Human Being - Thermal Efficiency

The Physics

An interesting subject is regarding how efficiently a human operates as if it were a machine! We know that automobiles of the 1970s generally operated at around 15% overall thermal efficiency (which has now been increased to around 21%). We know that electric power plants operate at about 30% overall thermal efficiency and then that the power grid distribution system operates at around 40% thermal efficiency, which results in around a 13% overall thermal efficiency, regarding the energy that started out in the coal or uranium and the electricity that actually gets to us. We know that photosynthesis in plants (such as corn and wheat crops) is only around 1% to 2% efficient regarding the energy received as sunlight. So what about us?

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 analyze two different things, the energy we necessarily use up to maintain life, called Basal Metabolism energy, and the energy we use up in doing productive work, whether that is physical labor or mental effort.

This presentation was first placed on the Internet in July 2006.

The exertion of mental effort is difficult to quantify. So we will assume the person does not have much in the way of creative thoughts here!

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. (For clarification, a Calorie [capitalized] in Nutrition is actually a thousand calories in Physics, or a kilo-calorie [lower case]) No problem there. By the way, energy can be described in a number of different ways, and so there are conversion factors which will be useful below: A Calorie = 3.968 Btu = 1.16 watt-hour. 641.2 (kilo-) Calories equals one horsepower-hour of energy. Energy RATE or consumption or POWER can be described in terms of 1 Calorie/hour = 3.968 Btu/hr = 1.16 watt = 0.00156 horsepower.

The energy in a 2,000 Calorie daily dietary intake can therefore be described equally as an INPUT of 3.12 horsepower-hour or 7,900 Btus or 2.325 kiloWatt-hour of energy. MOST this energy is used to maintain life as metabolism, and therefore eventually becomes lost as heat energy that is radiated, convected or conducted away from the body in various ways. These are not constant losses, generally smaller during rest and sleeping, but if we look at 1/24 of the above amounts we can see the AVERAGE HOURLY heat production/heat losses of the body as being about around 100 watt-hours or 330 Btus or around 90 Calories [which is 90,000 calories!] or about 1/7 horsepower-hour. These metabolic losses are essentially unavoidable.

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We can therefore say that a human body has to give off around 90 Calories of heat per hour (100 during daytime activity, less when sleeping, commonly around 80 Calories per hour but possibly as low as 20 Calories per hour) or 100 watts or 330 Btu/hr of heat.

The number, regarding energy in the food we eat, 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 many types 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 food energy. (Officially, it is generally given as being 4.0 Calories per gram for either carbohydrates or proteins, which is an average number. That is 4.0 * 454 or 1816 Calories per pound.) There ARE exceptions, such as lipids or triglycerides (fats) having a greater energy content at around 3,500 Calories per pound. That is generally described as being 9.0 Calories per gram, depending on the specific fatty acids which are in the triglyceride molecules.

No one has ever told you the following, and probably for good reason, as it can seem complicated! But it is really simple if you only try to grasp the very basics! The great difference between these two categories of food materials is primarily due to the fact that carbohydrates and proteins generally have chemical compositions where more than half the weight is of oxygen atoms (such as glucose being C6H12O6, where 40% of the weight is as carbon, 7% is as hydrogen and 53% is as oxygen. Only the carbon and hydrogen represent fuels or energy storage, while the oxygen is simply the included oxidant. In contrast, fats, or more correctly triglycerides are virtually entirely carbon and hydrogen with very few oxygen atoms. A glycerol (C3H5) is esterified (CO2H) with three fatty acids, such as palmitic acid, oleic acid, and alpha-linolenic acid. This results in a large molecule which is C55H98O6. In this specific case, 77.3% of the weight is carbon and 11.4% is hydrogen, with only 11.2% being oxygen. With twice the carbon percentage in the molecule, and also greater amounts of hydrogen, the total binding energy is more than double, accounting for the 9 Calories/gm rather than 4.0. Too much information? Sorry!

A little more! The fact that lipids or triglycerides are nearly entirely carbon and hydrogen atoms, means that this is an extremely compact form of energy storage. It really makes sense that nature came up with lipids for the greatest energy storage for emergencies in the smallest possible volume of space used up. And it is possible to learn even more about these Biochemical issues if the sort of energy auditing in the graphic later is done for lipids instead of the glucose in the analysis here. But we will back off the complicated stuff now!

Maybe one more parting shot! It turns out that bodyfat (or triglycerides) has virtually the same energy content (per pound) as COAL or petroleum does, around 3,500 to 4,000 Calories per pound! Really remarkable, and all because there are virtually no oxygen atoms in any of those fuels or in bodyfat! This will NOT come up on Jeopardy!

