Popular Science Monthly/Volume 58/December 1900/Discussion and Correspondence
ENERGY AND WORK OF THE HUMAN BODY.
In discussing 'The Human Body as an Engine,' I referred to some experiments made at Middletown with the Atwater-Rosa Respiration Calorimeter, in which a man lived several days in each of the experiments in a sealed chamber of about 180 cubic feet capacity, eating, sleeping and working, while under minute observation. The potential energy supplied to the subject of the experiment through the food which he ate was determined by serving him with accurately weighed portions of the various articles of the prescribed diet, and analyzing and burning in a small calorimeter carefully selected samples of the same. The energy yielded by the subject consisted of three portions, all of which were carefully determined. These were: (1) the heat of radiation and respiration which was measured by the calorimeter, (2) mechanical work done within the calorimeter and (3) potential energy carried off in the refuse products of the body. The immediate purpose of the work was to verify experimentally the law of the conservation of energy for the living body; to show that the total energy taken into the body is equal to the sum of all the energy given out by the body during the same period (provided there is no net gain or loss of energy by the body); to show, indeed, that the fundamental law of physics applies to the animal body, as it does to an engine or a dynamo or any other machine or mechanical system. The law has been amply verified for inanimate systems; it seemed desirable to test it for an organic system. The statement was made in the article referred to that "In some cases the man under investigation worked regularly eight hours a day, the work done being measured by apparatus designed for the purpose." Some inquiry having been made as to how this work was measured, and whether it is possible, after all, to do this, the editor has asked me to answer the inquiry through the columns of the Monthly.
Confusion often arises in considering questions like the present one through inexact ideas concerning force and work. When force is exerted through a finite distance, work is done and energy is transferred from one body to another; and the work done is equal to the energy so transferred. It is also equal to the force exerted in the direction of the motion multiplied by the distance through which the force acts. For example, when a man lifts a stone he exerts a force equal to that of gravity upon the stone through a certain vertical distance; and the work done is equal to the force exerted (that is, to the weight of the stone) multiplied by the height it is lifted. The energy expended by the body is here transferred to the stone in its elevated position. This energy stored up in the stone is called potential energy, and it remains constant in amount so long as the stone remains at the same level. If the stone falls to a lower level its potential energy is reduced, but kinetic energy equal to the decrease of potential energy appears as heat.
If the man lifts the stone one inch the work is only one thirty-sixth part as much as if he lifts it three feet. If he pull on the stone but does not move it, no work is done, in the mechanical sense. Muscle has contracted and work is doubtless done within the body, but so far as the stone is concerned no work is done. So a man may hold a heavy weight in his hand or on his shoulder, sustaining it with considerable effort against the force of gravity, and yet no work is done on the stone so long as it is not raised to a higher level. If the stone is carried in a horizontal plane, no work is done on the stone; while if it is carried down hill or lowered vertically, negative work is done on the stone. That is, since the stone possesses less potential energy at the foot of the hill than at the top (the difference being equal to the weight of the stone multiplied by the difference of altitude), the stone has lost energy, and this energy lost by the stone has been communicated to the man, who has had work done upon him by the stone, albeit he may have lugged it down the hill or lowered it from an elevated position with considerable effort.
When a car is propelled by an electric motor deriving its current from a storage battery carried on board the car, the energy of the car consists of three parts: (A) Mechanical potential energy due to the mass of the car being at some elevation above the surface of the earth. (B) Kinetic energy, due to the motion of the car as a whole and of its parts with respect to one another and the heat of the car. (C) Chemical potential energy stored up in the battery. When the car is running up grade, energy is being expended not only in overcoming friction, but also in lifting the car against the force of gravity. In doing this, energy is transferred from C to A. When the car descends again to its former level the energy stored up in A is given up, less energy is therefore required from the battery to propel the car, and the battery is accordingly in so much spared. If the grade be steep, the motor may actually be driven as a dynamo, and the current which is thereby generated may be stored up in the battery. In this case energy is transferred from A to C, and at the bottom of the hill the energy C may be greater than that at the top. The battery has done negative work on the car coming down the hill: that is, the car has done work on the battery and stored up energy.
The same considerations apply to the animal body. If a man carries himself up a hill, he is doing work upon his body in so elevating it against the force of gravity, and if he weighs 150 pounds and ascends an altitude of 10,000 feet, he has done 1,500,000 foot-pounds of work upon his body. This represents the quantity of energy which has been transferred from his tissues to his body as a mass; from chemical potential energy to mechanical potential energy. The tissues correspond to the storage battery, the muscles to the motor and the man's weight to that of the car. So when the man walks down the mountain again he does negative work, lowering his body (like lowering the car), involving the transfer of potential energy from his body as a mass to his tissues. Just what form the energy takes as it is so transferred is not altogether clear, but the distinction between the potential energy of the body as a mass, due to its elevation above the surface of the earth, and the potential and kinetic energy resident in the tissues of the body, is one of fundamental importance and should be kept clearly in view.
We may consider the man to be a complex machine, weighing, say, 150 pounds and having a quantity of potential and kinetic energy stored up within his body, which store of energy is drawn upon whenever external work is to be done, and which, besides, is being constantly expended in keeping the body warm and performing the internal work of the body. The energy of the body, like that of the electric car, then, consists of three portions, viz.: (A) Mechanical potential energy of the body as a whole, due to its position with respect to the earth. This is zero when it is at the earth's surface, or say the sea level, and increases as it rises above the sea level. (B) Kinetic energy, due to the heat of the body and to the motion of the body as a whole and of its several parts with respect to each other. (C) A store of chemical potential energy in its tissues and in food undergoing assimilation. Now when a man walks up hill, A increases, B remains nearly constant (increasing slightly), while O decreases rapidly, due partly to the increase of A and partly to the loss of heat by radiation and respiration. When he walks down hill, A is transferred to C or B, or both, and because of this acquisition C decreases more slowly than it would do if it received nothing from A, while yet giving off energy at the same rate. The man does positive work upon his body when he lifts it against the force of gravity, storing up potential energy A; he does negative work when he goes down hill, and the energy A passes to the interior of the body.
Suppose a laborer lifts 20,000 pounds of brick 5 feet; he does 100,000 footpounds of work, this energy being transferred from A to the bricks, and it will remain in the bricks as long as they remain at their elevated position. Next, suppose he lowers the same bricks to their former position. This 100,000 footpounds of energy is now transferred back from the bricks to the laborer's body. Because he is expending energy all the time he will possess less energy at the end of the task than at the beginning. Nevertheless, he does not lose as much as though he had not received the 100,000 foot-pounds of energy from the bricks, and had given off the same amount of energy in other ways.
We do not understand the process whereby the body converts chemical potential energy of tissue into mechanical energy; that is, we do not understand how the body does work. Still less do we understand how negative work is done; that is, how the body receives energy from without when it lowers a weight or walks down hill. That it does so acquire energy we cannot doubt. But whether it appears at once as heat, or as some other form of energy, and where the energy so received first appears, has not been proved. Neither have experiments been carried out to determine the relation between (1) the quantity of negative work done in a given period, (2) the total heat radiated from the body in the same period, (3) the amounts of oxygen absorbed and carbon dioxid respired, and (4) the excess of energy expended over that expended in the same length of time during rest. Indeed, to repeat the experiments already done with the respiration calorimeter balancing the total income and outgo of energy for a given period, with this important difference, that the subject of the experiment was doing negative work (that is, having work done on him by an external agent) would be an extremely interesting and valuable piece of work.
Consider now what occurs in walking on a level. The foot and leg are lifted, work is done in lifting them, and energy is stored up in them; they are advanced and lowered to the ground, and this stored up mechanical potential energy is then recovered by the system. The center of gravity of the body as a whole is also raised slightly at each step, but the work done in raising it is only equal to the energy yielded by the body when it descends again to the former level. Assuming an absence of friction against the ground and the atmosphere, the total external work done in walking on a level is zero. Force is exerted in holding the body erect or in holding the arm in an extended position. But no work is done in either case, for the force is not exerted through any distance. So also force is exerted by the huge cables which sustain the Brooklyn Bridge against gravity, but no work is done by these cables so long as the bridge is not lifted. Force is exerted by the foundations of a building in resisting the attraction of gravitation upon the mass of the superstructure, but no work is done by the foundation in so sustaining the weight. What the internal work of the body may be when muscle is contracted and force exerted without doing external work is another matter. That question is deserving of careful study, and the respiration calorimeter might perhaps lend itself to such an inquiry.
In the experiments referred to, the man under investigation received daily a known quantity of potential energy in the form of food. Part of this was converted into external mechanical energy and was measured; of the remainder, part appeared as heat and part was carried away in the refuse products of the body. The internal work of the body is ultimately converted into heat, and appears in the total heat of radiation and respiration. Thus energy is expended in causing the heart to beat and the blood to circulate and the lungs to expand. This internal work is not stored up, but is transformed into heat and radiated away with that which results directly from combustion. But external work done, like turning a grindstone or sawing wood, is not represented in the heat radiations of the body.
In order to do the desired amount of work within the calorimeter, the man operated a stationary bicycle, which was geared to a small dynamo. The front wheel of the bicycle was removed, and the rear wheel served as a driving pulley for the dynamo. The latter generated a current, the energy of which was measured by an ammeter and a voltmeter. When this current passed out of the calorimeter, its energy was not included in the heat measured by the calorimeter. But in some cases the current flowed through an incandescent lamp inside the calorimeter. Then the mechanical energy done by the man was all turned to heat within the calorimeter; part of it through friction in the bicycle and dynamo, part through the electric current which flowed through the lamp. The former was measured as accurately as possible by seeing how much energy was required to drive the bicycle when using the dynamo as a motor, supplying current to the latter from a battery and measuring the energy so supplied by an ammeter and volt-meter. The quantity of heat resulting from this friction must be subtracted from the total heat measured, in order to ascertain the quantity which was given off from the man's body directly as heat. And in those cases where the electric lamp was inside the chamber (and hence the work done by the subject was converted into heat within the chamber) this total amount must be subtracted from the heat measured to give the amount of heat given off as such by the subject of the experiment.
Thus we measure the quantity of external work done; but nothing is here learned about the internal work. The latter is converted into heat within the body and, when radiated away, is measured with the rest by the calorimeter. The amount of external work done in driving this bicycle-dynamo combination in one of the experiments (which continued for 96 hours) was equivalent to 256 large calories per day. This was about 40 watts for eight hours, or 788,000 foot-pounds, or 394 foot-tons. The total quantity of energy yielded was 3,726 large calories on the average for each of the four days. Since 256 is about 7 per cent, of 3,726, we see that the man converted 7 per cent, of the energy contained in his food into mechanical energy, 93 per cent, appearing in the heat of radiation and respiration. This gives the man, regarded as a machine for doing mechanical work, a 24hour efficiency of 7 per cent. During the eight hours in which work was done the total consumption of energy was about 1,850 calories. Dividing the work done by this figure, we have for the mechanical efficiency during working time, 14 per cent. But there is still another way of reckoning this efficiency. Inasmuch as a large part of the energy supplied to the body would have been required to do internal work and keep the body warm, if no work had been done, we can fairly charge against the work done only the excess of energy supplied during the days when work was done over that required by the same man when no appreciable external work was done. The average quantity of energy supplied in several experiments in which the man did no considerable external work was 2,500 large calories. The excess in the work experiment was therefore 1,226 calories. Dividing the work done, 256 calories, by the excess of energy absorbed, 1,226, and the quotient is .21. Thus 21 per cent, of this excess of energy absorbed was converted into work, or the efficiency of the man as a machine for doing work is 21 per cent. This is far greater than the efficiency of small portable steam engines, such as could be compared with respect to size or power with a human machine, and equals or surpasses that of the largest compound condensing engines taken in connection with the most perfect water-tube boilers.
The bicycle-dynamo combination is not the most effective device upon which to develop mechanical power; and in the experiments quoted no attempt was made to secure the maximum efficiency of conversion of the potential energy of foodstuffs into mechanical energy. Although many experiments have already been carried out, further experiments are needed to show more fully what the human machine is capable of doing, and what circumstances are favorable to a high efficiency of conversion.
It may be of interest to show how a man's weight varies during twenty-four hours. The accompanying diagrams give the variation in the weight of the man under investigation in one of the rest experiments; that is, in a four-days' experiment, where no mechanical work was done, except that involved in eating, dressing and making some records and observations within the calorimeter. The routine followed each day was nearly but not exactly the same, and the fluctuations of weight are accordingly similar but not identical each day.
Increase of weight is due to food and drink taken into the body and oxygen respired from the atmosphere. Decrease of weight is due to feces and urine leaving the body, and carbon dioxid and water vapor carried away from the lungs and skin. Part of these changes in weight occur more or less suddenly, while the change due to respiration, in which oxygen is absorbed and carbon dioxid and water vapor are evolved, is gradual. In the diagrams the sudden changes are indicated by vertical lines, the numbers indicating the quantity of the change in grams. The gradual changes due to respirations are indicated by sloping lines, the number in each case indicating the net loss in grams; that is, the difference between the quantity of carbon dioxid and water vapor exhaled and the oxygen absorbed. All the vertical lines indicating sudden decrease in weight are due to urine except the two (on the second and fourth days) which are marked 'feces.'
Starting at 7 o'clock on the morning of the first day with a weight of 68,420 grams, the subject loses 45 grams in one hour by respiration. This loss by respiration was determined to be 270 grams in six hours, and in making up this diagram it was assumed to be uniform during the six hours. The loss by carbon dioxid is almost exactly 25 per cent. greater than the gain by oxygen absorbed. Sitting on a good balance, one can literally see one's self grow lighter as one quietly breathes one's self away. Breakfast adds 675 grams, respiration reduces his weight by 110 grams up to 10.30, when a drink of water adds 200 grams; a further loss of 110.3 grams by respiration is followed by a loss of 341 grams of urine, then 28 by respiration, and at 1.30 dinner adds 804 grams. The weight drops during the afternoon and then supper brings it up to the maximum of the day. During the night the weight falls again, so that at 7 o'clock on the second morning it is almost exactly the same as at the start. It is noteworthy that the loss by respiration is nearly as great during sleep as during the morning and afternoon hours, there being a loss of 254 grams in six hours during sleep as compared with 270 in six hours during the day.
The variations in weight in the three succeeding days can be followed from the diagram. These diagrams were made from the records of the experiment, and the computed weights agreed quite well with actual weighings made at several different times during the experiment.
Such diagrams have not as yet been prepared for work experiments, but they could not fail to be of great interest in the cases we have been considering; namely, where the subject of the experiment does first positive work, then negative work, and, finally, positive and negative work together.
|Edward B. Rosa.|
- Popular Science Monthly for September, 1900.
- Copied from an article by the writer in the 'Physical Review' for March, 1900, 'On the Metabolism of Matter in the Living Body.'