UNIVERSITY OF TORONTO
STUDIES
PAPERS FROM THE PHYSICAL
LABORATORIES
No. 18: A METHOD OF DETERMINING THE SPECIFIC HEAT
OF A GAS AT CONSTANT PRESSURE, BY H. F. Dawes
(REPRINTED FROM TRANSACTIONS OF THE ROYAL SOCIETY OF Canada, 1906)
THE UNIVERSITY LIBRARY: PUBLISHED BY

THE LIBRARIAN, 1907

University of Toronto Studies
COMMITTEE OF MANAGEMENT
Chairman: MAURICE HUTTON, M.A., LL.D.,
Acting President of the University
Professor W. J. ALEXANDER, PH.D.
Professor W. H. ELLIS, M.A., M. B.
Professor A. Kirschmann, Ph.D.
PROFESSOR J. J. MACKENZIE, B.A.
PROFESSOR R. RAMSAY WRIGHT, M. A., B.Sc., LL. D.
Professor GEORGE M. Wrong, M.A.
General Editor: H. H. LANGTON, M.A.,
Librarian of the University

SECTION III., 1906
[189]
TRANS. R. S. C.
n
XII.-A Method of Determining the Specific Heat of a Gas at Constant
Pressure.
By H. F. DAWES, M.A., University of Toronto.
(Communicated by Prof. J. C. McLennan, and read May 23, 1906.)
The classical determination of this constant for several gases was
made by Regnault.¹ His method consisted in passing a stream of heated
gas through an ordinary water calorimeter and determining the quantity
of heat given up by observing the rise in temperature of the water. The
quantity of gas used in any experiment was determined from observations
on the pressure, and the temperature of the gas together with the volume.
of the reservoir in which it was stored. The gas was heated by passing
it through a long spiral tube of copper immersed in a bath of
boiling oil. From the heating bath it passed directly into the calori-
meter traversing it in a spiral copper tube. It was assumed that the air
entered the calorimeter at the temperature of the oil bath, and left it at
the temperature of the water.
Besides the heat given up by the gas a certain amount was com-
municated to the calorimeter by conduction and by radiation both from
the bath and from other bodies in the room. In order to determine the
amount of heat derived from these sources observations were made on
the temperature of the calorimeter for a certain time before the gas was
allowed to pass through and again after the flow was stopped.
Defects.
In attempting to repeat this experiment with apparatus precisely
similar to that used by Regnault it was found that the arrangement had
several disadvantages. In the first place the calorimeter used was not
very delicate, i.e., it required a comparatively large quantity of heat to
make a sufficiently great difference between the initial and final tempera-
tures of the calorimeter.
Since both the specific heat and the density of a gas are very small,
it is necessary to use a large quantity of gas and to make the initial tem-
'perature very high in order to have the required quantity of heat avail-
able. To obtain a sufficiently high temperature, boiling oil was used in
the heating bath and this made the experiment very disagreeable and
difficult to work with.
1
Regnault. Memoires de l'Academie des Sciences de l'Institut Imperial
de France. Tome XXVI. pp. 1-112.
•
1
190
ROYAL SOCIETY OF CANADA
Again, with Regnault's apparatus, the arrangement for measuring
the initial temperature of the gas was somewhat defective. On account
of the very rapid fall of temperature along the tube through which the
gas passed from the oil bath to the calorimeter it was scarcely permiss-
able to assume that it entered the calorimeter at the temperature of the
oil bath.
11.-The Bunsen Ice Calorimeter.
A modified form of the calorimeter used by Regnault for the deter-
mination of the specific heat of gases is also used to find the specific heat
of liquids or solids. Another form of calorimeter which has been used
for liquids and solids but not for gases is the Bunsen Ice Calorimeter.
The construction of this type of calorimeter is shewn diagrammatically
in Fig. 1. A glass test tube B is sealed into the upper end of a larger
cylindrical glass vessel A. The lower end of A is joined to a U tube AC
which carries a cup C at its upper end. A hollow stopper furnished
with a three way tap D prolonged into a graduated capillary tube E is
fitted into this end. By means of this tap communication can be made
from the cup D, which the stopper carries, either to C or to E or from O
to E.
