Thermal Efficiency of a Human Being

These "overall thermal efficiency" figures are a rigorous scientific evaluation of any machine, taking the total developed energy or power (such as the actual energy and power that an automobile creates and makes available to its wheels) divided by the total amount of energy that is available from the source fuel (such as the 126,000 Btu of energy available from a gallon of conventional gasoline) (times 100 to get percent). This number is really one of the best guides for an overall comparison of different types of machines.

In the case of human efficiency, we must necessarily include two different things, the energy we necessarily use up to maintain life, called metabolic energy, and the energy we use up in doing productive work, whether that is physical labor or mental effort.

We generally have a decent idea of the energy that we take in as food. A 2,000 Calorie daily diet regimen means that the person takes in food that includes 2,000 (kilo-) Calories of thermochemical energy in it. No problem there. By the way, 641.2 (kilo-) Calories equals one horsepower-hour of energy.

This number is technically NOT true! The actual total chemical energy that is in the food and liquids we take in is actually greater than that! The difference between the two is generally referred to as the Atwater factors. Physics easily proves that one pound of nearly any type of organic food material contains around 8,000 to 10,000 Btus of actual chemical energy in it (if the water is removed). This is around 2,000 to 2,500 Calories of energy. We actually all ingest more than a pound every day, generally around 22 to 30 ounces of actual food content (after subtracting the water in it). Just a quarter-pound hamburger and its fries and drink are more than a pound! In fact, for comparison, a single 16-ounce drink is one pound (but in that case, it is mostly water). What's the deal? Well, not only do we ingest food each day, but we also excrete and eliminate it; it turns out that MUCH of the volume of food we eat later leaves us, where our body does not even try to process it! An average person might take in around 25 ounces of food values each day but then excretes around 9 ounces per day, which, in a Physics sense, contains around 1,200 Calories of chemical energy which the body did not absorb and an assortment of organic materials that the body no longer needed. The remainder, the amount that the body actually digests, is therefore around 16 ounces, or one pound, or around 2,250 Calories, the usual description of a healthy food intake. That factor depends somewhat on each person's Digestion Efficiency, and also the types of food that are eaten, but the proportion is assumed to be fairly consistent among people. Therefore, the number that is expressed as Calories in food calculations actually ONLY considers the portions that actually get digested and skips the energy that remains in the materials that we excrete or eliminate. A "baked potato" might be a good example. In FOOD VALUE, it is often described as being around 145 Calories, depending on size. Say it is around 200 for the rather large baked potatoes that I generally eat. On a scale, they weigh around 12 ounces each, 3/4 of a pound. IF they were entirely organic materials, that weight would indicate that the amount of CHEMICAL ENERGY in it, should be about 1600 Calories (3/4 of a pound, which would contain around 2,200 Calories or 9,000 Btus of chemical energy which was received from the Sun in the process of photosynthesis and growing). It turns out that a potato, like other foods, contains a good deal of water in it. IF that potato was 70% water and 30% organic molecules, that would mean we have around 480 Calories of Chemical Energy in it. It appears that we might then imply from that that human digestion only deals with around 1/2 of the actual organic chemicals in that potato, converting it into the 200 Calories of Food Value, and our body passes much of the remaining 280 Calories of chemical energy in that potato as excrement (and eliminated as urine). You know that excrement quickly decomposes chemically, and also that there are a lot of creatures, such as dung beetles, which live on the energy remaining in that excrement. Human Digestion has DIFFERENT usage-efficiency ratios for different foods. In this case, we are suggesting that for a baked potato, it might be about 40% (200 / 480). I have not found that anyone has ever scientifically researched in this area. However, there are certainly many people who recommend eating roughage or fiber, which are known to be