The increment in weight of the absorbers for water and carbon dioxide
and the loss in weight of the oxygen cylinder give only an approximate
idea of the amounts of carbon dioxide and water-vapor produced and
oxygen absorbed during the period, and it is necessary to make
correction for change in the composition of the air as shown by the
residual analyses and for fluctuations in the actual volume. In order to
compute from the analyses the total carbon-dioxide content of the
residual air, it is necessary to know the relation of the air used for
the sample to the total volume, and thus we must know accurately the
volume of air passing through the gas-meter.
In the earlier apparatus 10-liter samples were used, and the volume of
the respiration chamber was so large that it was necessary to multiply
the values found in the residual sample by a very large factor, 500.
Hence, the utmost caution was taken to procure an accurate measurement
of the sample, the exact amounts of carbon dioxide absorbed, and
water-vapor absorbed. To this end a large number of corrections were
made, which are not necessary with the present type of apparatus with a
volume of residual air of but about 1,300 liters, and accordingly the
manipulation and calculations have been very greatly simplified.
While formerly pains were taken to obtain the exact temperature of the
air leaving the gas-meter, with this apparatus it is unnecessary. When
the earlier type of apparatus was in use there were marked changes in
the temperature of the calorimeter laboratory and in the water in the
meter which were naturally prejudicial to the accurate measurement of
the volume of samples, but with the present control of temperature in
this laboratory it has been found by repeated tests that the temperature
of the water in the meter does not vary a sufficient amount to justify
this painstaking measurement and calculation. Obviously, this
observation also pertains to the corrections for the tension of aqueous
vapor. It has been found possible to assume an average laboratory
temperature and reduce the volume as read on the meter by means of a
constant factor.
The quantity of air passing through the meter is so adjusted that
exactly 10 liters as measured on the dial pass through it for one
analysis. The air as measured in the meter is, however, under markedly
different conditions from the air inside the respiration chamber. While
there is the same temperature, there is a material difference in the
water-vapor present, and hence the moisture content as expressed in
terms of tension of aqueous vapor must be considered. This obviously
tends to diminish the true volume of air in the meter.
Formerly we made accurate correction for the tension of aqueous vapor
based upon the barometer and the temperature of the meter at the end of
the period, but it has now been found that the reduction of the meter
readings to conditions inside of the chamber can be made with a
sufficient degree of accuracy by multiplying the volume of air passing
through the meter by a fraction, _(h-t)/h_, in which _h_ represents the
barometer and _t_ the tension of aqueous vapor at the temperature of the
laboratory, 20° C. Since the tension of aqueous vapor at the laboratory
temperature is not far from 15 mm., a simple calculation will show that
there may be considerable variations in the value of _h_ without
affecting the fraction materially, and we have accordingly assumed a
value of _h_ as normally 760 mm., and the correction thus obtained is
(760 - 15)/760 = 0.98, and all readings on the meter should be
multiplied by this fraction.
On the one hand, then, there is the correction on the meter itself,
which correction is +1.4 per cent (see page 75); and on the other hand
the correction on the sample for the tension of aqueous vapor, which is
-2.0 per cent, and consequently the resultant correction is -0.6 per
cent. From the conditions under which the experiments are made, however,
it is rarely possible to read the meter closer than ±0.05 liter, as the
graduations on the meter correspond to 50 cubic centimeters. It will be
seen, then, that this final correction is really inside the limit of
error of the instrument, and consequently with this particular meter now
in use no correction whatever is necessary for the reduction of the
volume. The matter of temperature corrections has been taken up in great
detail in an earlier publication, and where there are noticeable
differences in temperature between the meter and the calorimeter chamber
the calculation is very much more complicated.
For practical purposes, therefore, we may assume that the quantity of
air passed through the meter, as now in use, represents exactly 10
liters measured under the conditions obtaining inside of the respiration
chamber, and in order to find the total amount of water-vapor present in
the chamber it is necessary only to multiply the weight of water found
in the 10-liter sample by one-tenth of the total volume of air
containing water-vapor.
The total volume of air which contains water-vapor is not far from 1,360
liters; consequently multiplying the weight of water in the sample by
136 gives the total amount of water in the chamber and the piping. The
volume of air containing carbon dioxide is that contained in the chamber
and piping to the first sulphuric-acid vessel plus 16 liters of air
above the sulphuric acid and connections in the first porcelain vessel,
and in order to obtain the amount of carbon dioxide from the sample it
is only necessary to multiply the weight of carbon dioxide in the sample
by 137.6.