In setting up the instrument for use the upper part of A was filled
with pure distilled water free from air, and lower part of A, the tube C
and part of the capillary with pure boiled mercury. By means of the
tap D the end of the mercury thread could be moved to any selected pos-
ition.
A part of the water in A was frozen and formed into a cap of ice
around the immersed part of B as indicated in the diagram. In mak-
ing all measurements, A, B, and the lower part of C were kept surround-
ed by ice in order to maintain the apparatus at zero temperature.
The measurement of heat by this calorimeter depends on the fact
that water changes its volume on solidifying. If a quantity of heat is
communicated through B to the water in A a certain quantity of ice will
be melted. This will cause a diminution in the volume of the contents
of A, and a consequent receding of the mercury thread in E. From the
known values of the latent heat and the specific gravity of ice, the
amount of heat communicated may be determined for any change of
volume produced.
An investigation with this type of calorimeter shewed that its deli-
cacy was such that an addition of one calorie made a change of about
1 1-3 millimeter divisions in the position of the end of the capillary
thread. With the apparatus used by Regnault, on the other hand, an
addition of about 600 calories was required to make a difference of one
[DAWES]
SPECIFIC HEAT OF A GAS AT CONSTANT PRESSURE
191
degree in the thermometer reading. Besides its greater sensi-
tiveness the Bunsen calorimeter possesses the advantage of not requiring
any correction for radiation errors since no heat is communicated by this
means on account of the surrounding ice jacket.
III.-NEW METHOD.
A.-Apparatus.
In the experiment described below a method was devised by which
this calorimeter could be used with special advantage in determining the
specific heat of a gas, and at the same time some of the defects of the
Regnault arrangement avoided. Fig. 2 is a diagram of the arrangement
of the apparatus as finally adopted after considerable development. The
gas was stored under pressure in a reservoir A and kept at zero tempera-
ture by means of ice in the vessel surrounding it. The flow of gas was
regulated by a valve B, and its pressure was indicated by a water mano-
meter C. A phosphoric pentoxide drying tube D was inserted in its
path to absorb any moisture coming from the manometer. The gas was
heated as it passed through a tube in a water bath E and was kept at a
temperature of 100° as far as the mouth of the calorimeter by means
of a steam jacket. It passed through the test tube of the calorimeter F
in a copper tube of special construction shewn on a larger scale in Fig. 3
The gas entered this tube through the inlet d and issued from it by the
outlets a and b, each of which could be closed by a valve. The lower
part of the tubing was coiled, as shewn in the figure, and immersed in
water to the height e. With the valve b open and a closed the gas passed
directly out without going through the bent portion of the tube. The
difference of temperature between the points c, d, was measured by
means of a copper-iron thermocouple, the wires of which passed out
through air-tight caps at a and b, and thence to a galvanometer.
B.—CALIBRATION.
(1) The Thermocouple.
The thermocouple was calibrated before the wires were sealed into
the tubes, one junction being kept in melting ice and the other placed in
a water bath along with a standard thermometer. The deflections of the
galvanometer were observed for a series of different temperatures, and
the results are shown in Fig. 4.
(2) The Gauge.
The relation between the quantity of gas which passed out of the
reservoir and the corresponding fall of pressure was found in the follow-
192
ROYAL SOCIETY OF CANADA
ing way. The volume of the reservoir was 7 litres, so that it contained
7 m grams of gas at standard temperature and pressure, m being the
mass of one litre. Hence by Boyle's Law, for every millimetre fall of
pressure 7m/760 grams of gas must have escaped. The calibration of
the gauge was checked by means of a mercury manometer, and its read-
ings reduced to millimeters of mercury. In an experiment with atmos-
pheric air for which m=1.293 the quantity of air which issued from the
reservoir was calculated for a series of different pressure falls and the
results of this calculation are exhibited in Fig. 5. In this figure the
ordinates represent the quantities of air which escaped when the pressure
fell to zero from une values indicated by the corresponding abscissæ.
