constant. This equation expresses the prop-
erty of a parabola that the square of the distance of any
point from the axis is proportional to the distance of the
same point from the tangent through the. vertex. The
curve in the figure is drawn for the case where the tem-
perature of the one junction is zero. If it be above zero,
the parabola corresponding will have the same axis as this
one, but will lie below it. The temperature corresponding
to the maximum ordinate will be the same. It is the
neutral point for the given pair of metals.

In particular cases the curve is a straight line ; in others



296



ELECTRICITY AND MAGNETISM.



it is made up of parts of parabolas, with their axes parallel,
but with their vertices turned alternately in opposite direc-
tions (Peddie).

243. Thermo-electric Diagram. - - The relation be-
tween E.M.F. and temperature just described led Lord
Kelvin and Professor Tait to adopt an elegant method
of constructing a thermo-electric diagram. The t.hcrmo-



-1-15

+10

+5


-5
-10
-15



100



200



400



500 C



ecxr



electric power of any couple is the E.M.F. corresponding to
a temperature difference of one degree between the two
junctions. It is, in other words, the rate of variation of
the E.M.F. with temperature. By a simple application
of the Differential Calculus to the equation of the last
article, we obtain for this rate of variation,

= 2b(Tt\

at

This expression represents the thermo-electric power, and
it is the equation of a straight line. If then this line for



THERMAL RELATION*. -97

some standard metal be made to coincide with the axis of
temperature, the lines obtained from observations on couples
of other metals with it will in general be straight lines ;
taken together, these lines form a thermo-electric diagram.
The point of intersection of any pair of lines corresponds
with the temperature of maximum E.M.F. for this pair of
metals. Thus the copper-iron lines cross at 274.o ; this is
therefore the temperature at which the thermo-electric
power of these metals becomes zero. It is also the neutral
temperature for the pair. Fig. 121 is the thermo-electric
diagram for several metals compared with lead. The inter-
sections of some of these lines lie beyond the limits of
Tait's experimental diagram. The palladium-copper lines
if produced would meet at 170 C. Dewar and Fleming
have found, by means of the low temperature obtained by
liquid oxygen, that thermo-electric inversion for this pair
does occur at about 170.

244. Electromotive Force in the Thermo-electric
Diagram. From the manner in which a thermo-electric
diagram is constructed, it follows that the E.M.F. between
any pair of metals between two temperatures is equal to
the area of the figure included between the ,ordinates cor-
responding to those temperatures and the thermo-electric
lines of the metals. Thus, if the cooler junction of a
copper-iron couple be at 100 and the warmer at 200,
the effective E.M.F. in the circuit will be represented by
the area abed ; but if the warmer junction be at 400, the
E.M.F. will be equal to the difference of the areas abn and
iSd'n. If the triangle above the intersection n be larger
than the one below , the E.M.F. will be reversed.

The ordinates represent thermo-electric powers. But

de/dt = Thermo-electric poiver,
and therefore de = Thermo-electric power x dt.



298 ELECTRICITY ANL> MAGNETISM.

Now de is the small E.M.F. corresponding to a small tem-
perature difference dt, and the second member of the last
equation is a small area whose length is a line ab and whose
width is an element of temperature measured at right angles
to ab. The E.M.F. for any finite temperature-difference
is therefore an area such as abed, which is made up of a
number of small areas corresponding to minute temperature-
differences.

245. Thermo-electric Series. - - A thermo-electric
series is a table of metals showing their thermo-electric
relation to one another. Since the thermo-electric power
depends on the absolute temperature of the junctions, such
a list is good only for some definite mean temperature.
The following series gives the E.M.F. in microvolts
(millionths of a volt) between each metal and lead, witli a
difference of one degree between the junctions when their
mean temperature is 20 C. :

Bismuth 89 Silver + 3.0

Cobalt -22 Zinc + 3.7

German silver . . . 11.75 Copper + 3.8

Mercury 0.418 Iron + 17.5

Lead . . . .^ . . 0.0 Antimony, axial . . + 22.6

Tin +0.1 Antimony, equatorial . + 26.4

Platinum . . . . + 0.9 Tellurium . . . . +502

Gold +1-2 Selenium . . . . +807

When a junction of any pair of these metals is moderately
heated, the current flows across it from the metal standing
higher in the list toward the one standing lower. For the
smaller values of the thermo-electric powers, the results
obtained by different observers are not very concordant.

246. The Thermopile. The E.M.F. of a single ther-
mal element is very small; to get a larger E.M.F. a



THERM A L BE LA TIONS.



299




number of similar couples may be joined in series. With

ti such couples in series the potential difference between

the extreme terminals is n times that of a single couple,

and the internal resistance of the

series is still very low. Fig. 122

shows the method of connecting in

series. If the bars A are antimony

and B bismuth, then heating the

junctions <\ f, , will cause a current

to flow through the circuit in the

direction of the arrow ; but if these

junctions be cooled, or the alternate ones cZ, 6?, be heated,

'the current will circulate in the other direction.