Since in the calculation of the total amount of residual oxygen volumes
rather than weights of gases are used, it is our custom to convert the
weights of carbon dioxide and water-vapor in the chamber to volumes by
multiplying by the well-known factors. The determination of oxygen
depends upon the knowledge of the true rather than the apparent volume
of air in the system, and consequently the apparent volume must be
reduced to standard conditions of temperature and pressure each time the
calculation is made. To this end, the total volume of air in the
inclosed circuit (including that in the tension-equalizer, amounting to
1,400 liters in all) is reduced to 0° and 760 millimeters by the usual
methods of computation. The total volume of air (which may be designated
as _V_) includes the volumes of carbon dioxide, water-vapor, oxygen, and
nitrogen. From the calculations mentioned above, the volumes of
water-vapor and carbon dioxide have been computed, and deducting the sum
of these from the reduced volume of air gives the volume of oxygen plus
nitrogen. If the volume of nitrogen is known, obviously the volume of
oxygen can be found.
At the beginning of the experiment, it is assumed that the chamber is
filled with ordinary air. By calculating the amount of nitrogen in the
chamber at the start as four-fifths of the total amount, no great error
is introduced. In many experiments actual analyses of the air have been
made at the moment of the beginning of the experiment. The important
thing to bear in mind is that having once sealed the chamber and closed
it tightly, no nitrogen can enter other than that admitted with the
oxygen, and hence the residual amount of nitrogen remains unaltered save
for this single exception. If care is taken to keep an accurate record
of the amount of nitrogen admitted with the oxygen, the nitrogen
residual in the chamber at any given time is readily computed. While
from an absolute mathematical standpoint the accuracy of this
computation can be questioned, here again we are seeking an accurate
record of differences rather than an absolute amount, and whether we
assume the volume of the air in the chamber to contain 20.4 per cent of
oxygen or 21.6 per cent is a matter of indifference. It is of importance
only to note the increases in the amount of nitrogen, since these
increases represent decrease in the residual oxygen and it is with the
changes in the residual oxygen that we particularly have to do.
INFLUENCE OF FLUCTUATIONS IN TEMPERATURE AND PRESSURE ON THE APPARENT
VOLUME OF AIR IN THE SYSTEM.
The air, being confined in a space with semi-rigid walls, is subjected
naturally to variations in true volume, depending upon the temperature
and barometric pressure. If the air inside of the chamber becomes
considerably warmer there is naturally an expansion, and were it not for
the tension-equalizer there would be pressure in the system. Also, if
the barometer falls, there is an expansion of air which, again, in the
absence of the tension-equalizer, would produce pressure in the system.
It is necessary, therefore, in calculating the true volume of air, to
take into account not only the apparent volume, which, as is shown
above, is always a constant amount at the end of each period, but the
changes in temperature and barometric pressure must also be noted. Since
there is a volume of about 1,400 liters, a simple calculation will show
that for each degree centigrade change in temperature there will be a
change in volume of approximately 4.8 liters. In actual practice,
however, this rarely occurs, as the temperature control is usually
inside of 0.1° C. and for the most part within a few hundredths. A
variation in barometric pressure of 1 millimeter will affect 1,400
liters by 1.8 liters.
In actual practice, therefore, it is seen that if the barometer falls
there will be an expansion of air in the system. This will tend to
increase the volume by raising the rubber diaphragm on the
tension-equalizer, the ultimate result of which is that at the final
filling with oxygen at the end of the period less is used than would be
the case had there been no change in the barometer. In other words, for
each liter expansion of air inside of the system, there is 1 liter less
oxygen required to bring the apparent volume the same at the end of the
period. Similarly, if there is an increase in temperature of the air,
there is expansion, and a smaller amount of oxygen is required than
would be the case had there been no change; and conversely, if the
barometer rises or the temperature falls, more oxygen would be supplied
than is needed for consumption. It is thus seen that the temperature and
barometer changes affect the quantity of oxygen admitted to the chamber.
INFLUENCE OF FLUCTUATIONS IN THE AMOUNTS OF CARBON DIOXIDE AND
WATER-VAPOR UPON RESIDUAL OXYGEN.
Any variations in the residual amount of carbon dioxide or water-vapor
likewise affect the oxygen. Thus, if there is an increase of 1 gram in
the amount of residual carbon dioxide, this corresponds to 0.51 liter,
and consequently an equal volume of oxygen is not admitted to the
chamber during the period, since its place has been taken by the
increased volume of carbon dioxide. A similar reasoning will show that
increase in the water-vapor content will have a similar effect, for each
gram of water-vapor corresponds to 1.25 liters and therefore influences
markedly the introduction of oxygen. All four of the factors, therefore
(barometric pressure, temperature, residual carbon dioxide, and residual
water-vapor), affect noticeably the oxygen determination.