Back to the matter at hand. Our ACTUAL diet is a mixture of carbohydrates, proteins and fats. The AVERAGE energy content for that mixture is generally around 5 Calories per gram, which is around 2200 Calories per the pound of food that we actually digest. So when anyone refers to a daily diet of 2200 Calories or 2000 Calories, there are a lot of approximations involved!

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). Note that just a quarter-pound hamburger and its fries and drink are far more than a pound (including the water)! In fact, for comparison, a single 16-ounce drink is one pound (but in that case, it is nearly all 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 a significant amount 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 (which involves around 3400 Calories in a Physics sense), but then excretes around 9 ounces per day, which, in a Physics sense, contains around 1,200 Calories of chemical energy. Yes, the body did not even try to digest or absorb that last amount, along with an assortment of organic materials (and a LOT of dead bacteria) 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 2,200 Calories, the usual Nutrition description of a healthy food intake. So it is important to make sure whether any data is referring to the Nutrition value of a food or the actual Physics value. Nearly anything you will find regarding food ONLY refers to the Nutrition value, as few people seem to even care about the Physics perspective of all of this! (Humbug!)

In other words, the common descriptions of the (Nutrition) Calorie content of foods does NOT include the materials that the human body will not even try to digest!

That Atwater 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 by a normal healthy person 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 prefer. On a scale, they often 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 full 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 (30% of 1600) of Chemical Energy in it. It appears that we might then imply from that that human digestion might only digest 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 that 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 is certainly CHEMICAL energy in the roughage foods, on the same order as the 2,000 Calories per actual pound of organic matter (once the water is subtracted out). But since the bacteria in humans cannot decompose those materials, ZERO nutritional energy is captured from any amount of it!

An interesting example is cut lawn grass! If thoroughly washed, it is safe to eat. But human digestion virtually cannot digest any part of it, so the entire amount passes through the gastro-intestinal canal and gets excreted, while giving essentially ZERO Calories of food value to the body! (With salad dressing, it tastes similar to salad greens!) I tried that once to see if such an idea might represent a diet possibility for obese people who insist on eating massive amounts of food. It wasn't bad! Only the salad dressing would represent Caloric intake for the body! However, such a diet would NOT be good as a 100% food source, because the body needs an assortment of trace elements for healthy metabolism.

There seem to be some foods that we humans can digest at a high usage-efficiency ratio. It would also be interesting to scientifically 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.

As noted above, 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, the kernel shells are of materials very similar to cellulose, which we cannot easily digest, so they pass right through the human body undigested. This suggests 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% instead of 40%) of the Calories available from it. Seems to me that it would be an impressive diet! However, I could see how it could result in anemia if the person got carried away with it! Maybe vitamin supplements would be appropriate.

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 active day, without my body needing to burn up any bodyfat. 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 due to 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?

Early in the 20th century, factory owners did many studies regarding just how much actual work they could get out of their employees! It was generally found that a healthy 35-year-old (European) man could use up a total of 0.49 horsepower for an 8-hour shift. If you do the math, you can see that accounted for around 2,500 Calories used up during that work shift! (That worker's body would use up at least another 1,200 Calories of energy in the remaining 16 hours of that day for a total energy consumption of around 3,700 Calories per day.) People working in such factories HAD to eat enough food each day to account for that!

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 300 watts 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 (0.1 hp / 0.49 hp) during their work shift. More recent research has suggested that a maximal short-term 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! Note that these figures are for the Nutritional value of foods and not the (higher) Physics values. The Physics results therefore give efficiency figures that are lower, in the 13% to 17% range.

(Younger 20-year-old men were found to 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.

The body is interesting in that it chooses to allocate that 0.1 hp of available work as it finds necessary. Digestion is a process that requires quite a bit of energy. If there is no immediate requirement for physical activity or for mental exertion, the body will allocate nearly all of the available work toward digesting a meal. This greatly explains why we are often in a mood to take a nap after a Thanksgiving feast, as the body recognizes that it has a lot of food to digest! Creative thinking also seems harder right after a giant meal!

