83 Efficiency of the Human Body

The Energetic Functions of the Body[1]

An f M R I scan of a human head with energy consumption in the vision center shown by a bright spot. This brightness indicates the energy consumption.
This fMRI scan shows an increased level of energy consumption in the vision center of the brain. Here, the patient was being asked to recognize faces. Image credit: NIH via Wikimedia Commons

All bodily functions, from thinking to lifting weights, require energy. The many small muscle actions accompanying all quiet activity, from sleeping to head scratching, ultimately become thermal energy, as do less visible muscle actions by the heart, lungs, and digestive tract. The rate at which the body uses food energy to sustain life and to do different activities is called the metabolic rate. The total energy conversion rate of a person at rest is called the basal metabolic rate (BMR) and is divided among various systems in the body, as shown the following table:

Basal Metabolic Rates (BMR)
Organ Power consumed at rest (W) Oxygen consumption (mL/min) Percent of BMR
Liver & spleen 23 67 27
Brain 16 47 19
Skeletal muscle 15 45 18
Kidney 9 26 10
Heart 6 17 7
Other 16 48 19
Totals 85 W 250 mL/min 100%
The largest fraction of energy goes to the liver and spleen, with the brain coming next.  About 75% of the calories burned in a day go into these basic functions. A full 25% of all basal metabolic energy consumed by the body is used to maintain electrical potentials in all living cells. (Nerve cells use this electrical potential in nerve impulses.) This bioelectrical energy ultimately becomes mostly thermal energy, but some is utilized to power chemical processes such as in the kidneys and liver, and in fat production. The BMR is a function of age, gender, total body weight, and amount of muscle mass (which burns more calories than body fat). Athletes have a greater BMR due to this last factor.  Of course, during vigorous exercise, the energy consumption of the skeletal muscles and heart increase markedly. The following diagram summarizes the basic energetic functioning in the human body.
A box labeled "the body does work" has an arrow labeled "input" pointing inward from the left. The arrow starts from a box labeled "Chemical Potential Energy." An arrow labeled "output" points outward from the body box to the right and toward a pair of boxes labeled "Potential Energy" and "Kinetic Energy." The potential energy box contains the terms "chemical, electrical, spring, gravitational." The terms chemical and electrical are connected to the terms "growth/repair, nerve function, cellular metabolism, storage." The terms spring, gravitational, and kinetic energy are connected to the the term "motion." An arrow labeled "heat" points outward and upward from the top of the central purple box and toward a box labeled "thermal energy." Small, thin arrows connect the output and input arrows to the word "efficiency," and separately the input and heat arrows to the word "entropy."
The most basic functions of the human body mapped to the main concepts covered in this textbook.(Chemical potential energy is actually a form of electric potential energy, but we will not specifically discuss electric potential energy in this textbook so we have separated the two.)

 

The First Law of Thermodynamics

Heat

The body is capable of storing and thermal energy internally. Remembering that thermal energy is just the kinetic energy of atoms and molecules, we recognize that these two types of energy are stored microscopically and internal to the body. Therefore, we often lump these two types of microscopic energy into the (U). When on object is warmer then its surroundings then will be transferred from object to surroundings, but if the object is cooler than its surroundings then thermal energy will transferred into the object from its surroundings. The amount of thermal energy exchanged due to temperature differences is often called (Q). When heat is transferred out of the body to the environment, we say call this , as indicated in the previous figure.  We will learn more about how temperature and heat transfer are related in the next unit.

Energy Conservation

The states that energy cannot be created or destroyed. Therefore, if the body does useful work to transfer to its surroundings (W_{by}), or transfer to the environment as , then that energy must have come out of the body’s . We observe this throughout nature as the :

(1)   \begin{equation*} \Delta U =  Q - W_{by} \end{equation*}

Heat Engines

Your body uses stored internally to do , and that process also generates thermal energy, which you release as . The internal combustion engines that power most cars operate in similar fashion by converting chemical potential energy in fuel to thermal energy via , then converting some of the thermal energy into and dumping some into . Your body is capable of releasing the chemical potential energy in your food without combustion, which is good, because you are not capable of  using your from your to do . Machines that can use to do work, such as a combustion engine, are known as .  Heat engines are still governed by the , so any must have been thermal energy that was not used to do work. The thermal energy input that can be used to do work rather than wasted as determines the of the heat engine.

Reinforcement Exercises

You apply a 50 N force in order to slide an object 3 m. How much did you do?

If you exhausted 500 worth of while doing the useful work above, how much did your change?

