Henry S. (Henry Smith) Carhart.

Thermo-electromotive force in electric cells, the thermo-electromotive force between a metal and a solution of one of its salts online

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THERMO-

ELECTROMOTIVE FORCE
IN ELECTRIC CELLS

THE

THERMO-ELECTROMOTIVE
FORCE BETWEEN A METAL AND A
SOLUTION OF ONE OF ITS SALTS

BY
HENRY S. CARHART, Sc.D., LL.D.

PROFESSOR EMERITUS OF PHYSICS, UNIVERSITY OF MICHIGAN^
MEMBER, AMERICAN PHYSICAL SOCIETY ; AMERICAN ELEC-
TROCHEMICAL SOCIETY; AND INSTITUTION OF
ELECTRICAL ENGINEERS (LONDON)



ILLUSTRATED




NEW YORK
D. VAN NOSTRAND COMPANY

EIGHT WARREN STREET
JQ2O



COPYRIGHT, IQ20, BY
D. VAN NOSTRAND COMPANY



FOREWORD

THIS book is composed mostly of the author's
researches begun many years ago with those con-
cerning the analysis of the temperature coefficient
of voltaic cells. The earliest papers have sug-
gested others, which have gradually been added.
Some other matter germane to the subject has
been taken from the work of others, notably that
of Dr. Ernst Cohen on the Thermodynamics of
Normal Cells.

The chapter on the electromotive force of con-
centration cells has special interest because it
shows the application of the Helmholtz equation
to such cells as distinguished from voltaic cells.
It shows further that the Nernst equation is only
the equivalent of the second term of the Helmholtz
formula.

It will appear from this book that the thermo-
emf between metals and solutions of their salts
has manifold applications in electric cells. The
wide application of thermo-emf it is hoped will
appear as sufficient justification for the book
itself.

H. S. C.

PASADENA, CAL. 4 <> A ~ ~n
Jan. is, 1920 *f: O ^ I O I?



CONTENTS

PAGE

CHAPTER I
THERMO-ELECTROMOTIVE FORCE BETWEEN METALS.. i



CHAPTER II
ELECTROMOTIVE FORCE BETWEEN METALS AND LIQUIDS.. n

CHAPTER III

CONCENTRATION CELLS. . 20



CHAPTER IV
TEMPERATURE COEFFICIENTS 28

CHAPTER V
THERMODYNAMICS OF THE VOLTAIC CELL 43

CHAPTER VI
ELECTROMOTIVE FORCE OF CONCENTRATION CELLS 67

CHAPTER VII
THERMODYNAMICS OF CONCENTRATION CELLS 87

CHAPTER VIII
THERMODYNAMICS OF NORMAL CELLS 112

CHAPTER IX
THERMO-EMF WITHOUT TEMPERATURE DIFFERENCE.. iaa



THERMO-ELECTROMOTIVE
FORCE IN ELECTRIC CELLS

CHAPTER I

THERMO-ELECTROMOTIVE FORCE BETWEEN
METALS

1. Reversible Heat. "A reversible thermal
effect occurring at any part of a circuit must be
attributed to the existence at. this point of a
difference of potential existing independently of
the current." In 1834 Peltier discovered that
when an electric current is passed through a
junction between different metals, there is either
a development or an absorption of heat at the
junction, according to the direction in which
the current passes. Thus, let copper wires be
soldered to the ends A and B (Fig. i) of an iron
wire. Then if the current passes in the direc-
tion ABj heat will be absorbed at A and this
junction will be cooled; while at B heat will be
generated and the junction will be heated. If
the current is reversed, heat will be absorbed at
B and generated at A. This reversible heat



THERMO-ELECTROMOTIVE FORCE

^liGiws; :that there is an emf between the
copper and the iron at A, directed from copper
to iron, and an equal one at B if the tempera-
ture of the junctions is the same.

When the current encounters an emf in the
same direction as the current flow, energy is
added to the current through the agency of the
direct emf; and if the emf is thermoelectric, the
energy is supplied by the heat of the junction,



Fe



Fig. i

which accordingly cools. The current from A
toward B encounters at B a back emf which it
works against. It therefore gives up energy to
this junction which heats it, since the conditions
do not permit the energy liberated there to take
any other form. In an electric motor the energy
spent in driving the current against the back
emf of the armature takes the form of mechani-
cal work; in electrolysis it becomes the energy
of chemical separation. Peltier's discovery there-
fore proves the existence of an emf at a junc-
tion between different metals. The value of

dE

this emf at the absolute temperature T is T

dl



IN ELECTRIC CELLS 3

The ratio of the increase of emf with respect to

dE

temperature, , is known as the thermoelectric
(I JL

power of one metal with reference to another.
If this were constant, the emf would be propor-
tional to the absolute temperature. For a few
pairs of metals it is nearly constant for a wide
range of temperature. Hence the use of a metal-
lic junction for measuring temperature.

