DETERMINATION OF NUTRITIVE VALUES.
558. Nutritive Value of Foods.—The value of a food as a nutrient depends on the amount of heat it gives on combustion in the tissues of the body, i. e. oxidation, and in its fitness to nourish the tissues of the body, to promote growth and repair waste. The foods which supply heat to the body are organic in their nature and are typically represented by fats and carbohydrates. The foods which promote growth and supply waste are not only those which preeminently supply heat, but also include the inorganic bodies and organic nitrogenous matters represented typically by the proteids. It is not proper to say that one class of food is definitely devoted to heat forming and another to tissue building, inasmuch as the same substance may play an important rôle in both directions. As heat formers, carbohydrates and proteids have an almost equal value, as measured by combustion in oxygen, while fat has a double value for this purpose. The assumption that combustion in oxygen forms a just criterion for determining the value of a food must not be taken too literally. There are only a few bodies of the vast number which burn in oxygen that are capable of assimilation and oxidation by the animal organism. Only those parts of the food that become soluble and assimilable under the action of the digestive ferments, take part in nutrition and the percentage of food materials digested varies within wide limits but rarely approaches 100. It may be safely said that less than two-thirds of the total food materials ingested are dissolved, absorbed, decomposed and assimilated in the animal system. We have no means of knowing how far the decomposition (oxidation) extends before assimilation, and therefore no theoretical means of calculating the quantity of heat which is produced during the progress of digestion. The vital thermostat is far more delicate than any mechanical contrivance for regulating temperature and the quantity of food, in a state of health, converted into heat, is just sufficient to maintain the temperature of the body at a normal degree. Any excess of heat produced, as by violent muscular exertion, is dissipated through the lungs, the perspiration and other secretions of the body.
Pure cellulose or undigestible fiber, when burned in oxygen, will give a thermal value approximating that of sugar, but no illustration is required to show that when taken into the system the bodily heat afforded by it is insignificant in quantity.
Thermal values, therefore, have little comparative usefulness in determining nutritive worth, except when applied to foods of approximately the same digestive coefficient.
559. Comparative Value of Food Constituents.—It has already been noted that, judged by combustion in oxygen, carbohydrates and proteids have about half the thermal value possessed by fats. Commercially, the values of foods depend in a far greater degree on their flavor and cooking qualities than upon the amount of nutrition they contain. Butter fat, which is scarcely more nutritious than tallow, is worth twice as much in the market, while the prices paid for vegetables and fruits are not based to any great extent on their food properties.[574] In cereals, especially in wheat, the quantity of fat is relatively small, and starch is the preponderating element. In meats, carbohydrates are practically eliminated and fats and proteids are the predominating constituents.
In the markets, fats and proteids command far higher prices than sugars and starches. The relative commercial food value of a cereal may be roughly approximated by multiplying the percentages of fat and protein by two and a half and adding the products to the percentage of carbohydrates less insoluble fiber. This method was adopted in valuing the cereals at the World’s Columbian Exposition.[575]
560. Nutritive Ratio.—In solid foods the nutritive ratio is that existing between the percentage of proteids and that of carbohydrates, increased by multiplying the fat by two and a half and adding the product. In a cereal containing twelve per cent of protein, seventy-two of carbohydrates, exclusive of fiber, and three of fat, the ratio is 12: 72 + 3 × 2.5 = 6.5. Instead of calculating the nutritive ratio directly from the data obtained by analysis, it may be reckoned from the per cents of the three substances in the sample multiplied by their digestive coefficient. Since the relative amounts of proteids, fats and carbohydrates digested do not greatly differ, the numerical expression of the nutritive ratio is nearly the same when obtained by each of these methods of calculation.
Where the proportion of protein is relatively large the ratio is called narrow, 1: 4 ... 6. When the proportion of protein is relatively small the ratio is called broad 1: 8 ... 12. In feeding, the nutritive ratio is varied in harmony with the purpose in view, a narrow ratio favoring the development of muscular energy, and a wide one promoting the deposition of fat and the development of heat. These principles guide the scientific farmer in mixing rations for his stock, the work horses receiving a comparatively narrow and the beeves a relatively wide ratio in their food.
