Read Ebook: Respiration Calorimeters for Studying the Respiratory Exchange and Energy Transformations of Man by Benedict Francis Gano Carpenter Thorne M Thorne Martin

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As the water-vapor is absorbed by the sulphuric acid, there is a slight increase in volume of the acid. This naturally results in the diminution of the apparent volume of air and likewise again affects the amount of oxygen admitted to produce constant apparent volume at the end of each experimental period. The amount of increase which thus takes place for each experimental period is very small. It has been found that an increase in weight of 25 grams of water-vapor results in an increase in volume of the acid of some 15 cubic centimeters. Formerly this correction was made, but it is now deemed unnecessary and unwise to introduce a refinement that is hardly justified in other parts of the apparatus. Similarly, there is theoretically at least an increase in volume of the potash-lime by reason of the absorption of the carbon dioxide. This was formerly taken into consideration, but the correction is no longer applied.

RESPIRATORY LOSS.

With experiments on man, there is a constant transformation of solid body material into gaseous products which are carried out into the air-current and absorbed. Particularly where no food is taken, this solid material becomes smaller in volume and consequently additional oxygen is required to take the place of the decrease in volume of body substance. But this so-called respiratory loss is more theoretical than practical in importance, and in the experiments made at present the correction is not considered necessary.

CALCULATION OF THE VOLUME OF AIR RESIDUAL IN THE CHAMBER.

The ventilating air-circuit may be said to consist of several portions of air. The largest portion is that in the respiration chamber itself and consists of air containing oxygen, nitrogen, carbon dioxide, and water-vapor. This air is assumed to have the same composition up to the moment when it begins to bubble through the sulphuric acid in the first acid-absorber. The air in this absorber above the acid, amounting to about 14 liters, has a different composition in that the water-vapor has been completely removed. The same 14 liters of air may then be said to contain carbon dioxide, nitrogen, and oxygen. This composition is immediately disturbed the moment the air enters the potash-lime can, when the carbon dioxide is absorbed and the volume of air in the last sulphuric-acid absorber, in the sodium-bicarbonate can, and in the piping back to the calorimeter may be said to consist only of nitrogen and oxygen. The air then between the surface of the sulphuric acid in the last porcelain absorber and the point where the ingoing air is delivered to the calorimeter consists of air free from carbon dioxide and free from water. Formerly this section also included the tension-equalizer, but very recently we have in both of the calorimeters attached the tension-equalizer directly to the respiration chamber.

In the Middletown apparatus, these portions of air of varying composition were likewise subject to considerable variations in temperature, in that the temperature of the laboratory often differed materially from that of the calorimeter chamber itself, especially as regards the apparatus in the upper part of the laboratory room. It is important, however, to know the total volume of the air inclosed in the whole system. This is obtained by direct measurement. The cubic contents of the calorimeter has been carefully measured and computed; the volumes of air in the pipes, valve systems, absorbing vessels, and tension-equalizer have been computed from dimensions, and it has been found that the total volume in the apparatus is, deducting the volume of the permanent fixtures in the calorimeter, 1,347 liters. The corresponding volume for the bed calorimeter is 875. These values are altered by the subject and extra articles taken into the chamber.

From a series of careful measurements and special tests the following apparent volumes for different parts of the system have been calculated:

RESIDUAL ANALYSES.

CALCULATION FROM RESIDUAL ANALYSES.

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.

On the one hand, then, there is the correction on the meter itself, which correction is +1.4 per cent ; 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 is reduced to 0? and 760 millimeters by the usual methods of computation. The total volume of air 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.

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.

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 , affect noticeably the oxygen determination.

CONTROL OF RESIDUAL ANALYSES.

Of the three factors to be determined in the residual air, the oxygen unfortunately can not be directly determined without great difficulty. Furthermore, any errors in the analysis may be very greatly multiplied by the known errors involved in the determination of the true volume of the air in the chamber as a result of the difficulties in obtaining the average temperature of the air. Believing that the method of analysis as outlined above should be controlled as far as possible by other independent methods, we were able to compare the carbon dioxide as determined by the soda-lime method with that obtained by the extremely accurate method used by Sond?n and Pettersson. An apparatus for the determination of carbon dioxide and oxygen on the Pettersson principle has been devised by Sond?n and constructed for us by Grave, of Stockholm.

NITROGEN ADMITTED WITH THE OXYGEN.