When a number of bars of antimony and bismuth are

soldered together in this way, and packed together in the

form of a cube, with insulating material between adjacent
bars, so that opposite faces of the cube
form alternate junctions, the instrument is
called a thermopile (Fig. 123). If a face
of such a pile be blackened with lamp-
black and be provided with a reflecting
cone, the instrument becomes a sensitive
Fig. 123. detector of radiant heat (69).

247. The Peltier Effect. In 1834 Peltier discovered
the phenomenon which bears his name ; it is an extension
of the discovery of Seebeck. If a bismuth-antimony junc-
tion he heated, the current flows across from the former to
the latter. Peltier discovered that if a current from an
external E.M.F. be sent through such a compound bar from
bismuth B to antimony A (Fig. 124), the junction will be
cooled ; but if it be sent the other way, the junction will
be heated.




300



ELECTRICITY AND MAGNETISM.



The long arrow shows the direction of the current sent
through ; the small arrows at a and b indicate the direction
of the E.M.F. at the junctions. At a the thermal E.M.F.
is in the direction in which the current is flowing. Hence



Fig. 124.

at this junction work is done on the current, and the heat
of the metals is converted into the energy of the current.
At b the thermal E.M.F. opposes the current, which there-
fore does work on the junction and heats it.

The thermal effect at a junction of dissimilar substances
differs greatly from the thermal effect due to simple resist-
ance. The Peltier effect is reversible, the current heating
or cooling the junction according to its direction, while
the quantity of heat evolved or absorbed varies simply
as the current; the heat due to resistance is independent
of the direction of the current, and is proportional to the
square of its strength.

248. Experiment to show the Peltier Effect. Con-
nect one or two Leclanche cells with
a thermopile, as in Fig. 125. S is
a two-point switch. When it is
turned in the direction of the full
line, the battery circuit through the
thermopile is closed and the galva-
nometer circuit is open. When it
stands in the direction of the dotted
line, the battery is cut off and the
rig. 125. thermopile is connected with the




THERMAL RELATIONS. 301

galvanometer. In order to show that the current given
by the thermopile P is opposite in direction to the cur-
rent through it from the battery, insert in the circuit
of the galvanometer at T a copper-iron junction. With
the switch at 6, the current produced by heating this junc-
tion Hows from Cu to Fe^ and the direction of the gal-
vanometer deflection may be noted. Turn the switch for
a moment to a and then back again to b. The galvanom-
eter will show a current coming from the thermopile,
and the direction of the deflection will be the same as
when the junction T was warmed. Hence B must be the
positive and A the negative of the thermopile as a gen-
erator. But the current from the battery enters* the pile
at B and leaves it at A. The thermal effects produced by
the current through the pile are such as to generate a
counter E.M.F.

249. The Thomson Effect. For the
purpose of explaining electric inversion
in such couples as iron and copper, Lord
Kelvin assumed that the Peltier effect be-
comes zero at the neutral temperature.
No heat is then absorbed or evolved at a
junction at this temperature, but heat is
generated at the other junction, since the current there
meets a counter E.M.F. If in Fig. 126 the junction J is
at the neutral temperature T, and J' at a lower temperature
f, the current will flow in the direction of the arrows. At /',
therefore, it flows from Fe to OW, and heat is generated by

the Peltier effect. There is then no conversion of thermal
i

into electrical energy at the junctions ; but since there is
no other possible source of the energy of the current except
heat, Lord Kelvin was led to predict that heat is absorbed




302 ELECTRICITY AND MAGNETISM.

at parts of the circuit other than the junctions. This pre-
diction he subsequently verified by experiment.

In copper heat is absorbed when the current passes from
cold parts to hot parts ; in iron it is absorbed when the
current passes from hot parts to cold parts. This phenom-
enon is called the Thomson Effect, or the Electric Convec-
tion of Heat.

Consider a metallic bar ABC (Fig. 127) heated at the
middle B and cooled at the ends A and 0. Then the dis-
tribution of heat may be repre-
sented by the curve abc. But if
a current be passed from A to
(7, then in metals like copper the
curve of the distribution of heat
becomes somewhat like a'bc'.
Since a current in copper absorbs
heat as a liquid does in flowing

from the cold to the hot parts of a tube, electricity is some-
times said to have specific heat. It is positive in metals
like copper and negative in metals like iron. In lead the
Thomson effect is nearly or quite zero ; it is for this reason
that lead is chosen as the zero line of the thermo-electric
diagram.

25O. Thermo-electromotive Force between Metals
and Liquids. - - The thermo-electromotive forces origi-
nating at metal-liquid contacts have special interest because
of their relation to the temperature coefficient of voltaic
cells. These electromotive forces are larger than most of
those between metals. Thus, the thermo-electric power
of Zn ZnSO is 0.00076 volt for a mean temperature
of 18.5 C. ; that of Cu CuSO is 0.00069 volt for about
the same temperature. In microvolts these are 760 and 690




THERMAL RELATIONS. 303

respectively. Since the metal is positive to the liquid in
both cases, and there is no appreciable E.M.F. at the con-
tact of the two liquids, the temperature coefficient of a
Daniell cell is the difference of the above two thermo-
electric powers, or 0.00007 volt per degree C. It is, more-
over, negative because the thermal E.M.F. on the zinc side
is greater than on the copper side. This conclusion lias
been fully verified by experiment.