561. Calorimetric Analyses of Foods.—The general principles of calorimetry have been already noticed. The theoretical and chemical relations of calorimetry have been fully discussed by Berthelot, Thomsen, Ostwald and Muir.[576] In the analyses of foods the values as determined by calculation or combustion are of importance in determining the nutritive relations.
Atwater has presented a résumé of the history and importance of the calorimetric investigations of foods to which the analyst is referred.[577]
In the computation of food values the percentages of proteids, carbohydrates and fats are determined and the required data obtained by applying the factors 4100, 5500 and 9300 calories for one gram of carbohydrates, proteids and fats respectively.
For most purposes the computed values are sufficient, but it is well to check them from time to time by actual combustions in a calorimeter.
562. Combustion in Oxygen.—The author made a series of combustions of carbonaceous materials in oxygen at the laboratory of Purdue University in 1877, the ignition being secured by a platinum wire rendered incandescent by the electric current. The data obtained were unsatisfactory on account of the crudeness of the apparatus. The discovery of the process of burning the samples in oxygen at a high pressure has made it possible to get expressions of thermal data which while not yet perfect, possess a working degree of accuracy. The best form of bomb calorimeter heretofore employed is that of Hempel, as modified by Atwater and Woods.[578]
A section of this calorimeter, with all the parts in place, is shown in [Fig. 120].
In the figure the steel cylinder A, about 12.5 centimeters deep and 6.2 in diameter, represents the chamber in which the combustion takes place. Its walls are about half a centimeter thick and it weighs about three kilograms. It is closed, when all the parts are ready and the sample in place, by the collar C, which is secured gas tight by means of a powerful spanner. The cover is provided with a neck D carrying a screw E and a valve screw F. In the neck D, where the bottom of the cylinder screw E rests, is a shoulder fitted with a lead washer. Through G the oxygen used for combustion is introduced. The upper edge of the cylinder A is beveled and fits into a groove in the cover B, carrying a soft metal washer. To facilitate the screwing on of the cover, ball bearings KK, made of hard steel, are introduced between the collar and the cover. The platinum wires H and I support the platinum crucible holding the combustible bodies which are ignited by raising the spiral iron wire connecting them to the temperature of fusion by an electric current. The combustion apparatus when charged is immersed in a metal cylinder M, containing water and resting on small cylinders of cork. The water is stirred by the apparatus LL. The cylinder M is contained in two large concentric cylinders, N, O, made of non-conducting materials and covered with disks of hard rubber. The space between O and N may be filled with water. The temperature is measured by the thermometer P, graduated to hundredths of a degree and the reading is best accomplished by means of a cathetometer.
Fig. 120. Hempel and Atwater’s
Calorimeter.
563. The Williams Calorimeter.—The calorimeter bomb has been improved by Williams by making it of aluminum bronze of a spheroidal shape. The interior of the bomb is plated with gold. By an ingenious arrangement of contacts the firing is secured by means of a permanently insulated electrode fixed in the side of the bomb. The calorimetric water, as well as that in the insulating vessel, is stirred by means of an electrical screw so regulated as to produce no appreciable degree of heat mechanically. The combustion is started by fusing a fine platinum wire of definite length and thickness by means of an electric current. The heat value of this fusion is determined and the calories produced deducted from the total calories of the combustion. The valve admitting the oxygen is sealed automatically on breaking connection with the oxygen cylinder. The effluent gases, at the end of the combustion, may be withdrawn through an alkaline solution and any nitric acid therein thus be fixed and determined.[579]
564. Manipulation and Calculation.—The material to be burned is conveniently prepared by pressing it into tablets. The oxygen is supplied from cylinders, of which two should be used, one at a pressure of more than twenty atmospheres. By this arrangement a pump is not required.