materials that the human digestion system CANNOT digest at all! All fiber simply passes through a person, so that the Food Value of such materials is ZERO! No Calories at all, no matter how much you would eat of such materials! There may be some foods that we humans can digest at a high usage-efficiency ratio. It appears that peanut butter must be quite high, as the Food Value is very similar to the actual Chemical Energy in it. It would also be interesting to know how well we digest a diet of "lawn grass" (probably extremely minimally) or "fresh leaves" or "exclusively bread and water" or "exclusively beef". It is certainly possible to get a rough idea of these values in the way we have suggested here, of simply weighing a sample of food and using the accepted food value Calorie number (after accounting for water). But a serious scientific investigation seems called for. It might turn out that we could recommend a specific high-digestive-efficiency diet to people in countries where food is hard to find. I tend to wonder if that could also lead to an entirely different concept of "dieting" for people who want to or need to lose weight! I don't recommend eating rocks or sawdust, but there ARE some foods where the human body is simply lousy at digesting, such as dietary fiber! Cows have special bacteria in them that breaks down the cellulose of plant structures, where their stomachs and intestines can then digest those materials where we cannot. I even have noticed an interesting aspect in us relating to this. If you eat sweet corn AND CHEW IT, humans can digest it pretty well. However, IF YOU SIMPLY SWALLOW the kernels, they kernel shells are of materials very similar to cellulose, which we cannot digest, so they pass right through the human body undigested. This indicates that even the chewing habits of people can greatly affect the digestion-efficiency. Say that there were foods that only had a 10% digestion-efficiency (fiber or cellulose has a 0% digestion efficiency!) The person would eat "normal (excessive)" amounts of food but the body would only be able to chemically digest maybe 25% as much as normal. The person would FEEL full, for having eaten large meals, but the body metabolism would only have 25% (10%/40%) of the Calories available from it. Seems to me that it would be an impressive diet! Although I could see how it could result in anemia if the person got carried away with it! As a personal observation, I have occasionally decided to go for a week or so ONLY drinking orange juice, pineapple juice, cranberry juice, cherry juice, tomato juice, and occasionally V-8 vegetable juice. I drink a LOT of those liquids during that week, and actually take in plenty of food Calories for maintaining my metabolism and my active lifestyle. (A 46 ounce can of pineapple juice indicates that it contains around 720 food Calories in it. In a 24-hour period, I sometimes drink three full cans worth of those assorted liquids, which totals around the 2,200 Calories my body needs for a 24-hour day. I only do it for a week or so, because I eventually get bored with only those choices!) I have found that very little excretion occurs during such a week. That suggests to me that maybe our human digestion might have an extremely high usage-efficiency for juices??? If so, it could be EXTREMELY important information, both for dieters and for Third World countries. Nutritionists have long known that humans generally can capture about 4.0 Calorie per gram of carbohydrates, while fats yield around 9.0 Calorie per gram, and protein yields about 4.0 Calorie per gram. (These are the Atwater factors.) What is referred to as Fiber yields NO energy at all for the body! It is actually mostly the cellulose from plants, which the human body cannot digest at all! One wonders as above regarding if an overweight person might select a diet that has large amounts of fiber in it, to have the sensation of eating a lot of food and feeling full, but of having a far smaller percentage of the food then actually digested. There are limits to that, as excessive dietary fiber can interfere in the body digesting certain important trace minerals. Maybe our mamas were really on the right track when they insisted that we finished our fruits and vegetables! When Physicians try to determine why someone is overweight or obese, they seem to virtually always blame the BMR (basal metabolism rate) as being the cause. What if another important factor might be that some people are just able to digest a higher percentage of the food they eat? Such people would tend to gain weight, wouldn't they?