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 excess energy is turned into sugars and fats, and eventually into fats called lipids or triglycerides, 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 those existing lipids or triglycerides, fat and sugars is converted back into forms that can become energy, and some of the bodyfat are 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, either way, is greater than around 200 Calories in a day. It also turns out that the sorts of exercises usually done at Health Clubs in working out, tend to rarely even double our normal body energy consumption of about 100 Calories per hour (thereby burning off only another 100 Calories per full hour of such exercise, again rarely more than 200 [extra] Calories burned off in such an extended workout session). (There ARE exceptions! Researchers in Antarctica generally need to eat around 6,000 Calories each day to maintain their body weight because their bodies radiate immense amounts of heat due to the constant sub-zero temperatures. Olympic-level athletes need to eat impressive amounts of Calories each day. I understand that Michael Phelps, the swimmer with many Olympic Gold Medals, needs to eat around 12,000 Calories on many days, which is partly due to constant physical exertion but is also partly due to his body having to radiate and conduct large amounts of heat to the cool water which he is nearly always in. When professional football players retire, many continue to eat the large quantities of food that they had to eat during their career, and they often rapidly gain huge amounts of weight, which they then have great difficulty getting rid of.)

We note that bodyfat is a very compact source of energy supply (the whole point of it regarding survival!) and a pound of bodyfat contains around 3500 Calories of chemical energy stored in it. This indicates that two or three weeks are often likely necessary (3500 / 200 or about 18 days) to be able to lose even ONE pound of bodyfat!
People who try to lose weight by dieting and/or exercise get frustrated at such slow progress! (For success, they must have immense patience and incredible dedication to the effort, both of which seem opposite of modern hurry-up and have-it-now attitudes!)

So TV and magazine and newspaper and billboard 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 more than 1 pound every day. And such ads and concepts rarely also even attempt to get the person to also reduce the excess amounts of food they eat which caused them to become obese in the first place! If such a program could succeed, it would mean using up around an EXTRA 5000 Calories of energy from stored bodyfat each and every day. Even if the person did not eating anything at all for 50 days, the body's metabolism could only use up around 2200 Calories each day, where the actual total body weight loss would then be around 30 pounds in those 50 days! (Our bodies have an amazing ability to survive for many days when no food is available!) (By the way, people who go on long religious Fasts tend to lose MORE than this amount of total body weight, but that total loss also includes a large amount of WATER that is also lost in the process.) There is no easy way for our bodies to use up 5000 Calories per day! Do you see why such claims are exaggerations and/or misleading?

There is another way to look at all such claims. People selling such thihgs claim to make bodyfat "melt away" or equivalent, right? Bodyfats are all lipid or triglyceride molecules that are nearly completely carbon, hydrogen and oxygen atoms in complex combinations. You probably know of a basic law of science that says that nothing can either be created or destroyed (Conservation of Mass). Well, those lipids or triglycerides are commonly around 40% carbon. So WHERE does the carbon go? It can't just disappear! It must go somewhere! Can it VANISH in body heat? No, that would not account for the carbon atoms. Could it get excreted? No, because the digestive system is entirely separate from the body metabolic processes. You can rule out EVERYTHING, except for one thing! Your exhaled breath! Virtually the ONLY way that a human body can get rid of carbon atoms is to oxidized them into becoming carbon dioxide molecules, and then send them out of your body as exhaled air! Sadly, bodyfat can therefore never just "melt away"!

So, IF someone claims to cause bodyfat to be used up three times or ten times as fast as natural, they HAVE TO explain how THREE TIMES (or ten times) AS MUCH EXHALED BREATH had to also occur in order to carry the carbon atoms from all those bodyfat lipid or triglycerides molecules away from the body! Otherwise, all those carbon atoms have no easy way of going away!

There ARE a few very minor chemicals that get created which use up carbon atoms, but most of those stay in the body to be used for other purposes, and so they cannot represent actual REDUCTION of CARBON in the body! Those processes also affect VERY small amounts of the carbon, not enough to seriously even need to think about when considering amounts of bodyfat! And also, as our skin cells die and then rub off, we lost some carbon atoms by that process, but again, in fairly small quantities.

By the way, you might see the connection here between when you do serious exercise and then have to breathe heavily for a while? In doing strenuous exercise, you DO use up some bodyfat molecules (but a disappointingly small amount of them. We will shortly see in the Technical paragraph below that even when we exercise hard enough where our breath is TWICE normal, that only removes the carbon from around 1/1100 pound of bodyfat per minute. A full hour of such strenuous exercise and we can remove only around 1/20 pound of bodyfat!). Due to the requirements of the exercise, the body naturally accesses some of your energy supplies, first, the sugars, which are most easily accessed fast, but then the bodyfat stores. As those (sugar or) lipid or triglyceride molecules are oxidized, carbon dioxide molecules are formed, which get carried to the lungs and then exhaled with the next outgoing breath. If you do TWICE as much exertion, then twice as much of the lipid or triglyceride (bodyfat) molecules get oxidized, and twice as much exhaled breath is needed to carry all that carbon away from the body! Now you know! (You also breathe more heavily to get more oxygen INTO the body, to be able to do all that oxidization of all that carbon into carbon dioxide. The body has an immense number of unique chemical reactions, and we have greatly simplified the matter here!)