The Peltier effect may be expressed in calories,
in microvolts, or in joules. Expressed in joules
the Peltier effect PI at the temperature T\ is
the mechanical equivalent of the heat liberated
when one coulomb crosses the cold junction, and
the effect P 2 is the mechanical equivalent of the
heat absorbed at the hot junction at the tem-
perature 7^2 when one coulomb crosses this
junction. Then, since the circuit is a reversible
engine, so far as the Peltier effects are concerned
we have by thermodynamics 1

W Pif



where W equals the work done when one cou-
lomb goes around the circuit. But this work is
equal to the emf around the circuit. Hence
1 Maxwell's Theory of Heat.



THERMOELECTROMOTIVE FORCE



If the Peltier effect were the only reversible
one in the circuit and if the thermoelectric power
were constant, the emf around the circuit, whose
cold junction is kept at a constant temperature,
should be proportional to the difference between
the temperatures of the hot and the cold junction.

2. Thermoelectric Couples. A thermoelec-
tric couple, illustrated in Fig. i, consists of two
different metals joined together at their termi-
nals; one junction may be joined through inter-
mediate metals at one temperature. An emf
is present at the two junctions, but so long as all
the junctions are at the same temperature, the
two emfs at the two junctions (such as those
between iron and copper in Fig. i) are equal, in
opposite directions around the circuit, and coun-
terbalance each other. There is no emf around
the circuit unless one junction is at a higher
temperature than the other. In that case the
current will flow in a closed circuit in the direc-
tion of the larger emf at the warmer junction,
and by means of the Peltier effect heat will be
transferred from the hot junction to the cold
one. Such a current, known as a thermoelectric
current, was first observed by Seebeck in 1822,



IN ELECTRIC CELLS 5

The Peltier heat effect differs from the Joule
effect in two respects: It is due to emf at the
junctions and has no relation to resistance; it
is proportional to the first power of the current
strength, while the Joule effect, C 2 Rt, is propor-
tional to the square of the current.




3. The Neutral Point. When the emf and
the temperature difference of a thermal couple
are plotted as coordinates, the resulting curve is
approximately a parabola (Fig. 2). At the point
where the tangent to the curve is parallel to the
axis of temperatures the emf reaches its highest
value and the thermoelectric power is zero.
This point N is called the neutral point and the
corresponding temperature the neutral tempera-
ture. At this point the Peltier emf becomes
zero and the one metal is neutral to the other.

The curves for the different metals all pass



6 THERMO-ELECTROMOTIVE FORCE

through the origin of coordinates, since the emf
is always zero when both junctions are at the
same temperature, o C., for example. The neu-
tral temperature for a platinum-lead couple is
150 C., and for a zinc-lead couple, 260 C.
For a copper-iron couple it is about 275 C.
When the hotter junction passes the neutral
temperature for any couple, the Peltier emf
changes sign and the emf in the circuit falls.
It becomes zero when the temperature of the
hot junction is as far above the neutral tempera-
ture as that of the cold one is below it.

Since the curve connecting the circuit emf and
the temperature difference between the junctions
is a parabola, we may write

= a(T, - T,) + b -(T 2 - r,) 2

2

= a(T 2 - JO + -(Tf - aJTir, + TV).

2

The constants a and b depend on the nature of
the metals. Since TI is a constant, differentiat-
ing with respect to T 2 we have

dE b b ( .

= a+ 2-T 2 - 2-Ti = a + b(T 2 - TI) = zero

dT 2 2 2

for the maximum value of E. Therefore

TZ TI = - for the neutral point.
b



IN ELECTRIC CELLS 7

If in the expression for - above we substitute

dl 2

for TI TI its value corresponding to maximum

E, we have

dE Ja

7r =a ~ b (b
dl 2 \o

This expression shows that at the neutral
point both the thermoelectric power and the
Peltier effect are zero.

*y CL

If is substituted for T 2 TI in the ex-

b

pression above for E, we obtain E = o. Thus
if the temperature difference T 2 TI for the
maximum value of E is doubled, the emf of the
circuit drops to zero.