Unfortunately for those factory owners, only around 0.1 horsepower of that was actually available as useful work. That's about 64 Calories per hour or 75 watts. The other 0.39 horsepower (about 256 Calories per hour or 1,000 Btu/hr) was used up in metabolic activities and maintaining body temperature. In "staying alive!" Bummer! This data indicates that such human factory workers were capable of around 20% overall net thermal efficiency during their work shift. More recent research has suggested that a maximal efficiency for a human is probably around 25%, but that most existing mechanisms are not able to efficiently deal with the herky-jerky way we tend to create such work!

(Younger 20-year-old men could produce 15% more productive work [but still with around a net thermal efficiency of 20%, consuming larger amounts of food in the process] and 60-year-old men could produce 20% less work [again still with about the same net thermal efficiency] than the 35-year-old performance values.) The metabolic requirements depend on health and environmental conditions, particularly the air temperature. In an extremely cold environment the body must expend even more energy in maintaining body temperature.

These results encouraged factory owners to move toward automation where steam engines and electric and gasoline motors did most of the work.

When a person is not fully exerting oneself like in those factories, the metabolic rate drops somewhat. A sedentary or desk-person needs far less than that 0.39 horsepower rate for bodily functions, actually around 0.16 hp (or according to the ASHRAE Handbook charts, 390 to 450 Btu/hr or around 100 Calories per hour). This is getting close to the minimum possible metabolic rate which ensures survival, the so-called basal metabolic rate (or BMR) Relatively few Americans are now in factory jobs that are as demanding as those harsh tests considered. Therefore, the necessary daily dietary intake does not need to be as high as it was a hundred years ago.

If there is NOT a large amount of food to digest, the body will allocate most or all of that available work to either mental (thinking) activities or to physical activities or both.

IF you take in more Calories (actually kilo-calories or Kcal) in a day than you use up, the extra energy is turned into sugars and fats to be stored away for a possible future survival need, and you will gain weight. Equally, if you use up more Calories in a day than you take in, some of that existing fat and sugars is converted back into forms that can become energy, and some of the bodyfat is therefore converted into that work and weight is lost. The premise behind "working out" is closely related to this fact, and it would work to some extent, if it were not that all that exercise often creates a healthy appetite!

It is interesting that enormous numbers of TV, radio, newspaper and magazine ads talk about amazingly fast rates of weight loss, with some diet or some piece of exersize equipment! We tend to consume around 2200 Calories of food energy and use up roughly the same amount each day. It is rare when the difference is greater than around 200 Calories in a day. If we note that a pound of bodyfat contains around 3500 Calories of energy stored in it, this indicates that two or three weeks are likely necessary to be able to lose even ONE pound of bodyfat! And people who try to lose weight get frustrated at such slow progress! So the ads brag about losing 50 pounds in 50 days or something like that. Think about that. In order to lose 50 pounds of bodyfat in 50 days, it is necessary to lose or use up around 1 pound each day. That means using up 3500 Calories of (stored fat) food energy each day, and not eating anything at all for 50 days! There is no easy way for our bodies to use up 3500 Calories per day! Do you see why such claims are exaggerations and/or misleading?

Where the Energy Goes

In any case, nearly all of that wasted heat eventually gets to the skin to be either radiated or convected away; or the heat goes into warm air inside the lungs to be exhaled. We can do some rough calculations regarding these things.

For heat radiated away, there is a standard equation that describes this so-called Black Body Radiation. The Stefan-Boltzmann Law is that the amount of radiation is equal to a constant (called the Stefan-Boltzmann constant, s) times the area of surface times the FOURTH power of the absolute temperature. For a situation where a radiating object is within a room which is at a lower temperature, it becomes = s * A * (T₁⁴ - T₂⁴). (We are leaving out here the constants regarding the emissivities of the surfaces involved, assuming them both to be 1.0).

If all of a human's skin were at the same temperature, this could be easy! We have around 20 square feet of surface area (A) and the constant is 0.1713 * 10^-8 Btu/sf/hr/°R⁴. The head is maintained at a fairly high temperature, to ensure clear thinking in case of emergency! The arms and legs tend to be cooler. The way the body does this is by restricting or permitting blood to flow freely to different areas. (When someone falls in very cold water, the body attempts to nearly completely shut down blood flow to the limbs, to try to conserve body heat for the brain and torso where it is urgently needed.)

For our estimate, let's say that the body attempts to keep the AVERAGE skin temperature to be 5°F above the ambient room temperature. In that case, we would have 20 sf * 0.1713 * 10^-8 Btu/sf/hr/°K⁴ * ((77+459)⁴ - (72+459)⁴). This is about 104 Btu/hr, which is around 26 Calories per hour of RADIATED heat.

For convective heat losses, we are going to simplify by assuming that there is no wind. Therefore we can use formulas for Natural Convection. A very simplified version gives h = 0.2 * (T₁ - T₂)^1/3; for our situation above, h = 3.42. The convective heat loss is then that number times the surface area (of 20 sf) times the temp difference (5°F) or 340 Btu/hr. (around 85 Calories per hour) If a person were naked, this would apply, but the effect of clothing tends to insulate some parts of the body, particularly the very important torso, and we are going to suggest here that the effect of clothing will generally reduce this CONVECTIVE heat loss to around 70 Calories/hour.