It is impossible to obtain in the market absolutely chemically pure oxygen. All the oxygen that we have thus far been able to purchase contains nitrogen and, in some instances, measurable amounts of water-vapor and carbon dioxide. The better grade of oxygen, that prepared from liquid air, is practically free from carbon dioxide and water-vapor, but it still contains nitrogen, and hence with every liter of oxygen admitted there is a slight amount of nitrogen added. This amount can readily be found from the gasometric analysis of the oxygen and from the well-known relation between the weight and the volume of nitrogen the weight can be accurately found. This addition of nitrogen played a very important r?le in the calculation of the oxygen consumption as formerly employed. As is seen later, a much abbreviated form of calculation is now in use in which the nitrogen admitted with the oxygen does not influence the calculation of the residual oxygen.

REJECTION OF AIR.

In long-continued experiments, where there is a possibility of a noticeable diminution in the percentage of oxygen in the chamber--a diminution caused either by a marked fall in barometer, which expands the air inside of the chamber and permits admission of less oxygen than would otherwise be required, or by the use of oxygen containing a high percentage of nitrogen, thus continually increasing the amount of nitrogen present in the system--it is highly probable that there may be such an accumulation of nitrogen as to render it advisable to provide for the admission of a large amount of oxygen to restore the air to approximately normal conditions. In rest experiments of short duration this is never necessary. The procedure by which such a restoration of oxygen percentage is accomplished has already been discussed elsewhere. It involves the rejection of a definite amount of air by allowing it to pass into the room through the gas-meter and then making proper corrections for the composition of this air, deducting the volume of oxygen in it from the excess volume of oxygen introduced and correcting the nitrogen residual in order to determine the oxygen absorption during the period in which the air has been rejected.

INTERCHANGE OF AIR IN THE FOOD-APERTURE.

The volume of air in the food-aperture between the two glass doors is approximately 5.3 liters. When the door on the inside is opened and the material placed in the food-aperture and the outer door is subsequently opened, there is by diffusion a passage outward of air of the composition of the air inside of the chamber, and the food-aperture is now filled with room air. When the inner door is again opened this room air enters the chamber and is replaced by air of the same composition as that in the chamber. It is seen, then, that there may theoretically be an interchange of air here which may have an influence on the results. In severe work experiments, where the amount of carbon dioxide in the air is enormously increased, such interchange doubtless does take place in measurable amounts and correction should undoubtedly be made. In ordinary rest experiments, where the composition of the air in the chamber is much more nearly normal, this correction is without special significance. Furthermore, in the two forms of calorimeter now in use, the experiments being of but short duration, provision is made to render it unnecessary to open the food-aperture during the experiment proper. Consequently at present no correction for interchange of air in the food-aperture is made, and for the same reason the slight alteration in volume resulting from the removal or addition of material has also not been considered here.

USE OF THE RESIDUAL BLANK IN THE CALCULATIONS.

To facilitate the calculations and for the sake of uniformity in expressing the results, a special form of blank is used which permits the recording of the principal data regarding the analyses of air in the chamber at the end of each period. Thus at the head of the sheet are recorded the time, the number of the period, kind of experiment, the name or initials of the subject, and the statement as to which calorimeter is used. The barometer recorded in millimeters is indicated in the column at the left and immediately below the heading, together with the temperature of the calorimeter as expressed in degrees centigrade. The temperature of the calorimeter as recorded by the physical observer is usually expressed in the arbitrary scale of the Wheatstone bridge and must be transposed into the centigrade scale by means of a calibration table.

The data for the residual analyses are recorded in the lower left-hand corner: first the weight of the water absorbed from 10 liters of air passing through the meter; to the logarithm of this is added the logarithm of volume I; the result is the logarithm of the total weight of water-vapor in the ventilating air-current. To convert this into liters the logarithmic factor 09462 is added to the logarithm of the weight of water and is the logarithm of water expressed in liters. A similar treatment is accorded the weight of carbon dioxide absorbed from the air-sample, being ultimately the logarithm of the volume of carbon dioxide.

The calculation of the residual volume of nitrogen and the record of the additions thereto was formerly carried out with a refinement that to-day seems wholly unwarranted when other factors influencing this value are taken into consideration. For the majority of experiments the residual volume of nitrogen may be considered as constant in spite of the fact that some nitrogen is regularly admitted with the oxygen. The significance of this assumption is best seen after a consideration of the method of calculating the amount of oxygen admitted to the chamber.

RESIDUAL SHEET No. 1.

Calculation of residual amounts of nitrogen, oxygen, carbon dioxide and water-vapor remaining in chamber at 8.10 A. M., June 24, 1909.

Residual at end of Prelim. period. Exp.: Parturition. No......... Subject: Mrs. Whelan. Calorimeter: Bed.

ABBREVIATED METHOD OF COMPUTATION OF OXYGEN ADMITTED TO THE CHAMBER FOR USE DURING SHORT EXPERIMENTS.

Desiring to make the apparatus as practicable and the calculations as simple as possible, a scheme of calculation has been devised whereby the computations may be very much abbreviated and at the same time there is not too great a sacrifice in accuracy. The loss in weight of the oxygen cylinder has, in the more complicated method of computation, been considered as due to oxygen and about 3 per cent of nitrogen. The amount of nitrogen thus admitted has been carefully computed and its volume taken into consideration in calculating the residual oxygen. If it is considered for a moment that the admission of gas out of the steel cylinder is made at just such a rate as to compensate for the decrease in volume of the air in the system due to the absorption of oxygen by the subject, it can be seen that if the exact volume of the gas leaving the cylinder were known it would be immaterial whether this gas were pure oxygen, oxygen with some nitrogen, or oxygen with any other inert gas not dangerous to respiration or not absorbed by sulphuric acid or potash-lime. If 10 liters of oxygen had been absorbed by the man in the course of an hour, to bring the system back to constant apparent volume it would be necessary to admit 10 liters of such a gas or mixture of gases, assuming that during the hour there had been no change in the temperature, the barometric pressure, or the residual amounts of carbon dioxide or water-vapor.

Under these assumed conditions, then, it would only be necessary to measure the amount of gas admitted in order to have a true measure of the amount of oxygen absorbed. The measure of the volume of the gas admitted may be used for a measure of the oxygen absorbed, even when it is necessary to make allowances for the variations in the amount of carbon dioxide or water-vapor in the chamber, the temperature, and barometric pressure. From the loss in weight of the oxygen cylinder, if the cylinder contained pure oxygen, it would be known that 10 liters would be admitted for every 14.3 grams loss in weight.

From the difference in weight of 1 liter of oxygen and 1 liter of nitrogen, a loss in weight of a gas containing a mixture of oxygen with a small per cent of nitrogen would actually represent a somewhat larger volume of gas than if pure oxygen were admitted. The differences in weight of the two gases, however, and the amount of nitrogen present are so small that one might almost wholly neglect the error thus arising from this admixture of nitrogen and compute the volume of oxygen directly from the loss in weight of the cylinder.

As a matter of fact, it has been found that by increasing the loss in weight of the cylinder of oxygen containing 3 per cent nitrogen by 0.4 per cent and then converting this weight to volume by multiplying by 0.7, the volume of gas admitted is known with great accuracy. This method of calculation has been used with success in connection with the large chamber and particularly for experiments of short duration. It has also been introduced with great success in a portable type of apparatus described elsewhere. Under these conditions, therefore, it is unnecessary to make any correction on the residual volume of nitrogen as calculated at the beginning of the experiment. When a direct comparison of the calculated residual amount of oxygen present is to be made upon determinations made with a gas-analysis apparatus the earlier and much more complicated method of calculation must be employed.

CRITICISM OF THE METHOD OF CALCULATING THE VOLUME OF OXYGEN.

Since the ventilating air-current has a confined volume, in which there are constantly changing percentages of carbon dioxide, oxygen, and water-vapor, it is important to note that the nitrogen present in the apparatus when the apparatus is sealed remains unchanged throughout the whole experiment, save for the small amounts added with the commercial oxygen--amounts well known and for which definite corrections can be made. Consequently, in order to find the amount of oxygen present in the residual air at any time it is only necessary to determine the amounts of carbon dioxide and water-vapor and, from these two factors and from the known volume of nitrogen present, it is possible to compute the total volume of oxygen after calculating the total absolute volume of air in the chamber at any given time.

While the apparent volume of the air remains constant throughout the whole experiment, by the conditions of the experiment itself the absolute amount may change considerably, owing primarily to the fluctuations in barometric pressure and secondarily to slight fluctuations in the temperature of the air inside of the chamber. Although the attempt is made on the part of the observers to arbitrarily control the temperature of this air to within a few hundredths of a degree, at times the subject may inadvertently move his body about in the chair just a few moments before the end of the period and thus temporarily cause an increased expansion of the air. The apparatus is, in a word, a large air-thermometer, inside the bulb of which the subject is sitting. If the whole system were inclosed in rigid walls there would be from time to time noticeable changes in pressure on the system due to variations in the absolute volume, but by means of the tension-equalizer these fluctuations in pressure are avoided.