(3) The Calorimeter.
The bore of the capillary tube of the calorimeter was calibrated by
filling it with mercury and then running it out a little at a time and
weighing the parts run out. From this the mass of mercury occupying
each division was found for different parts of the tube.
The number of calories required to cause a displacement of one
gram was found as follows:—
Data:
1 gram of water gives out 80.025 calories on freezing.
1 gram of water occupies 1.00013 c.c at 0°C.
1 gram of ice occupies 1.090 x 1.00013 c.c at 0°℃
1 gram of mercury occupies .073553 c.c at 0°C.
Solution:
80.025 calories used in melting ice cause a change in volume of
1.00013
{
1.090
1.090 – 1
1.00013 {1.090
1}
c.c. and therefore cause a displacement of
1}:
X
1
.073553
grams of mercury.
Hence a displacement of one gram of mercury means the using of
.073553 x 80.025 calories 65,4 calories.
1.00013 (1.090 - 1)
From this value the number of calories causing a displacement of
one division at different parts of the scale was found. The results of
this calibration are illustrated by Fig 6, which shows at any point the
number of calories corresponding to a displacement of the mercury from
zero of the scale to that point.
[DAWES]
SPECIFIC HEAT OF A GAS AT CONSTANT PRESSURE
193
A preliminary experiment showed that the fall of pressure of the
gas in passing through the calorimeter was less than one fifth the pres-
sure indicated by the manometer C.
C. Method of Experiment.
B
In making a determination the following procedure was adopted.
When the water in E had been raised to the boiling point the valve a
was opened, and the gas allowed to pass through the apparatus.
Readings were taken on the calorimeter scale, and on the gauge
and on the thermocouple scale respectively once a minute.
was adjusted as required to keep the gas flowing uniformly.
The water manometer C was maintained at a difference of level of eight
millimeters, so that the fall in pressure of the gas as it passed through
the calorimeter was less than 8/5 millimeters of water. The galvano-
meter in a few minutes assumed a constant deflection, showing that the
temperature of the d junction had become steady. From the calorimeter
readings the average number of divisions per minute was determined by
finding, first, the average number per twenty minutes from a number
of sets of readings, and then taking one twentieth of that number. The
rate of fall of pressure was found in a similar manner from the read-
ings of the gauge.
After the gas had been flowing for a sufficient time, the valve b
was opened and a closed, so that the gas passed out without going through
the coil. The rate of flow was adjusted so that the thermocouple d
was kept at a temperature used in the previous observations. Readings
of the calorimeter and of the thermocouple scales were taken once a
minute as before, and the average number of divisions per minute on the
calorimeter scale was found in the way explained above.
From these readings the following deductions were made:-
(1) The temperature in degrees centigrade corresponding to the
thermocouple deflection was found from the curve of Fig. 4.
(2) The number of grams of gas per minute was found from the
rate of fall of the pressure by means of curve 5.
(3) By the aid of curve 6 the number of calories communicated per
minute to the calorimeter was deduced from the number of divisions
moved over per minute by the mercury thread.
D. Theory.
It will be seen that with the exception of the air which passed
through the coil (e) during the first set of observations the sources of
1
194
ROYAL SOCIETY OF CANADA
heat in the two cases were exactly the same.
Hence if " x" calories per
minute were communicated in the first case, and (“x¸") per minute in the
second, the gas must have given up (x − x¸) calories per minute. If
therefore the rate of flow was
y" grams per minute, and the fall of
temperature "t°C” the value of the specific heat as given by this set of
readings was
x-xo
yt
''
E. Measurement of Specific Heat for Dry Air.
A set of temperature, pressure, and calorimetric readings for dry
air is given in Table I, and curves illustrating them are shewn in Fig. 7.
TABLE I.
Time.
Gauge.
Time.
Calorimeter
Scale.
Thermocouple
Scale.
0.
22.9
.30
22.7
1
554.4
1.30
22.1
2
510.3
65.5
2.30
21.6
3
566.4
65.