4. Thermoelectric Diagram. In the last
article it was found that the thermoelectric
power dE/dT 2 = a + b(T 2 - TI). This is the
equation of a straight line. If therefore thermo-
electric power and difference of temperature are
plotted as coordinates, the result will be a straight
line. In Fig. 3 thermoelectric powers between
several metals and lead as the reference metal
are plotted as ordinates per degree C. and tem-
peratures of the hot junction as abscissae, the
cold junction being kept at o C. Such a series



8



THERMO-ELECTROMOTIVE FORCE



of straight lines compose a thermoelectric dia-
gram. The point of intersection of any pair of
lines is the neutral point for the, two correspond-
ing metals. Thus the copper-iron lines cross at
274.5; this is therefore the temperature at
which the thermoelectric power of these metals




becomes zero. It is also the neutral tempera-
ture for the pair. Figure 4 is the thermoelectric
diagram for several metals compared with lead.
The palladium-copper lines if produced would
meet at 170 C. Dewar and Fleming found
by means of the low temperature obtained by
liquid oxygen that thermoelectric inversion for
this pair does occur at about 170.



IN ELECTRIC CELLS 9

5. Electromotive Force in the Thermoelectric
Diagram. From the manner in which a ther-
moelectric diagram is constructed, it will be seen
that the emf between any pair of metals is
equal to the area of the figure included between
the ordinates corresponding to the two tempera-
tures and the thermoelectric lines of the metals.
Thus if the cooler junction of a copper-iron couple
be at 1 00 and the warmer at 200, the resultant
emf in the circuit is represented by the area
abed; while if the warmer junction be at 400,
the emf will be equal to the difference of areas
abn and c'd'n.

The ordinates represent thermoelectric powers
and

dE/dT = thermoelectric power;
therefore

dE = thermoelectric power X dT.

Now dE is the small increase of emf corre-
sponding to the small increase of temperature
dTj and the second member of the last equation
is a small area whose length is the line ab and
whose width is an element of temperature meas-
ured at right angles to ab. The emf of any
finite temperature difference is therefore an area
such as abed, which is made up of small areas
corresponding to minute temperature differences.



io THERMO-ELECTROMOTIVE FORCE

r 6. Thermoelectric Series. A thermoelectric
series is a table of metals showing their thermo-
electric relation to one another. Since the
thermoelectric 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 emf in microvolts
(millionths of a volt) between each metal and
lead, with a difference of one degree between the
junctions when their mean temperature is 20 C.:



Bismuth . .


. - 80 o


Silver


4- T. o


Cobalt


22 O


Zinc


+ 3 7


German silver


. ii 7$


Copper .


+ 38


Mercury


. - o 418


Iron


+ 17 tr


Lead


o o


Antimony axial


-f- 226


Tin


. . . + O.I


Antimony, equatorial


+ 26 4


Platinum . .


-f- o O


Tellurium . .


+ 502 o


Gold


. -f 1.2


Selenium


4- 807.0



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 thermoelectric powers, the results obtained
by different observers are not very concordant.



IN ELECTRIC CELLS n



CHAPTER II

HERMO-ELECTROMOTIVE FORCE BETWEEN
METALS AND LIQUIDS

7. Introductory. The laws of thermoelectric
force between metals have long been known, and
they have been described in the preceding chap-
ter only as a prelude to the study of the second
class of thermoelectromotive forces, namely,
those between metals and solutions of their
salts. These latter have been but little known
and only slightly appreciated. And yet they
have most interesting applications in electrolysis
and in voltaic and concentration cells. They are
readily distinguished from the well-known first
class because emf arising at the junction of
two metals Is a function of temperature only,
while an emf having its seat at the junction
of a metal and a solution of one of its salts is a
function not only of temperature but also of the
concentration of the salt solution, or of the con-
centration of the metal in the form of an amalgam.

It is therefore quite possible to have an emf
in circuit, in the absence of any difference of con-



12 THERM O-ELECTROMOTIVE FORCE

centration at the two electrodes, by reason of a
difference of temperature of the two metal-liquid
junctions; also, in the absence of any tempera-
ture difference, by reason of a difference either
in the concentration of the salt solutions bathing
the electrodes, or of the amalgams composing
them. This latter emf is properly called ther-
moelectric because the energy of the current
in a closed circuit when no other source of emf
is present represents the excess of heat absorbed
at one electrode above the heat generated at the
other during the passage of one coulomb. In
the absence of chemical energy and heat of dilu-
tion, the heat of the solutions or of the amal-
gams is the only energy present to be drawn
upon.

If this appears to the reader improbable, the
writer trusts that he will withhold judgment
until he has read and considered the thermo-
dynamic and experimental evidence appearing
later in this book.

8. Thermo-electromotive Force between Zinc
and Zinc Chloride. For the purpose of meas-
uring the effect of a change of temperature
between the electrode and the electrolyte, a
special form of cell was employed. It consisted
of two tubes communicating with each other



IN ELECTRIC CELLS 13

near their upper ends by a long tube of narrow
bore (Fig. 4). All three tubes were filled with a
solution of zinc chloride, density 1.395 g. per
cm. 3 at 15 C. Metallic zinc wires were used
as the electrodes. One electrode A was kept in
an ice bath, while the temperature of the other
was raised by short steps. The measurement
of the emf was made by the potentiometer







E

=\




\ \






A .


























1
















1
















1
















1
















1
















1
















T










V.


_/




i


V.


^




X






s


V

\









Fig. 4

method, the experimental cell being balanced
in series with a Clark standard cell. Thus the
closing of the key indicated at a glance which
pole of the experimental cell was positive. With
zinc in a solution of one of its salts the heating
of the electrode always produces an emf directed
from the solution to the metal; that is, the elec-
trode in B was always positive whether the
experimental cell contained a solution of zinc
chloride or zinc sulphate.
With the combination

Zn (warm) | ZnCl 2 1 Zn (cold)



14 THERMO-ELECTROMOTIVE FORCE

the relation between the emf and the difference
of temperature /or T 2 TI between the two
electrodes is a linear one represented by the
equation

E = 0.000590 (T 2 - TI).

In the table the observed and computed
emfs are set down for comparison.



Temp.


. Obs. emf


Comp. emf


Difference


8.1


o . 00490


0.00478


- 12


10-5


612


608


~ 4


I2. 3


750


726


-24


17.7


1040


1044


+ 4


22.2


1301


1310


+ 9


2 S .8


1499


1522


+ 23


28.6


1668


1687


+ 19


32-1


1913


1894


- 19


34-5


2050


2036


- H


39-i


2295


2307


+ 12



The observations are plotted in the straight
line of Fig. 5.

9. Thermo-electromotive Force with Amalgams.
Figure 6 was plotted from the emfs obtained
by setting up the two-limbed cell twice, each time
with the same zinc amalgam in both limbs.
The amalgam was in a half gram-molecule solu-
tion of zinc sulphate. One limb was kept in
ice at o, while the temperature of the other



IN ELECTRIC CELLS 15

was raised by steps from o to about 32. The
direction of the emf is from the solution to the
amalgam across the heated junction. It is
greater for the dilute amalgam than for the con-
centrated one. Curve A is for the dilute amal-
gam and curve B for the concentrated. These
curves are nearly straight lines, and the corre-
M.V.



20



10



10



20

Fig. S



30



spending thermoelectric power is about one
millivolt for the dilute and a little less than 0.8
millivolt for the concentrated amalgam. The
concentration of the one amalgam was one-
tenth that of the other.

Take another case. Two zinc amalgams were
made by weighing out masses of mercury as one
to two and depositing in them electrically the



i6



THERMO-ELECTROMOTIVE FORCE



same quantity of zinc. The weight of zinc was
0.6 and 1.2 per cent respectively of the weight
of mercury. The electrolyte was a concentrated
solution of zinc sulphate.

To measure the electrolytic thermo-electro-



30



20



M.Vs



10



X



10 Temp.Dif.
Fig. 6



30



motive force of the two amalgams, the two legs
of the H-form of cell, identical in every respect
as far as possible, were immersed in baths, one
containing mixed ice and water, and the other
water, the temperature of which was varied.
The entire cell, except the short portion connect-



IN ELECTRIC CELLS 17

ing the side tubes, was immersed. The results
are the following:

THERMO-ELECTROMOTIVE FORCE FOR THE MORE
DILUTE AMALGAM



Temp. C


Obs 1 . emf


Comp. emf


10.30


0.01077


0.01077


15.40


1611


1611


20.47


2140


2141


25-60


2676


2678


31 10


3251


3253


36.80


3852


3849


40.20


4214


4205



Equation:



= 0.001046 (T% T\).



THERMO-ELECTROMOTIVE FORCE FOR THE MORE
CONCENTRATED AMALGAM



Temp. C.


Obs. emf


Comp. emf


9.41


0.00956


0.00957


14-75


1496


1500


19.65


1996


1998


25-05 c


2542


2547


30.60


3110


3112


35-20


3582


3580


39-30


4000


3993



Equation: E 2 = 0.001017 (T 2 TI).

The thermo-electromotive force is directed from
the solution to the amalgam, and it increases as
the dilution of the amalgam increases. In other



i8



THERMO-ELECTROMOTIVE FORCE



words, the electrolytic thermo-electromotive force
is a function of the concentration as well as of
the temperature.

The two curves in Fig. 7 represent the observa-
tions for Ei and 2 respectively.



M.V.

8.0

7.8
7.6
7.4
T.2
7.0










































M.V.
40

30
20
10
















































































/






































&


x


































x<:


^


































.X


^


'


































^


x


































^


^


































X


*\


%


































*


f








































































X




































X


x


































-X


x




































x









































10 c



30



40



Fig. 7



10. Thermoelectric Behavior of Silver. 1 In
a thermoelectric element of a metal and a solu-
tion of one of its salts, in the case of zinc, copper,
cadmium, and mercury, the warm electrode is
the cathode, but in the case of silver the cold
electrode is the cathode, that is, the thermo-emf
is directed from the metal to the solution.

1 Henderson, Phys. Rev., Vol. XXIII, Aug., 1906.



IN ELECTRIC CELLS 19

The tests show that this is not due to oxida-
tion or other peculiarity of the electrode. Cells,
from which the air had been carefully removed,
gave the same result, both in direction and
magnitude.

Further, an increase in concentration of the
solution produces a decrease in the thermo-emf.
The maximum decrease occurs between one-
eightieth and one-tenth normal solution. In a
simple concentration cell with silver electrodes,
on the concentrated side the emf is smaller
than on the dilute side. Hence within the cell
the current flows from the electrode in the dilute
solution to that in the concentrated solution.
Thus silver goes into solution at the anode and
increases the concentration there, while at the
cathode silver goes out of solution and is de-
posited on the cathode, thus reducing the con-
centration there. As in the other cases, then,
the passage of the current tends to reduce the
difference of concentration, or the cell runs down.



20 THERMO-ELECTROMOTIVE FORCE



CHAPTER III
CONCENTRATION CELLS

11. Concentration Cells of Two Types. Two

types or classes of concentration cells should be
distinguished from each other:

1. Two electrodes of the same metal im-
mersed in a solution of a salt of this metal, the
concentration of the solutions being different at
the two electrodes.

2. Two electrodes consisting of an amalgam
of the same metal, both immersed in a solution
of a salt of the metal, the concentration of the
amalgams being different at the two electrodes.

When all sources of emf are taken into ac-
count, the formula for the first type worked out
on the solution pressure and osmotic pressure,
or Nernst theory, is as follows:

E = 0.0002 riog

n u + v Cz

Here i is the Van't Hoff factor of dissociation,
u and v the ionic velocities of the positive and
negative ions respectively, and c\ and Co the con-



IN ELECTRIC CELLS 21

centration of the solutions; n is the valence of
the metal ion. Llipke says of this formula:
"The minus sign in the above formula means
that within the concentration cell the current
goes from the dilute to the concentrated solu-
tion, so that the electrode in the latter is the
cathode and in the former the anode."

It will be observed that by this formula the
emf is proportional to the absolute temperature
T of the cell. This suggests that the emf of
such a cell is thermal in origin; in other words,
that concentration cells are devices for convert-
ing some of the heat of the solutions and sur-
roundings into electric energy.

We shall arrive at the same conclusion if we
consider the Helmholtz equation for the emf of

a voltaic cell,

H dE

E = ^F + T W

where H is either the heat equivalent of the chem-
ical reactions or the heat of dilution in the cell.
If the Helmholtz equation is generally ap-
plicable, it follows that when H is zero, the
only source of electrical energy is the heat of
the cell and its surroundings represented by the
second term. Usually H has either a positive
or a negative value arising from the heat of dilu-



22



THERMO-ELECTROMOTIVE FORCE



tion of the solutions of different concentration.
Obviously the emf of a concentration cell is at
least in part thermoelectric, and it remains to
apply the principles of electrolytic thermo-electro-
motive force to concentration cells.

12. Relation between Thermo-EMF and
Concentration. Figure 8 shows the results of

Zn-Zn 804.




0.8



VwVs



CONCENTRATIONS
Fig. 8



the determination of thermo-emf per degree C.
for Zn-ZnS0 4 with concentrations ranging from
i/ioo gram-molecule to one gram-molecule to
the liter. The ordinates express the results in
millivolts per degree C., the temperature of the
two sides being o and about 30. The meas-
urements were made by means of a cell similar
to the one shown in Fig. 4. One limb was kept
in a bath of ice-cold water, and the other in a



IN ELECTRIC CELLS 23

bath of water at about 30. A series of six
such cells were placed in the same baths and
were filled with solutions of different concentra-
tion of the same salt solution. The two zinc
electrodes were moved along from one cell to the


1 3 4 5 6

Online LibraryHenry S. (Henry Smith) CarhartThermo-electromotive force in electric cells, the thermo-electromotive force between a metal and a solution of one of its salts → online text (page 1 of 6)