In practical use, a known weight of the substance to be burned is placed in the platinum capsule, the cover of the bomb screwed on, after all adjustments have been made, and the apparatus immersed in the water contained in M, which should be about 2° below room temperature. All the covers are placed in position and the temperature, of the water in M begins to rise. Readings of the thermometer are taken at intervals of about one minute for six minutes, at which time the temperature of the bomb and calorimetric water may be regarded as sensibly the same. The electric current is turned on, the iron wire at once melts, ignites the substance and the combustion rapidly takes place. In the case of bodies which do not burn readily Atwater adds to them some naphthalene, the thermal value of which is previously determined. The calories due to the combustion of the added naphthalene are deducted from the total calories obtained.
The temperature of the water in M rises rapidly at first, and readings are made at intervals of one minute for five minutes, and then again after ten minutes. The first of the initial readings, the one at the moment of turning on the current, and the last one mentioned above are the data from which the correction, made necessary by the influence of the temperature of the room, is calculated by the following formulas.[580]
The preliminary readings of the thermometer at one minute intervals are represented by t₁, t₂, t₃ ... tₙ₁. The last observation tₙ₁ is taken as the beginning temperature of the combustion and is represented in the formulas for calculations by Θ₁. The readings after combustion are also made at intervals of one minute, and are designated by Θ₂, Θ₃ ... Θₙ. The readings are continued until there is no observed change between the last two. Generally this is secured by five or six readings.
The third period of observations begins with the last reading Θₙ, which in the next series is represented by tʹ₁, tʹ₂ ... tʹₙ₂.
In order to make the formulas less cumbersome let
| tₙ₁ - t₁ | = v, |
| n₁ - 1 |
| tʹₙ₁ - tʹ₁ | = vʹ, |
| n₂ - 1 |
| t₁ + t₂ + t₃ ... tₙ₁ | = t, |
| n₁ |
| and | tʹ₁ + tʹ₂ + tʹ₃ ... tʹₙ₂ | = tʹ. |
| n₂ |
The correction to be made to the difference between Θₙ - Θ₁ for the influence of the outside temperature is determined by the formula of Regnault-Pfaundler, which is as follows:
| ∑ Δt = | v - vʹ | ( | ⁿ⁻¹ | ∑ | Θr + | Θₙ + Θ₁ | - nt ) - (n - 1)v, |
| tʹ - t | ₁ | 2 |
| n-1 | |
| in which ∑ | Θr |
| 1 |
is calculated from the observation of the thermometer Θ₁, Θ₂ etc., made immediately after the combustion. It is equal to the sum of observations Θ₁, Θ₂ etc., increased by an arbitrary factor equivalent to (Θ₂ - Θ₁)/9, which is made necessary by reason of the irregularity of the temperature increase during the first minute after combustion, the mean temperature during that minute being somewhat higher than the mean of the temperatures at the commencement and end of that time.
The quantity of heat formed by the combustion of the iron wire used for igniting the sample is to be deducted from the total heat produced. This correction may be determined once for all, the weight of the iron wire used being noted and that of any unburned portion being ascertained after the combustion.
Ten milligrams of iron, on complete combustion, will give sixteen calories.
In the combustion of substances containing nitrogen, or in case the free nitrogen of the air be not wholly expelled from the apparatus before the burning, nitric acid is formed which is dissolved by the water produced.
The heat produced by the solution of nitric acid in water is 14.3 calories per gram molecule. The quantity of nitric acid formed is determined by titration and a corresponding reduction made in the total calculated calories.
In the titration of nitric acid it is advisable to make use of an alkaline solution, of which one liter is equivalent to 4.406 grams of nitric acid. One cubic centimeter of the reagent is equivalent to a quantity of nitric acid represented by one calorie.
Since the materials of which the bomb is composed have a specific heat different from that of water, it is necessary to compute the water thermal value of each apparatus.
The hydrothermal equivalent of the whole apparatus is most simply determined by immersing it at a given temperature in water of a different temperature.[581] With small apparatus this method is quite sufficient, but there are many difficulties attending its application to large systems weighing several kilograms. In these cases the hydrothermal equivalent may be calculated from the specific heats of the various components of the apparatus.