The third method that the body discards heat is by exhaled breath. In normal breathing, we generally exhale about 0.5 liter of air about twelve times every minute. This is therefore around 6 liters of air per minute. This air is at our core body temperature, of 98.6°F temperature, air that had been inhaled a few seconds earlier at room temperature. If the room is at 68°F that means the room air had been raised in temperature (by the body) by around 30°F. The 6 liters of air/minute is 360 liters/hour or about 13 cubic feet per hour which has a weight of around 1 pound of air per hour. Air has a thermal capacity of around 0.24 Btu/lb/°F. In raising 1 pound of air by 30°F, that means that the amount of heat added to the air (from inside our body) is (30 * 1 *.24) or around 7 Btu/hr of EXHALED heat in the dry air.

There is also water vapor in the exhaled breath. As the air is inside the lungs, the relative humidity there quickly rises to 100%. Therefore, water along the walls of the lungs evaporates into the air to be exhaled. This is additional heat energy that gets carried away. Using standard analysis, the partial pressure of the saturated water vapor at 98.6°F is around 0.9 PSI. This defines the (weight) proportion of the water vapor and the dry air to be around one to 27. We will not go through all the math here but it is pretty simple to determine how much weight of water vapor is exhaled per hour. Most of the energy is involved in evaporating the water into water vapor, but then it also has to be warmed from the inhaled breath air temperature up to the 98.6°F that gets exhaled. Evaporating sufficient water at room temperature and then raising it to 98.6°F for the 6 liters of air represents around 1/25 pound of water per hour being evaporated and heated, or around 40 Btu/hr. The heat of vaporization of water is around 1,000 Btu/pound).

Between these two components of the exhaled breath, we have around 47 Btu/hr or 12 Calories/hr lost due to EXHALED BREATH. We must remember that this was based on a 68°F room, and standard (waking, sedentary) rates of breathing and depth of breathing. For example, during sleep, the respiration rate generally slows down and becomes more shallow, so those heat losses become less, while during heavy exercise or exertion, respiration becomes faster and often deeper, so that greater heat losses in the breath occur then.

This then gives a daytime resting total of around (26 + 70 + 12) or around a ballpark estimate of 110 Calories per hour of heat energy sent away from the body. During the night, the heat loss is generally slightly lessened. A ballpark number we could consider a day of losing 110 Calories for 16 hours, or 1760 Calories per day as being credible. During our eight hours of sleep, it has been scientifically confirmed that we normally lose around 80 Calories per hour, so we have a 24-hour day total of around 110 * 16 + 80 * 8 or 2400 Calories, a number that is is reasonable agreement with the accepted value of food energy consumption for a sedentary adult individual.

(The body also has the capability of dumping quite a lot of heat by sweating, where the evaporation of the water removes heat from the room air very close to the skin, and therefore increases the [local] temperature differentials we discussed above. [This is why your skin feels cooler when you sweat.] This then allows the body to dump substantial amounts of heat when the body is in danger of overheating. In a sedentary situation, the body creates a very small amount of sweat, and we are ignoring that energy loss here.) Remembering that a pound of water (or sweat) involves around 1,000 Btus (or 250 Calories) for its evaporation, you probably see why Marathon runners need to grab so much water along the race, in order to replace water lost through sweating. Due to all the exertion of such a race, the body is generating so much heat energy, partly due to actual physical work done but far more due to the many chemical reactions that must occur in the accelerated metabolism, that a large amount of heat must be released from the body. Rather than the body letting the skin temperature rise to 120°F or more in order to release that much energy by radiation and convection, it chooses to sweat to release a lot of the energy. It is quite an amazing system!

This then accounts for a ballpark of 2,200 or 2,400 Calories of input energy, (for relatively sedentary existence) in rough agreement with what dieticians say.

We might note that we are examining all this from a Physics perspective, where Energy can never be either created or destroyed. When we refer to a human taking in an amount of energy equal to 2,200 Calories (for metabolic activities) it might first seem that the metabolic activities therefore "use up" all that energy and that there should be no balance of energy. But if we examine the WHOLE picture, where all the metabolic activities are able to complete, THEY also eventually result in degrading all the energy into heat. This discussion is therefore correct in accounting for exactly as many Calories or Btus of energy IN and OUT. There are only a few exceptions to this. During the GROWTH of a child, additional structures are created, and so energy in IS greater than energy out. Similarly, when a person gains or loses weight (body fat) an imbalance occurs, since one pound of human bodyfat has the energy content of around 3,600 Calories.