The same difficulties pertain here which were experienced with the earlier type of apparatus in determining the average temperature of the volume of air inside of the chamber. We have on the one hand the warm surface of the man's body, averaging not far from 32? C. On the other hand we have the cold water in the heat-absorbers at a temperature not far from 12? C. Obviously, the air in the immediate neighborhood of these two localities is considerably warmer or colder than the average temperature of the air. The disposition of the electric-resistance thermometers about the chamber has, after a great deal of experimenting, been made such as to permit the measurement as nearly as possible of the average temperature in the chamber. But this is at best a rough approximation, and we must rely upon the assumption that while the temperatures which are actually measured may not be the average temperature, the fluctuations of the average temperature are parallel to the fluctuations in the temperatures measured. Since every effort is made to keep these fluctuations at a minimum, it is seen that the error of this assumption is not as great as might appear at first sight. However, the calculation of the residual amount of oxygen in the chamber is dependent upon this assumption and hence any errors in the assumption will affect noticeably the calculation of the residual oxygen.

Under these conditions it is hoped to secure a more satisfactory comparison of the analyses as made by means of the Sond?n apparatus and as calculated from the composition of the residual air by the gravimetric analysis. It remains a fact, however, that no matter with what skill and care the gasometric analysis is made, either gravimetrically or volumetrically, the calculation of the residual amount of oxygen presents the same difficulties in both cases.

From the weights of the sulphuric-acid and potash-lime vessels, the amounts of water-vapor and carbon dioxide absorbed out of the air-current are readily obtained. The loss in weight of the oxygen cylinder increased by 0.4 per cent gives the weight of oxygen admitted to the chamber. It remains, therefore, to make proper allowance for the variations in composition of the air inside the chamber at the beginning and end of the different periods. From the residual sheets the amounts of water-vapor, carbonic acid, and oxygen present in the system at the beginning and end of each period are definitely known. If there is an increase, for example, in the amount of carbon dioxide in the chamber at the end of a period, this increase must be added to the amount absorbed out of the air-current in order to obtain the true value for the amount produced during the experimental period.

A similar calculation holds true with regard to the water-vapor and oxygen. For convenience in calculating, the amounts of water-vapor and carbon dioxide residual in the chamber are usually expressed in grams, while the oxygen is expressed in liters. Hence, before making the additions or subtractions from the amount of oxygen admitted, the variations in the amount of oxygen residual in the system should be converted from liters to grams. This is done by dividing by 0.7.

CONTROL EXPERIMENTS WITH BURNING ALCOHOL.

After having brought to as high a degree of perfection as possible the apparatus for determining carbon dioxide, water, and oxygen, it becomes necessary to submit the apparatus to a severe test and thus demonstrate its ability to give satisfactory results under conditions that can be accurately controlled. The liberation of a definite amount of carbon dioxide from a carbonate by means of acid has frequently been employed for controlling an apparatus used for researches in gaseous exchange, but this only furnishes a definite amount of carbon dioxide and throws no light whatever upon the ability of the apparatus to determine the other two factors, water-vapor and oxygen. Some of the earlier experimenters have used burning candles, but these we have found to be extremely unsatisfactory. The necessity for an accurate elementary analysis, the high carbon content of the stearin and paraffin, and the possibility of a change in the chemical composition of the material all render this method unfit for the most accurate testing. As a result of a large number of experiments with different materials, we still rely upon the use of ethyl alcohol of known water-content. The experiments with absolute alcohol and with alcohol containing varying amounts of water showed no differences in the results, and hence it is now our custom to obtain the highest grade commercial alcohol, determine the specific gravity accurately, and burn this material. We use the Squibb pyknometer and thereby can determine the specific gravity of the alcohol to the fifth or sixth decimal place with a high degree of accuracy. Using the alcoholometric tables of Squibb or Morley, the percentage of alcohol by weight is readily found, and from the chemical composition of the alcohol can be computed not only the amount of carbon dioxide and water-vapor formed and oxygen absorbed by the combustion of 1 gram of ethyl hydroxide containing a definite known amount of water, but also the heat developed during its combustion.

With the construction of this apparatus it was found impracticable to employ the type of alcohol lamp formerly used with success in the Wesleyan University respiration chamber. Inability to illuminate the gage on the side of the lamp and the small windows on the side of the calorimeter precluded its use. It was necessary to resort to the use of an ordinary kerosene lamp with a large glass font and an Argand burner. Of the many check-tests made we quote one of December 31, 1908, made with the bed calorimeter:

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