3.30
21.3
4
572.9
64.5
4.30
20.9
LO
5
579.
64.5
5.30
20.6
6
585.1
64.
6.30
20.1
7
591.8
64.5
7.30
19.9
со
598.
64.5
8.30
19.55
9
604.1
64.5
9.30
19.2
10
610.3
64.5
10.30
18.9
11
617.
64.5
11.30
18.6
12
623
64.5
12.30
18.5
13
629.9
64.5
13.30
18.2
14
636
64.5
14.30
18.
15
642.4
64.5
15.30
17.5
16
649
64.5
16.30
17.1
17
655.2
64.5
17.30
16.7
18
661.8
04.5
18.30
16.4
19
668.5
64.5
19.30
16.2
20
675.0
64.5
[DAWES] SPECIFIC HEAT OF A GAS AT CONSTANT PRESSURE
TABLE I-(Continued.)
195.
Time.
Gauge.
Time.
Calorimeter
Scale.
Thermocouple
Scale.
20.30
15.8
21
681.6
64.5
21.30
15.1
22
688.2
61.5
22.30
15.
23
694.9
64.5
23.30
!
14.6
24
701.3
64.5
24.30
14.2
25
708.
64.5
25.30
14.
26
715
64.5
26.30
13.6
27
721.3
64.5
27.30
13.3
28
728
64.5
1
28.30
12.95
29
734.9
64.5
29.30
12.4
30
741.5
64.5
30.30
12.
31
748.5
64.5
31.30
11.6
32
755
64.5
1
32.30
11.4
33
762
64.5
33.30
11.
31
769
61.5
34.30
10.7
35
775.4.
64.5
35.30
36
782
61.5
36.30
10.35
37
789.1
64.5
The first of these curves (A) shews that after the first few minutes
the temperature became steady and remained so during the experiment.
The scond and third (B and C), shew respectively that the air flowed
through the calorimeter uniformly, and that the heat was communicated
to it at a uniform rate.
The determination of the value of the specific heat at constant
pressure for air from this set of readings is summed up in the following:
Denoting the rate of motion of the calorimeter thread when the air
was flowing through the coil by A, and when it was issuing from the
outlet b by B, the results obtained were as follows:-
Average value of A = 6.612 divisions per minute.
Temperature fall between terminals of thermocouple = 21.9°
Average value of B = 4.982 divisions per minute.
Temperature fall 21.8°
Reduced value of B corresponding to temperature fall of 21.9° = 5.0071
divisions per minute.
J
A
196
ROYAL SOCIETY OF CANADA
.-Calorimeter scale divisions due to the heat from the air (6.612 - 5.0071)
1.6049. From Fig. 7 and its corresponding readings the number
of calories per minute due to the heat imparted by the air 1.20327.
II.- Average fall of pressure = .3399 gauge divisions per minute, 17.09 mm.
mercury per minute and consequently the average rate of flow =
.20355 grams per minute.
Combining I and II the value .2697 was obtained for the specific heat at
constant pressure.
F. Discussion.
In the published account of the experiments in which he determined
this constant. Regnault gives the results of eight-four determinations.
These vary from .22 to .24 the average value being .2375. The result
found from the observations given above, while somewhat higher than
those found by Regnault is still sufficiently near to his values to demon-
strate the usefulness of the method.
G. Alterations Suggested.
""
One or two changes in the arrangement have suggested themselves,
but owing to lack of time, have not as yet been tried. In the first place
the junction of the two tubes at d might be made quite near to the upper
end of the test tube of the calorimeter, and the thermojunction moved
up to correspond. This would not alter “ X as used in the above dis-
cussion, but would make a much greater value of "t" and a correspond-
ingly smaller value of "x" since the heat given up by the air between the
present position of d and that suggested is at present included in "x..
Again, an ebonite connection in the tube d would lessen the conduction
from the steam jacket, ebonite being a poor conductor of heat. This
would lessen the values of "x" and "x" by equal amounts. Both these
changes would lessen the percentage error in the final result.
H. Advantages of the Method.
Some advantages of this method over that used by Regnault may
be enumerated.
(1) By this method the calorimetry is more perfect than in the
experiments of Regnault, since the calorimeter (a) is very much more
sensitive and (b) it requires no correction for radiation on account of
belonging to the constant temperature type.
(2) Heat communicated by all sources other than the gas itself, for
example, by conduction from the steam jacket down the tube, d, and
from the air of the room down a and b, is accounted for by a single
direct observation.
1
[DAWES]
SPECIFIC HEAT OF A GAS AT CONSTANT PRESSURE
197
(3) Again, in this method the measurement of the initial tem-
perature of the gas is exact, since all heat given up by it after it passes
the thermocouple is accounted for in the calorimeter readings.
(4) It is necessary to heat the gas only to a comparatively low
temperature in order to have as favourable a determination as that of
Regnault with the very high temperatures he used. Hence the disad-
vantages and limitations of using boiling oil as a heating bath are
avoided. The method may be readily applied to gases which are de-
composed at high temperatures.
(5) The determination of the specific heat of a gas is reduced to
the measurement of rates, so that the initial and final adjustments of
conditions have not to be considered or allowed for.
(6) The method may be readily adapted to the measurement of
the specific heat of liquids so that it gives promise of becoming generally
useful.
The writer would in conclusion express his sincere thanks to Prof.
J. C. McLennan for his kindly interest in this investigation, and his
helpful suggestions during its progress.
Physical Laboratory, University of Toronto.
A
+
198
ROYAL SOCIETY OF CANADA

B
E
Fig. 1
Fig. 2
[DAWES] SPECIFIC HEAT OF A GAS AT CONSTANT PRESSURE
B
3
199

d
Է
200
Fig. 8
To Galvanometer
Temperature in degrees Centigrade
40
35
30
30
25
20
15
10
5
ROYAL SOCIETY OF CANADA

10
20
30
40
50
60
70
80
Fig 4
Calibration of Thermocouple
90
100
Scale divisions
UNIVERSITY PRESS, TORONTO
NO. L
800
700
Calories from zero of scale '
600
500
400
[DAWES] SPECIFIC HEAT OF A GAS AT CONSTANT PRESSURE
25
5
10
Grams of Dry Air
15
20
5
10
15
20
25
30
35
UNIVERSITY PRESS TORONTO
40
Scale Reading
300
அ
200
100
No. 1
Fig 5
Calibration of Gauge
100
200
300
400
500
600
700
800
Fig.6
Calibration of Calorimeter
900
1000
Scale Reading
UNIVERSITY PRESS, TORONTO
NO. I
201


202
ROYAL SOCIETY OF CANADA
ŠA Thermocouple
100
25
~B Gauge
SC Calorimeter
800
90
7709
80
20 740
70
710
60 15
680
50
650
40
10 620
30
590
20
5
560
10
530
り
​500
10
20
૩૦
40
Time
UNIVERSITY PREBS, TORONTO
NO. 1.
Fig. 7
A Readings of Thermocouple
B
C
Gauge
"19
Calorimeter
.
:


1


UNIVERSITY OF TORONTO STUDIES.
The "Papers from the Physical Laboratories," to be issued
special series of University of Toronto Studies, date from the
1900. The following were published by the Physical Departmen
a very limited edition and are no longer in print. For the sake o
complete record the numbering of the Papers, as forming a serie:
of University of Toronto Studies, is made continuous with the earlier
series and commences with number 18. The earlier numbers, except
those to which a price is attached, are not now available either for
sale or gift.
No.
No.
No.
No.
No.
No.
1: Electric Screening in Vacuum Tubes, by J. C. Mc-
LENNAN.
Trans. Roy. Soc. of Canada, second series, Vol.
VI, Sec. III (1900).
2: Electrical Conductivity in Gases traversed by Cathode
Rays, by J. C. MCLENNAN.