The author lias applied the same method of analysis to
other cells, such as the Clark without zinc-sulphate crystals,
and the calomel cell ; the results with all of them show
that the temperature coefficient is determined by the super-
position of the several thermal electromotive forces at the
contacts of the dissimilar substances in the cell, whenever
this coefficient is not complicated by the solution and re-
cr\ stallization of salts. Whether the resultant temperature
coefficient shall be positive or negative depends on the
relative values and signs of the thermal electromotive
forces on the two sides of the cell.

PROBLEMS.

1. The poles of a voltaic cell are joined by two wires in parallel
alike in every respect, except that one is twice as long as the other.
What are the relative quantities of heat generated in the two?

2. The E.M.F. of a battery is 20 volts and its internal resistance
2 ohms. The potential difference between its poles when connected
by a wire ^1 is 16 volts ; it falls to 14 volts when A is replaced by
another wire B. Calculate the number of calories of heat generated
in the external circuit in 3 min. in the two cases.

3. A current of 10 amperes passes through a resistance of 2 ohms
for 14 sec. Find the number of calories of heat generated.

4. The resistances of two wires are as 3 to 4. Find the relative
quantities of heat produced in the same time, (1) when they are
joined in series, (2) when connected in parallel between the poles
of a voltaic cell.



304 ELECTRICITY AND MAGNETISM.

5. A battery has an E.M.F. of 8.5 volts; the total resistance in
the circuit is 20 ohms, including an electrolytic cell. The heat gen-
erated per second in a 5.12-ohm coil included in the circuit is 0.12
calorie. What is the counter E.M.F. of the electrolytic cell ?

6. If one junction of an antimony-bismuth pair be at 20 and the
other at 65 C., what will be the E.M.F. ?

7. A ring is made partly of copper and partly of iron wire.
Compare the E.M.F. if one junction be kept at and the other at
100 C. with the E.M.F. obtained by keeping one junction at 175 and
the other at 275 C.



PROPERTIES OF MAGNETS. 305



CHAPTER XX.

PROPERTIES OF MAGNETS.

251. Relation to Electricity. - - The most important
properties of an electric circuit are its magnetic relations.
Magnetism is more readily and conveniently evoked by
electric currents than by any other means. In fact, von
Siemens said that ic the electric current, or generally elec-
tricity in motion, is the only known source of all magnet-
ism." But the magnetic properties of an electric current
must be studied by means of magnets ; it is, therefore,
necessary that some preliminary study of the properties of
a magnet should precede the study of the magnetic rela-
tions and effects of electric currents.

252. Fundamental Phenomena. Black oxide of iron,
known as magnetite, is widely distributed, and is some-
times found to possess the property of

attracting iron. If a piece of it be sus-
pended by an untwisted thread (Fig. 128)
its longer dimension will point not far
from north and south. Such bodies are
called mac/nets. The property of orienta- 1
tion has been utilized in navigation for
several centuries, and from this fact the
magnet in early times acquired the name of lodestone, or
leading stone.




306



ELECTRICITY AND MAGNETISM.




253. Artificial Magnets. If a piece of hard iron or
steel be stroked with a lodestoiie it will acquire the same
magnetic properties ; fine iron filings will cling to it, and
if suspended it will point north and south. The end which
points northward is called the north-seeking pole and the

s other end the south-

8H. seeking pole ; the
magnet is said to
possess polarity. If
a bar magnet be dipped into iron filings they will cling to
it in tufts near the ends (Fig. 129), but there will be few
or none near the middle. This region is called the equator.
If a long thin rod be magnetized longitudinally the ends act
as centres of force or poles, and the imaginary line joining
these poles is the magnetic axis. The remainder of the mag-
net is apparently nearly devoid of magnetic properties. In
short thick magnets the poles are less definitely defined.

A thin pointed bar of magnetized steel, provided with a
cap having hard steel or agate set in it, so that it may
turn freely on a sharp steel point around a vertical axis, is
called a magnetic needle (Fig. 130).



254. First Law of Magnetic
seeking pole of a bar
magnet be presented to
the N-seeking pole of a
magnetic needle (Fig.
130), they will mutually
attract each other; but
if the N-seeking pole be
brought near the same
pole of the needle, re-
pulsion will be observed.



Force. If the S-





Fig. 130.



The law of attraction and repul-



PEOPEETIES OF MAGNETS. 307

sion is accordingly formulated as follows : Like magnetic
p'Ji'M repel an<l unlike poles attract each other.

255. Magnetic Substances. A magnetic substance
is one capable of being affected by a magnet. A piece of
soft iron will attract either pole of a magnetic needle, but
it does not itself retain the property of attracting other
masses of iron, and does not possess the power of orienta-