This analysis does not include the "productive" work output. When the body is more active, the metabolic activity increases, to power all the needed operations inside the body, while also producing productive work output which could be as much as an additional 1/4 of that (as noted above). In what is considered heavy work by ASHRAE, the amount of productive work done can be around 0.15 horsepower, or 96 Kcal/hr or 110 watts. The body has to increase its metabolic rate to accomplish everything necessary, with the net efficiency being around 20%. Therefore, the body is actually then using up around 480 Kcal/hr or 550 watts of total consumed energy. This must all be disposed of by radiation and convection from the skin (therefore bloodflow near the skin is increased so that the skin temperature rises to accomplish this) and the rate and depth of breathing is increased to also dump more heat, and finally, the body sweats to dispose of additional heat.

The numbers above are generally meant to apply to adult men of around 200 pounds weight. Women generally have smaller total surface area and therefore they need to use less energy to maintain their core body temperature, so they tend to need to eat less, and therefore have lower daily dietary intake. But the reasoning is still completely valid.

That is around 100 Calories per mile. If each mile is run in six minutes, that is around 1000 Calories per hour, an amazing amount. This is around 1.5 horsepower of energy consumption. Note that only around 0.3 horsepower of that is USEFUL power (the running) (our 20% efficiency again) while the remaining 1.2 horsepower is all used inside the body for metabolic processes. Where our sedentary person discussed before needed around 100 Calories per hour for metabolic processes in the body, the Marathon runner needs to consume about 800 Calories per hour (plus about 200 Calories per hour for the actual mechanical work of running, the air resistance and the rest). Those represent the extremes of the range of metabolic activity in humans.

If we wished, we could calculate the skin temperature and breath quantities (in ways that were presented above) to determine where and how all that energy had to leave the body. Hotter skin temperature enables greater heat loss by both convection and radiation. Faster breathing enables greater heat loss by those processes discussed above. However, these numbers do NOT account for all the energy that must be discarded, and so even the amount of sweating can be calculated!

With that disclaimer, there is a very simple way to learn what level of work any person is capable of! Say that there is some tall building nearby, where stairs have steps that are exactly 8" different in height. Say you weigh 180 pounds. Now say that you can run UP such stairs at the rate of 24 steps in each 10 seconds. In that case, what you would have done was to RAISE 180 pounds up a distance of 16 vertical feet (the 24 steps) in ten seconds. In other words, you would have done WORK of 2,880 ft-lbs in ten seconds, or 288 foot-pounds per second. One horsepower is equal to 550 foot-pounds per second, so you would have done just over one-half horsepower for those ten seconds!

This same is true for any stairs or any ladder. For a few seconds, anyone can (carefully) run up a few stairs or climb a few steps on a ladder or go up a small hill. Measure the TIME (in seconds), the HEIGHT, and your body WEIGHT. That HEIGHT times your WEIGHT divided by the number of seconds it took, will always give foot-pounds per second. Just divide that by 550 to get actual horsepower! For a few seconds, most people can produce one full horsepower of actual work like that, but a horse can do that level of work for hours on end!

In the one case (heavy blankets, hot room and/or electric heating pad), the body uses up 20 Calories per hour for the 8 hours of sleep, or a total of around 160 Calories during the night. In the other case (think covers, cooler room) the body uses up the more natural 80 Calories per hour of sleep for those 8 hours or 640 Calories during the night. The difference of these two situations appears to be 480 Calories per night.

The premise is then that over a week, maybe an additional 3500 Calories (7 * 480) might get used up by the body by sleeping with just a sheet instead of a heavy blanket. Since one pound of bodyfat has an energy content of about 3500 Calories, this might suggest that it may be possible to lose about one full pound of bodyfat EVERY WEEK just because of this blanket/sheet difference!

Possibly the weirdest weight-loss system ever!

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C Johnson, Physicist, Physics Degree from Univ of Chicago