(a) Phil. Trans., A. Vol. 195 (1900), pp. 49-77·
(b) Zeitschrift f. Physik. Chemie XXXVII, 5 (1901).
3: On a kind of Radioactivity imparted to certain Salts by
Cathode Rays, by J. C. McLennan.
(a) Phys. Zeit. Vol. 2, No. 49, pp. 704-706 1901).
(b) Phil. Mag., Feb. 1902.
4: On excited Radioactivity, by R. M. STEWART.
Trans. Roy. Soc. of Canada, second series, Vol.
VIII, Sec. III (1902).
5: Induced Radioactivity excited in Air at the Foot of
Waterfalls, by J. C. MCLENNAN..
(a) Phys. Zeit., 4, No. 10, pp 295-298 (1903).
(b) Phil. Mag., April 1903.
(c) Physical Review, Vol. XVI, No. 4 (1903).
(d) University of Toronto Studies, Physical Science
Series, No. 1.
0.50
6: Some Experiments on the Electrical Conductivity of
Atmospheric Air, by J. C. MCLENNAN and E. F. BURTON. 0.50
(a) Physical Review, Vol. XVI, No. 3 (1903).
(b) University of Toronto Studies, Physical Science
Series, No. 2 (1903).
No. 7: On the Radioactivity of Metals Generally, by J. C. Mc-
LENNAN and E. F. BURTON.
(a) Trans. Roy: Soc. of Canada, Second Series Vol.
IX, Sec. III (1903).
(b) Phys. Zeit. 1903, No. 20, pp. 553-556.
(c) Phil. Mag., Sept. 1903.
(d) University of Toronto Studies, Physical Science
Series, No. 3 (1903).
0.25




.0.
8: On the Potential Difference required to produce Elec-
trical Discharges in Gases at Low Pressure; an
Extension of Paschen's Law, by W. R. CARR.
Trans. Roy. Soc. of Canada, Second Series, Vol.
VIII, Sec. III (1902).
No. 9: On the Laws governing Electric Discharges in Gases
at Low Pressures, by W. R. CARR.
Phil. Trans. A. Vol. 201, pp. 403-433 (1903).
No. 10: On the Character of the Radiation from Ordinary
Metals, by E. F. BURTON.
Phys. Rev. Vol. XVIII, No. 3 (1904).
No. 11 The Metric System of Weights and Measures, by
J. C. MCLENNAN.
Proc. of Select Standing Committee on Agriculture
and Colonization of the House of Commons, Canada,
March 29, 1904.
No. 12: On the Radioactivity of Natural Gas, by J. C. MCLENNAN.
Trans. Roy. Soc. of Canada, Second Series, Vol. X,
Section III (1904).
No. 13: On a Radioactive Gas from Crude Petroleum, by
E. F. BURTON.
(a) University Studies, Phys. Sci. Series, No. 4(1904).
(b) Phil. Mag. Oct., 1904.
No. 14: On the Radioactivity of Mineral Oils and Natural
Gases, by J. C. MCLENNAN.
Proceedings of the International Electrical Congress
of St. Louis, 1904.
No. 15: Note on the Use of Sensitive Quadrant Electrometers,
by J. C. MCLENNAN.
Phys. Rev. Vol. XX, No. 3 (1905).
No. 16: On the Decay of Excited Radioactivity from Natural
Gases, by Miss L. B. JOHNSON.
Phys. Rev. Vol. XX, No. 3 (1905).
No. 17: On the Secondary Radiation excited in Different Metals
by the y Rays from Radium, by H. F. Dawes.
Phys. Rev. Vol. XX, No. 3 (1905).
No. 18: On a New Method of Determining the Specific Heat
of a Gas at Constant Pressure, by H. F. Dawes..
Trans. Roy. Soc. of Canada, Second Series, Vol. XII,
Section III (1906).
No. 19: On the Magnetic Susceptibility of Mixtures of Salt
Solutions, by J. C. MCLENNAN and C. S. Wright
Phys. Rev. Vol. XXIV, No. 3 (1907).
0.25
0.25
•
J
0.25
零
​