This brief discussion is intended to show you that virtually ALL the carbon that can leave your body must leave by your exhaled breath, and that all the impressive claims of flashy advertising which claim otherwise are simply not credible. IF some program causes you to BREATHE MORE HEAVILY, either deeper breathing or faster breathing or both, THAT WILL directly increase your body's ability to get rid of undesired bodyfat. So the next time you see any of those ads on TV or elsewhere, THINK about whether they are describing any credible way where your breathing is increased. If not, there is no realistic reason to spend money to buy what they are promoting!

On a more technical level, each INCOMING breath draws in air which is at the natural 0.038% of carbon dioxide, and each outgoing breath contains around a maximum of 4.4% of carbon dioxide. When sitting, we breathe around 12 times per minute and each normal breath is around 0.5 liter of air. This all means that in each minute of normal breathing, we exhale around 0.25 liter of carbon dioxide. This means that each minute, we each exhale around 0.5 gram of carbon dioxide, or around 1/1000 of a pound. (In an entire year of normal breathing, we each exhale around 600 pounds of carbon dioxide!) This includes around 1/3500 pound of actual carbon atoms per minute. If they had come from normal foods (averaging 40% carbon atoms), that represents around 1/1400 pound of food which would disappear during that minute (of normal breathing). At around 2200 Calories per pound of average normal food, that means that around 1.6 Calories of food (or other energy sources) gets used up every minute.

If the carbon atoms had come from lipid or triglycerides bodyfat molecules instead, a far more concentrated source of stored energy, only around 1/2200 pound of bodyfat would need to get used up during that minute (of normal breathing). This situation would occur if the person went on a fast without eating any food, or if the person exerted himself more than could be supported by the food recently eaten. At 3500 Calories per pound of bodyfat, that again means that around 1.6 Calories of bodyfat would get used up every minute. Since a day includes 1440 minutes, that again would account for the 2,200 Calories of energy that our metabolism needs to use up every day to keep us alive. This then proves that each minute of regular breathing involves exhaling the carbon atoms from the equivalent of either 1/1400 pound of average food or 1/2200 pound of bodyfat. That is essentially the ONLY significant process the body has of removing carbon from itself, which it does in order to supply energy for its many processes!

Where the Energy Goes

- There are a LOT of (metabolic) processes that go on in the human body, nearly all of which use up energy! The heart pumps blood, the lungs pump air, and countless chemical reactions occur to accomplish various functions. Virtually all of them result in HEAT being created as a result. In some circumstances, such heat is considered waste. But in the body of any warm-blooded animal, that heat is very important, in maintaining a constant warm body temperature. Many of those chemical reactions cannot happen very well in cold environments, and so the heat that seems wasted is actually accomplishing a very important task. Cold-blooded animals have less efficient chemical processes and so they tend to have less efficient brains and muscles.

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, σ) 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 (which radiates energy back to the body), it becomes = σ * 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! An adult man has around 20 square feet of surface area (A) and the Stefan-Boltzmann constant is 0.1713 * 10-8 Btu/sf/hr/°R4. The head is maintained at a fairly high temperature, to ensure that the brain is capable of clear thinking in case of emergency! The arms and legs tend to be cooler. The way the brain-body does this is by restricting or permitting blood to flow freely to different areas, by squeezing tiny muscles which are next to or around each blood vessel. (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 (or generally, for anyone other than nudists, the temperature of the air trapped within clothing!). In that case, we would have 20 sf * 0.1713 * 10-8 Btu/sf/hr/°R4 * ((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. This value depends tremendously on the type and amount of clothing worn.

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%. (This is actually IMPORTANT to the body in getting rid of a lot of the roughly one pound of water that is produced as a waste product of the body's basal metabolism each day, the other waste product than carbon dioxide.) 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 somewhat lessened. As 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 in reasonable agreement with the accepted value of food energy consumption for a sedentary adult individual.

Notice that ALL of these numbers are extremely dependent on the clothing we have on and also the temperature of the room we are in. We keep saying ballpark for these reasons. Our point here is simply to show the logic and the math by which this data can be processed, such that any reader might then do a more precise analysis based on specific clothing and room temperature!

(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 have been 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 3,500 or 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.