In calculating these values the specific heats of the various components of the apparatus are as follows:
| Brass | 0.093 |
| Steel | 0.1097 |
| Platinum | 0.0324 |
| Copper | 0.09245 |
| Lead | 0.0315 |
| Oxygen | 0.2389 |
| Glass | 0.190 |
| Mercury | 0.0332 |
| Hard rubber | 0.33125 |
Example.—It is required to calculate the hydrothermal value of a calorimeter composed of the following substances:
| Hydrothermal value. | ||
| Steel bomb and cover, 2850 grams × 0.1097 | 312.65 | grams. |
| Platinum lining, capsule and wires, 120 grams × 0.0324 | 3.89 | ” |
| Lead washer, 100 grams × 0.0315 | 3.15 | ” |
| Brass outer cylinder, 500 grams × 0.093 | 46.50 | ” |
| Mercury in thermometer, 10 grams × 0.0332 | 0.33 | ” |
| Glass (part of thermometer in water), 10 grams × 0.19 | 1.90 | ” |
| Brass stirring apparatus (part in water), 100 grams × 0.093 | 9.30 | ” |
| Total water value of system | 377.72 | ” |
When a bomb of 300 cubic centimeters capacity is filled with oxygen at a pressure of twenty-four atmospheres it will hold about ten grams of the gas, equivalent to a water value of 2.40 grams. Hence the water value of the above system when charged, assuming the bomb to be of the capacity mentioned, is 380.12 grams.
If the cylinder holding the water be made of fiber or other non-conducting substance, its specific heat is best determined by filling it in a known temperature with water at a definite different temperature.
It is advisable to have the water cylinder of such a size as to permit the use of a quantity of water for the total immersion of the bomb which will weigh, with the water value of the apparatus, an even number of grams. In the case above, 2622.28 grams of water placed in the cylinder will make a water value of 3,000 grams, which is one quite convenient for calculation.
565. Computing the Calories of Combustion.—In the preceding paragraph has been given a brief account of the construction of the calorimeter and of the methods of standardizing it and securing the necessary corrections in the data directly obtained in its use. An illustration of the details of computing the calories of combustion taken from the paper of Stohmann, Kleber and Langbein, will be a sufficient guide for the analyst in conducting the combustion and in the use of the data obtained.[582]
Weight of substance burned, 1.07 grams.
Water value of system (water + apparatus), 2,500 grams.
Preliminary thermometric readings, t₁ = 26.8; t₂ = 27.2; t₃ = 27.7; t₄ = 28.1; t₅ = 28.5; tₙ₁ = 28.9.
Thermometric reading after combustion, Θ₁ = 28.9; Θ₂ = 202; Θ₃ = 213; Θ₄ = 214.2; Θₙ = 214.0.
Final thermometric readings, tʹ₁ = 214.0; tʹ₂ = 213.8; tʹ₃ = 213.6; tʹ₄ = 213.5; tʹ₅ = 213.3; tʹ₆ = 213.1; tʹ₇ = 212.9; tʹ₈ = 212.7; tʹ₉ = 212.6; tʹ₁₀ = 212.4; tʹₙ₂ = 212.2.
From the formulas given above the following numerical values are computed:
- v = 0.42.
- vʹ = -0.18.
- t = 27.9.
- tʹ = 213.1.
- n = 5.
| n-1 | |||
| ∑ | Θr = Θ₁ + Θ₂ + Θ₃ + Θ₄ + | Θ₂ - Θ₁ | = 667. |
| 1 | 9 | ||
Substituting these values in the formula of Regnault-Pfaundler, the value of the correction for the influence of the external air is
| ∑ Δt = | [ | 0.42 - (-0.18) | ( | 677 + | 214 + 29 | - (5 × 27.9) | ) | - (4 × 0.42) | ] | = 0.45, |
| 213.1 - 27.9 | 2 |
which is to be added to the end temperature (Θₙ = 214.0).
The computation is then made from the following data:
| Corrected end temperature (Θₙ + 0.45) | 214.45 | = | 15°.3699 |
| Beginning temperature (Θ₁) | 28.90 | = | 12°.8406 |
| Increase in temperature | 185.55 | = | 2°.5293 |
| Total calories 2.5293 × 25000 | = | 6323.3 | |
| Of which there were due to iron burned | 9.1 | ||
| ” ” ” ” nitric acid dissolved | 8.2 | ||
| Total calories due to one gram of substance | 5893.5 | ||
The thermometric readings are given in the divisions of the thermometer which in this case are so adjusted as to have the number 28.90 correspond to 12°.8406, and each division is nearly equivalent to 0°.014 thermometric degree.
The number of calories above given is the proper one when the computation is made to refer to constant volume. By reason of the consumption of oxygen and the change of temperature, although mutually compensatory, the pressure may be changed at the end of the operation. The conversion of the data obtained at constant volume referred to constant pressure may be made by the following formula, in which [Q] represents the calories from constant volume and Q the desired data for constant pressure, O the number of oxygen atoms, H the number of hydrogen atoms in a molecule of the substance, and 0.291 a constant for a temperature of about 18°, at which the observations should be made.
| Q = [Q] + | ( | H | - O | ) | 0.291. |
| 2 |
566. Calorimetric Equivalents.—By the term calorie is understood the quantity of heat required to raise one gram of water, at an initial temperature of about 18°, one degree. The term ‘Calorie’ denotes the quantity of heat, in like conditions, required to raise one kilogram of water one degree.
For purposes of comparison and for assisting the analyst in adjusting his apparatus so as to give reliable results, the following data, giving the calories of some common food materials, are given:
| Substance. Proteids. | Calories. | Chemical composition. | ||||
|---|---|---|---|---|---|---|
| C. | H. | N. | S. | O. | ||
| Per cent. | Per cent. | Per cent. | Per cent. | Per cent. | ||
| Serum albumin | 5917.8 | 53.93 | 7.65 | 15.15 | 1.18 | 22.09 |
| Casein | 5867.0 | 54.02 | 7.33 | 15.52 | 0.75 | 22.38 |
| Egg albumin | 5735.0 | 52.95 | 7.50 | 15.19 | 1.51 | 22.85 |
| Meat free of fat and | 5720.0 | 52.11 | 6.76 | 18.14 | 0.96 | 22.66 |
| extracted with water | ||||||
| Peptone | 5298.8 | 50.10 | 6.45 | 16.42 | 1.24 | 25.79 |
| Proteids (mean) Glycerids. | 5730.8 | 52.71 | 7.09 | 16.02 | 1.03 | 23.15 |
| Butterfat | 9231.3 | |||||
| Linseed oil | 9488.0 | |||||
| Olive oil | 9467.0 | |||||
| Carbohydrates. | Formula. | |||||
| Arabinose | 3722.0 | C₅H₁₀O₅ | ||||
| Xylose | 3746.0 | C₅H₁₀O₅ | ||||
| Dextrose | 3742.6 | C₆H₁₂O₆ | ||||
| Levulose | 3755.0 | C₆H₁₂O₆ | ||||
| Sucrose | 3955.2 | C₁₂H₂₂O₁₁ | ||||
| Lactose | 3736.8 | C₁₂H₂₂O₁₁ + H₂O | ||||
| Maltose | 3949.3 | C₁₂H₂₂O₁₁ | ||||
567. Distinction between Butter and Oleomargarin.—Theoretically the heats of combustion of butter fat and oleomargarin are different and de Schweinitz and Emery propose to utilize this difference for analytical purposes.[583] The samples of pure butter fat examined by them afforded 9320, 9327 and 9362 calories, respectively. The calories obtained for various samples of oleomargarin varied from 9574 to 9795. On mixing butter fat and oleomargarin, a progressive increase in calorimetric power is found, corresponding to the percentage of the latter constituent. Lards examined at the same time gave from 9503 to 9654 calories.