Body Efficiency

The of the human body in converting into is known as the of the body.  We often calculate the body’s mechanical efficiency, as a percentage:

(2)   \begin{equation*} e_{body} = \frac{W_{by}}{Chemical\, Potential\, Energy\, Used}\times 100\,\bold{\%} \end{equation*}

The mechanical efficiency of the body is limited because energy used for metabolic processes cannot be used to do useful work. Additional  generated during the chemical reactions that power muscle contractions along with in joints and other tissues reduces the efficiency of humans even further.[2].

“Alas, our bodies are not 100 % efficient at converting food energy into mechanical output. But at about 25 % efficiency, we’re surprisingly good considering that most cars are around 20 %, and that an Iowa cornfield is only about 1.5 % efficient at converting incoming sunlight into chemical [potential energy] storage.”  [3]For an excellent discussion of human and comparisons with other machines and fuel sources, see MPG of a Human by Tom Murphy, the source of the previous quote.

Everyday Example: Energy to Climb Stairs

Assuming a 20% in climbing stairs, how much does your decrease when a 65 kg person climbs a 15 high flight of stairs? How much does the person transfer to the environment as ?

First, lets calculate the change in :

    \begin{equation*} \Delta PE_g =mg\Delta h = (65\,\bold{kg}) (9.8\,\bold{m/s/s})(15\,\bold{m}) = 9,555\, \bold{J} \end{equation*}

The person did in converting in their body to mechanical energy, specifically . However, they are only 20% efficient, which means that only 1/5 of the chemical potential energy they use goes into doing useful work. Therefore the change in chemical potential energy must have been 5x greater than the mechanical work output

    \begin{equation*} Chemical\, Potential\, Energy\, Used = (5 \times 9,555\, \bold{J})= 47,775\,\bold{J} \end{equation*}

The used came out of the person’s so:

    \begin{equation*} \Delta U = - 47,775 \,\bold{J} \end{equation*}

We can use the to find the thermal energy exhausted by the person:

(3)   \begin{equation*} \Delta U =  Q - W_{by} \end{equation*}

Rearranging for Q:

    \begin{equation*} Q = \Delta U + W_{by} = -  47,775 \,\bold{J}+ 9,555\, \bold{J} = -38,220\, \bold{J} \end{equation*}

We find that the heat is negative, which makes sense because the person exhausts thermal energy out of the body and into to the environment while climbing the stairs.

Alternatively, we could have known right off that the must be 4/5 of the total loss of , because only 1/5 went into doing useful . So the exhaust heat should be:

    \begin{equation*} Q = \Delta U \times (4/5)= -  47,775 \,\bold{J} \times 4/5 = -38,220\, \bold{J} \end{equation*}

Food Calories

For historical reasons we often measure and in units of (cal) instead of .  There are 4.184 Joules per calorie. We measure stored in food with units of 1000 calories, or kilocalories (kcal) and we sometimes write kilocalories as Calories (Cal) with with capital C instead of a lowercase c. For example, a bagel with 350 Cal has 350 kcal, or 350,000 cal. Converting to Joules, that would be 350,000 \,\bold{cal} times (4.184 \,\bold{J}/bold{cal}) =1,464,400\, \bold{J} in the bagel.

Everyday Examples

What fraction of a bagel would you need to eat in order to make up for the 47,775 J  loss of internal energy (as ) that we calculated in the previous everyday example about climbing stairs?

There are 1,464,400  J/bagel

Therefore we need to eat:

    \begin{equation*} \frac{47,775 \,\bold{J}}{1,464,400\, \bold{J}/bagel} = 0.03\, Bagels\, or\, 3\, \bold{\%}\, of \, a\, bagel \end{equation*}

Reinforcement Exercises

How many of energy are stored in a 260 Calorie candy bar?

How many candy bars would you need to eat to make up for the loss of we found in the previous stair climbing example?

Conservation of Mass and of Energy

A person is measuring the amount of oxygen in blood and metabolic rate using a pulse oxymeter. The pulse oxymeter is strapped to the person’s wrist, and the index finger is inside the clip.
A pulse oxymeter is an apparatus that measures the amount of oxygen in blood. Oxymeters can be used to determine a person’s metabolic rate, which is the rate at which food energy is converted to another form. Such measurements can indicate the level of athletic conditioning as well as certain medical problems. (credit: UusiAjaja, Wikimedia Commons)

The digestive process is basically one of oxidizing food, so energy consumption is directly proportional to oxygen consumption. Therefore, we can determine the the actual energy consumed during different activities by measuring oxygen use. The following table shows the oxygen and corresponding energy consumption rates for various activities.

Energy and Oxygen Consumption Rates for an average 76 kg male
Activity Energy consumption in watts Oxygen consumption in liters O2/min
Sleeping 83 0.24
Sitting at rest 120 0.34
Standing relaxed 125 0.36
Sitting in class 210 0.60
Walking (5 km/h) 280 0.80
Cycling (13–18 km/h) 400 1.14
Shivering 425 1.21
Playing tennis 440 1.26
Swimming breaststroke 475 1.36
Ice skating (14.5 km/h) 545 1.56
Climbing stairs (116/min) 685 1.96
Cycling (21 km/h) 700 2.00
Running cross-country 740 2.12
Playing basketball 800 2.28
Cycling, professional racer 1855 5.30
Sprinting 2415 6.90

Everyday Examples: Climbing Stairs Again

In the previous examples we assumed stated that our mechanical efficiency when climbing stairs was 20%. Let’s use the data in the above table to verify that assumption. The data in the table is for a 76 kg person climbing 116 stairs per minute. Let’s calculate the rate at which that person did mechanical work while climbing stairs and compare that rate at which they used up internal energy (originally from food).

The minimum standard step height in the US is 6.0 inches[4] (0.15 m) then the gravitational potential energy of a 76 kg person will increase by 130 J with each step, as calculated below:

    \begin{equation*} \Delta PE = mg\Delta h = (76\,\bold{kg})(9.8\,\bold{m/s/s})(0.15\,\bold{m}) = 112\,\bold{J} \end{equation*}

When climbing 116 stairs per minute the rate of energy use, or power, will then be:

    \begin{equation*} P = (112\,\bold{J})\left(116\, \frac{stairs}{\bold{min}}\right)\left(\frac{1\,\bold{min}}{60\,\bold{sec}}\right) = 216 \,\bold{W} \end{equation*}

According to our data table the body uses 685 W to climb stairs at this rate. Let’s calculate the efficiency:

    \begin{equation*} e = \frac{216\,\bold{W}}{685 \,\bold{W}} = 0.32 \end{equation*}

As a percentage, this person is 32% mechanically efficient when climbing stairs. We may have underestimated in the previous examples when we assumed a 20% efficiency for stair climbing.

Reinforcement Exercises

Every kilogram of fat that metabolized will release roughly 7,800 Calories, or 7,800,000 calories. Convert that energy to Joules.

Apply unit analysis and the data in the previous table to estimate how long you need climb stairs in order to break down 1 kg of fat.

We often talk about “burning” calories in order to lose weight,  but what does that really mean scientifically?. First, we really we mean lose because that is the measure of how much stuff is in our bodies and weight depends on where you are (it’s different on the moon). Second, our bodies can’t just interchange and — they aren’t the same physical quantity and don’t even have the same units. So how do we actually lose mass by exercising? We don’t actually shed the atoms and molecules that make up body tissues like fat by “burning” them. Instead, we break down the fat molecules into smaller molecules and then break bonds within those molecules to release , which we eventually convert to and .  The atoms and smaller molecules that resulting from breaking the bonds combine to form carbon dioxide and water vapor (CO2 and H2O) and we breath them out. We also excrete a bit as H2O in sweat and urine. The process is similar to burning wood in campfire — in the end you have much less of ash than you did original wood. Where did the rest of the mass go? Into the air as CO2 and H2O. The same is true for the fuel burned by your car. For more on this concept see the first video below. The really amazing fact is that your body completes this chemical process without the excessive temperatures associated with burning wood or fuel, which would damage your tissues. The body’s trick is to use enzymes, which are highly specialized molecules that act as catalysts to improve the speed and of chemical reactions, as described and animated in the beginning of the second video below.

 

General Efficiency

Similar to the body , the efficiency of any energetic process can be described as the amount of energy converted from the input form to the desired form divided by the original input amount. The following chart outlines the efficiencies of various systems at converting energy various forms. The chart does not account for the cost, hazard risk, or environmental impact associated with the required fuel, construction, maintenance, and by-products of each system.

The Efficiency of the Human Body Compared to Other Systems
System Input Energy Form Desired Output Form Max Efficiency
Human Body Chemical Potential Mechanical 25 %
Automobile Engine Chemical Potential Mechanical 25 %
Coal/Oil/Gas Fired Stream Turbine Power Plants Chemical Potential Electrical 47%
Combined Cycle Gas  Power Plants Chemical Potential Electrical 58 %
Biomass/Biogas Kinetic Electrical 40%
Nuclear Kinetic Electrical 36%
Solar-Photovoltaic Power Plant Sunlight (Electromagnetic) Electrical 15%
Solar-Thermal Power Plant Sunlight (Electromagnetic) Electrical 23%
Hydroelectric and Tidal Power Plants Gravitational Potential Electrical 90%+

[5][6][7]

Check out the energy systems tab in this simulation to visualize different energy conversion systems

Energy Forms and Changes


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