After providing a suitable apparatus for bringing away the heat
generated inside the chamber and for preventing the loss of heat by
maintaining the walls adiabatic, it is still necessary to demonstrate
the ability of the calorimeter to measure known amounts of heat
accurately. In order to do this we pass a current of electricity of
known voltage through a resistance coil and thus develop heat inside the
respiration chamber. While, undoubtedly, the use of a standard
resistance and potentiometer is the most accurate method for measuring
currents of this nature, thus far we have based our experiments upon the
measurements made with extremely accurate Weston portable voltmeter and
mil-ammeters. Thanks to the kindness of one of our former co-workers,
Mr. S. C. Dinsmore, at present associated with the Weston Electrical
Instrument Company, we have been able to obtain two especially exact
instruments. The mil-ammeter is so adjusted as to give a maximum current
of 1.5 amperes and the voltmeter reads from zero to 150 volts. The
direct current furnished the building is caused to pass through a
variable resistance for adjusting minor variations in voltage and then
through the mil-ammeter into a manganin resistance-coil inside the
chamber, having a resistance of 84.2 ohms. Two leads from the terminals
of the manganin coil connect with the voltmeter outside the chamber, and
hence the drop in potential can be measured very accurately and as
frequently as is desired. The current furnished the building is
remarkably steady, but for the more accurate experiments a small degree
of hand regulation is necessary.
The advantage of the electrical method of controlling the apparatus is
that the measurements can be made very accurately, rapidly, and in short
periods. In making experiments of this nature it is our custom first to
place the resistance-coil in the calorimeter and make the connections.
The current is then passed through the coil, and simultaneously the
water is started flowing through the heat-absorbing system and the whole
calorimeter is adjusted in temperature equilibrium as soon as possible.
When the temperature of the air and walls is constant and the
thermal-junction system in equilibrium, the exact time is noted and the
water-current deflected into the meter. At the end of one hour, the
usual length of a period, the water-current is deflected from the meter,
the meter is weighed, and the average temperature-difference of the
water obtained by averaging the results of all the temperature
differences noted during the hour. Usually during an experiment of this
nature, records of the water-temperatures are made every 4 minutes;
occasionally, when the fluctuations are somewhat greater than usual,
records are made every 2 minutes.
The calculation of the heat developed in the apparatus is made by means
of the formula C × E × _t_ × 0.2385 = calories, in which C equals the
current in amperes, E the electromotive force, and _t_ the time in
seconds. This gives the heat expressed in calories at 15° C. This
procedure we have followed as a result of the recommendation of Dr. E.
B. Rosa, of the National Bureau of Standards. In order to convert the
values to 20°, the unit commonly employed in calorimetric work, it has
been necessary to multiply by the ratio of the specific heat of water at
15° to that of water at 20°. Assuming the specific heat of water at 20°
to be 1, the specific heat at 15° is 1.001.[16]
Of the many electrical check-tests made with this type of apparatus, but
one need be given here, pending a special treatment of the method of
control of the calorimeter in a forthcoming publication. An electrical
check-experiment with the chair calorimeter was made on January 4, 1909,
and continued 6 hours. The voltmeter and mil-ammeter were read every few
minutes, the water collected in the water-meter, carefully weighed, and
the temperature differences as measured on the two mercury thermometers
were recorded every 4 minutes.
The heat developed during the experiment may be calculated from the data
as follows: Average current = 1.293 amperes; average E. M. F. = 109.15
volts; time = 21,600 seconds; factor used to convert watt-seconds to
calories = 0.2385. (1.293 × 109.15 × 21600 × 0.2385) × 1.001 = 727.8
calories produced.
During the 6 hours 237.63 kilograms of water passed through the
absorbing system.
The average temperature rise was 3.04° C., the total heat brought away
was therefore (237.63 × 3.04) × 1.0024[17] = 724.1 calories.
Thus in 6 hours there were about 3.7 calories more heat developed inside
the apparatus than were measured by the water-current, a discrepancy of
about 0.5 per cent.
Under ideal conditions of manipulation, the withdrawal of heat from the
calorimeter should be at just such a rate as to exactly compensate for
the heat developed by the resistance-coil. Under these conditions, then,
there would be no heat abstracted from nor stored by the calorimeter and
its temperature should remain constant throughout the whole experiment.
Practically this is very difficult to accomplish and there are minor
fluctuations in temperature above and below the initial temperature
during a long experiment and, indeed, during a short experimental
period. If a certain amount of heat has been stored up in the
calorimeter chamber or has been abstracted from it, there should be
corrections made for the variations in the temperature of the chamber.
Such corrections are impossible unless a proper determination of the
hydrothermal equivalent has been made. A number of experiments to
determine this hydrothermal equivalent have been made and the results
are recorded beyond, together with a discussion of the nature of the
experiments. As a result of these experiments it has been possible to
make correction for the slight temperature changes in the calorimeter.
It is interesting to note that these fluctuations are small and there
may therefore be a considerable error in the determination of the
hydrothermal equivalent without particularly affecting the corrections
applied in the ordinary electrical check-test. The greatest difficulty
experienced with the calorimeter as a means of measuring heat has been
to secure the average temperature of the ingoing water. The temperature
difference between the mass of water flowing through the pipes and the
outer wall of the pipe is at best considerable. The use of the
vacuum-jacketed glass tubes has minimized the loss of heat through this
tube considerably, but it is advisable that the bulb of the thermometer
be placed exactly in the center of the water-tube, as otherwise too high
a temperature-reading will be secured. When the proper precautions are
taken to secure the correct temperature-reading, the results are most
satisfactory.
In testing both calorimeters a large number of electrical check
experiments have led to the conclusion that discrepancies in results
were invariably due, not to the loss of heat through the walls of the
calorimeter, but to erroneous measurement of the temperature of the
water-current.