It might be useful here to discuss a related subject, regarding what happens when we exercise hard. We will consider here a world-class Marathon runner. In the intense running of 26 miles, it may seem surprising but it is well documented that ONLY around 2,600 Calories of additional energy is used up during the entire race (total body needs are therefore around 4800 Calories on that day (2200 for metabolism + 2600 for the work of running the race)! Note that this is ONLY around 3/4 of one pound of (extra) bodyfat that gets consumed due to the running. That is a LONG way to run to only lose less than one pound of bodyfat!

However, the actual body weight drops by far more than this, primarily due to the massive amounts of water vapor that is also lost through the breath and by sweating. The runners MUST grab a lot of those water bottles along the race course, to avoid having severe medical problems!

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 ENHANCED 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 use up about 800 Calories of metabolic energy per hour (plus about 200 more 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!

In a sedentary day, a person takes around 12 breaths per minute for 16 hours and fewer during sleeping, for an approximate total of around 17,000 breaths during the entire 24 hours of a day. We know that the lungs must exhale all the carbon of the food and bodyfat which gets used up, and we already calculated above that each MINUTE of normal breathing accounts for exhaling the carbon from around 1.6 Calories, that means that each individual breath exhales around 0.13 Calories worth of either food or bodyfat, or around 1/26,000 pound of bodyfat accounted for in each normal exhaled breath! (Bodyfat happens to be an extremely compact form of stored energy, and if food has recently been eaten where food energy can be used instead of bodyfat, it is around 1/17,000 pound of food accounted for in each exhaled breath.) Deeper breaths exhale more carbon dioxide, and faster breathing the same. There are a lot of unusual ways in which we can describe bodily processes!

We might therefore say that, if you intend to lose ONE pound of bodyfat, your body would need to exhale around an EXTRA 26,000 normal breaths! Given that we normally exhale around 17,000 breaths each day, it might now be clearer why losing bodyfat is not as easy as we might wish it to be!

The following should NOT be done or tried without full consent from your Doctor! It resembles the treadmill stress-test that Clinics sometimes put people through to determine their state of health, WHERE THEY HAVE MEDICAL SPECIALISTS STANDING RIGHT THERE IN CASE THE PERSON over-stresses themselves and has a heart attack or the equivalent.

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 (180 lb * 16 ft) 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 of net productive work for those ten seconds!

If you instead could only (slowly) walk up 8 of those stairs in the ten seconds, the numbers come out to be around 1/6 hp of productive work done 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 healthy people can produce one full horsepower of actual work like that, but a horse can do that level of work for hours on end!

The analysis of this web-page is the basis for a unique potential weight-loss concept of another web-page, Dieting - A Physicist's Weight Loss System. Modern people tend to use heavy covers when they sleep, or have the room quite warm, or have a heating pad or warm waterbed. That situation can reduce the body's heat loss down to around 20 Calories/hour during sleep instead of the normal 80 Calories/hour mentioned above. (Researchers have found that 20 Calories per hour seems to be as low as a human adult can get down to, in the effort of the body to avoid overheating (hyperthermia). (Breathing is slowed at an appropriate rate to get rid of the correct amount of carbon dioxide created at the slower metabolic rate.) Over an eight-hour period of sleep, this difference (60 Calories/hour) would represent a total of 480 Calories of heat that your body does NOT get rid of!

In the one example 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 (thin 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!

Different subject!

The public is sometimes incorrectly worried that the increase in concentration of carbon dioxide in the atmosphere itself might be dangerous. Nope! Inside your (closed) home in winter, you might have concentrations of 4,000 ppmv (parts per million by volume), ten times greater than the natural air outside which is now around 388 ppmv. In old auditoriums which have lousy air circulation systems, a three-hour lecture or Sermon to thousands of people can sometimes result in 10,000 ppmv, which can have the effect to make many people a little drowsy! And in submarines, up to 20,000 ppmv of carbon dioxide is allowable! The actual main danger is regarding the established fact that the additional carbon dioxide in the atmosphere represents a "blanket effect" to keep heat from escaping the earth. Many Agronomists believe that if the average Earth temperature rises to just 80°F [27°C] (it is now around 59°F [15°C]), that plants (crops) worldwide will no longer be capable of lifting sufficient water from the soil to keep their leaves from drying out and dying. If all the plants die, then there will be no food for animals or humans. The fear is that this might occur within one or two centuries. There is a credible possibility that we might have ALREADY set in motion a greater temperature increase than that.

This presentation was first placed on the Internet in July 2006.

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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago