Chapter 11 Heat and Life
TABLE 11.1 Metabolic Rates for Selected Activities
Metabolic rate
Activity
(Cal/m2-hr)
Sleeping
35
Lying awake
40
Sitting upright
50
Standing
60
Walking (3 mph)
140
Moderate physical work
150
Bicycling
250
Running
600
Shivering
250
In this chapter, we will examine energy consumption, heat flow, and tem perature control in animals. Although most of our examples will be specificto people, the principles are generally applicable to all animals.
11.1
Energy Requirements of People
All living systems need energy to function. In animals, this energy is used tocirculate blood, obtain oxygen, repair cells, and so on. As a result, even atcomplete rest in a comfortable environment, the body requires energy to sustain its life functions. For example, a man weighing 70 kg lying quietly awakeconsumes about 70 Cal/h (1 cal 4.18 J; 1,000 cal 1 Cal; 1 Cal/h 1.16 W).
Of course, the energy expenditure increases with activity.
The amount of energy consumed by a person depends on the person’s weight and build. It has been found, however, that the amount of energy
consumed by a person during a given activity divided by the surface area ofthe person’s body is approximately the same for most people. Therefore, theenergy consumed for various activities is usually quoted in Cal/m2-hr. Thisrate is known as the metabolic rate. The metabolic rates for some humanactivities are shown in Table 11.1. To obtain the total energy consumption perhour, we multiply the metabolic rate by the surface area of the person. Thefollowing empirical formula yields a good estimate for the surface area.
Area (m2) 0.202 × W 0.425 × H 0.725
(11.1)
Here W is the weight of the person in kilograms, and H is the height of theperson in meters.
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The surface area of a 70-kg man of height 1.55 m is about 1.70 m2. His metabolic rate at rest is therefore (40 Cal/m2-hr) × 1.70 m2 68 Cal/hr, orabout 70 Cal/hr as stated in our earlier example. This metabolic rate at rest iscalled the basal metabolic rate.
11.2
Energy from Food
C6H12O6 + 6O2 → 6CO2 + 6H2O + energy
(11.2)
For every gram of glucose ingested by the body, 3.81 Cal of energy is releasedfor metabolic use.
The caloric value per unit weight is different for various foods. Measure ments show that, on the average, carbohydrates (sugars and starches) and proteins provide about 4 Cal/g; lipids (fats) produce 9 Cal/g, and the oxidation ofalcohol produces 7 Cal/g.2 The oxidation of food, which releases energy, does not occur spontaneously at normal environmental temperatures. For oxidation to proceed at bodytemperature, a catalyst must promote the reaction. In living systems, complexmolecules, called enzymes, provide this function.
In the process of obtaining energy from food, oxygen is always consumed.
It has been found that, independent of the type of food being utilized, 4.83 Calof energy are produced for every liter of oxygen consumed. Knowing thisrelationship, one can measure with relatively simple techniques the metabolicrate for various activities (see Exercise 11-1).
The daily food requirements of a person depend on his or her activities.
A sample schedule and the associated metabolic energy expenditure per squaremeter are shown in Table 11.2. Assuming, as before, that the surface area ofthe person whose activities are shown in Table 11.2 is 1.7 m2, his/her totalenergy expenditure is 3940 Cal/day. If the person spent half the day sleepingand half the day resting in bed, the daily energy expenditure would be only1530 Cal.
For most people the energy expenditure is balanced by the food intake.
For example, the daily energy needs of the person whose activities are shown 2The high caloric content of alcohol presents a problem for people who drink heavily. The body utilizes fully the energy released by the oxidation of alcohol. Therefore, people who obtaina significant fraction of metabolic energy from this source reduce their intake of conventionalfoods. Unlike other foods, however, alcohol does not contain vitamins, minerals, and othersubstances necessary for proper functioning. As a result, chronic alcoholics often suffer fromdiseases brought about by nutritional deficiencies.
Chapter 11 Heat and Life TABLE 11.2 One Day’s Metabolic Energy Expenditure
Energy expenditure
Activity
(Cal/m2)
8 hr sleeping (35 Cal/m2-hr)
280
8 hr moderate physical labor (150 Cal/m2-hr)
1200
4 hr reading, writing, TV watching (60 Cal/m2-hr)
240
1 hr heavy exercise (300 Cal/m2-hr)
300
3 hr dressing, eating (100 Cal/m2-hr)
300
Total expenditure
2320
TABLE 11.3 Composition and Energy Content of Some Common Foods Total
Protein
Carbohydrate
Fat
Total
Food
weight (g) weight (g) weight (g) weight (g) energy (Cal)
976
32
48
40
660
Egg, 1
50
6
0
12
75
Hamburger, 1
85
21
0
17
245
Carrots, 1 cup
150
1
10
0
45
Potato (1 med., baked)
100
2
22
0
100
Apple
130
0
18
0
70
Bread, rye, 1 slice
23
2
12
0
55
Doughnut
33
2
17
7
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in Table 11.2 (surface area 1.7 m2) are met by the consumption of 400 g ofcarbohydrates, 200 g of protein, and 171 g of fat.
The composition and energy content of some common foods are shown in Table 11.3. Note that the sum of the weights of the protein, carbohydrates, andfat is smaller than the total weight of the food. The difference is due mostlyto the water content of the food. The energy values quoted in the table reflectthe fact that the caloric content of different proteins, carbohydrates, and fatsdeviate somewhat from the average values stated in the text.
If an excess of certain substances, such as water and salt, is ingested, the body is able to eliminate it. The body has no mechanism, however, for eliminating an excess in caloric intake. Over a period of time the excess energyis used by the body to manufacture additional tissue. If the consumption ofexcess food occurs simultaneously with heavy exercise, the energy may be utilized to increase the weight of the muscles. Most often, however, the excessenergy is stored in fatty tissue that is manufactured by the body. Conversely,if the energy intake is lower than the demand, the body consumes its own tissue to make up the deficit. While the supply lasts, the body first utilizes itsstored fat. For every 9 Cal of energy deficit, about 1 g of fat is used. Undersevere starvation, once the fat is used up, the body begins to consume its ownprotein. Each gram of consumed protein yields about 4 Cal. Consumption ofbody protein results in the deterioration of body functions, of course. A relatively simple calculation (see Exercise 11-4) shows that an average healthyperson can survive without food but with adequate water up to about 50 days.
Overweight people can do better, of course. The “Guinness Book of WorldRecords” states that Angus Barbieri of Scotland fasted from June, 1965, toJuly, 1966, consuming only tea, coffee, and water. During this period, hisweight declined from 472 lb to 178 lb.
For a woman, the energy requirements increase somewhat during preg nancy due to the growth and metabolism of the fetus. As the following calculation indicates, the energy needed for the growth of the fetus is actually rathersmall. Let us assume that the weight gain of the fetus during the 270 days ofgestation is uniform.3 If at birth the fetus weighs 3 kg, each day it gains 11 g.
Because 75% of tissue consists of water and inorganic minerals, only 2.75 g ofthe daily mass increase is due to organic materials, mainly protein. Therefore,the extra Calories per day required for the growth of the fetus is Calories required 2.75 g protein × 4 Cal 11 Cal/day
day g protein To this number, we must add the basal metabolic consumption of the fetus.
At birth, the surface area of the fetus is about 0.13 m2 (from Eq. 11.1); therefore, at most, the basal metabolic consumption of the fetus per day is about0.13 × 40 × 24 125 Cal. Thus, the total increase in the energy requirementof a pregnant woman is only about (125 + 11) Cal/day 136 Cal/day. Actually, it may not even be necessary for a pregnant woman to increase her foodintake, as the energy requirements of the fetus may be balanced by decreasedphysical activity during pregnancy. Various other aspects of metabolic energybalance are examined in Exercises 11-2 to 11-5.
11.3 Regulation of Body Temperature
Chapter 11 Heat and Life
The body temperature is sensed by specialized nerve centers in the brain and by receptors on the surface of the body. The various cooling or heatingmechanisms of the body are then activated in accord with the temperature. Theefficiency of muscles in performing external work is at best 20%. Therefore, atleast 80% of the energy consumed in the performance of a physical activity isconverted into heat inside the body. In addition, the energy consumed to maintain the basic metabolic processes is ultimately all converted to heat. If this heatwere not eliminated, the body temperature would quickly rise to a dangerouslevel. For example, during moderate physical activity, a 70-kg man may consume 260 Cal/hr. Of this amount, at least 208 Cal is converted to heat. If thisheat remained within the body, the body temperature would rise by 3 C◦/hr.
Two hours of such an activity would cause complete collapse. Fortunately, thebody possesses a number of highly efficient methods for controlling the heatflow out of the body, thereby maintaining a stable internal temperature.
Most of the heat generated by the body is produced deep in the body, far from the surfaces. In order to be eliminated, this heat must first be conductedto the skin. For heat to flow from one region to another, there must be atemperature difference between the two regions. Therefore, the temperatureof the skin must be lower than the internal body temperature. In a warmenvironment, the temperature of the human skin is about 35◦C. In a coldenvironment, the temperature of some parts of the skin may drop to 27◦C.
The tissue of the body, without blood flowing through it, is a poor con ductor. Its thermal conductivity is comparable to that of cork (see Table 9.2).
(Kc for tissue without blood is 18 Cal-cm/m2-hr-C◦.) Simple thermal conductivity through tissue is inadequate for elimination of the excess heat generatedby the body. The following calculation illustrates this point. Assume that thethickness of the tissue between the interior and the exterior of the body is 3 cmand that the average area through which conduction can occur is 1.5 m2. Witha temperature difference T between the inner body and the skin of 2◦C, theheat flow H per hour is, from Eq. 9.3, H KcAT 18 × 1.5 × 2 18 Cal/hr
(11.3)
L
3
In order to increase the conductive heat flow to a moderate level of say 150 Cal/hr, the temperature difference between the interior body and the skinwould have to increase to about 17 C◦.
151
Fortunately the body possesses another method for transferring heat. Most of the heat is transported from the inside of the body by blood in the circulatorysystem. Heat enters the blood from an interior cell by conduction. In this case,heat transfer by conduction is relatively fast because the distances between thecapillaries and the heat-producing cells are small. The circulatory system carriesthe heated blood near to the surface skin. The heat is then transferred to theoutside surface by conduction. In addition to transporting heat from the interiorof the body, the circulatory system controls the insulation thickness of the body.
When the heat flow out of the body is excessive, the capillaries near the surfacebecome constricted and the blood flow to the surface is greatly reduced. Becausetissue without blood is a poor heat conductor, this procedure provides a heatinsulating layer around the inner body core.
11.4 Control of Skin Temperature
Because the heat conductivity of air is very low (2.02 Cal-cm/m2-hr-C◦), ifthe air around the skin is confined—for example, by clothing—the amountof heat removed by conduction is small. The surface of the skin is cooledprimarily by convection, radiation, and evaporation. However, if the skin is incontact with a good thermal conductor such as a metal, a considerable amountof heat can be removed by conduction (see Exercise 11-6).
11.5
Convection
When the skin is exposed to open air or some other fluid, heat is removedfrom it by convection currents. The rate of heat removal is proportional to theexposed surface area and to the temperature difference between the skin andthe surrounding air. The rate of heat transfer by convection H c (see Eq. 9.4)is given by
H c K cAc(Ts − Ta)
(11.4)
where Ac is the skin area exposed to the open air; Ts and Ta are the skin andair temperatures, respectively; and K c is the convection coefficient, which hasa value that depends primarily on the prevailing wind velocity. The value ofK c as a function of air velocity is shown in Fig. 11.1. As the plot shows, theconvection coefficient initially increases sharply with wind velocity, and thenthe increase becomes less steep (see Exercise 11-7).
152
Chapter 11 Heat and Life FIGURE 11.1 Convection coefficient as a function of air velocity.
The exposed area Ac is generally smaller than the total surface area of the body. For a naked person standing with legs together and arms close to thebody, about 80% of the surface area is exposed to convective air currents.
(The exposed area can be reduced by curling up the body.)
Note that heat flows from the skin to the environment only if the air is colder than the skin. If the opposite is the case, the skin is actually heated bythe convective air flow.
Let us now calculate the amount of heat removed from the skin by con vection. Consider a naked person whose total surface area is 1.7 m2. Standingstraight, the exposed area is about 1.36 m2. If the air temperature is 25◦C andthe average skin temperature is 33◦C, the amount of heat removed is
H
×
c .36K c .9K c Cal/hr Under nearly windless conditions, K c is about 6 Cal/m2-hr-C◦ (see Fig. 11.1),and the convective heat loss is 65.4 Cal/hr. During moderate work, the energyconsumption for a person of this size is about 170 Cal/hr. Clearly, convectionin a windless environment does not provide adequate cooling. The wind 153
11.6 Radiation Hr involves thefourth power of temperature; that is,
Hr eσ T 4 − T 4
1
2
However, because in the environment encountered by living systems the temperature on the absolute scale seldom varies by more than 15%, it is possible touse, without much error, a linear expression for the radiative energy exchange(see Exercise 11-8a and b); that is, Hr KrAre(Ts − Tr)
(11.5)
where Ts and Tr are the skin surface temperature and the temperature of thenearby radiating surface, respectively; Ar is the area of the body participatingin the radiation; e is the emissivity of the surface; and Kr is the radiationcoefficient. Over a fairly wide range of temperatures, Kr is, on the average,about 6.0 Cal/m2-hr-C◦ (see Exercise 11-8c).
The environmental radiating surface and skin temperatures are such that the wavelength of the thermal radiation is predominantly in the infrared regionof the spectrum. The emissivity of the skin in this wavelength range is nearlyunity, independent of the skin pigmentation. For a person with Ar 1.5 m2,Tr 25◦C and Ts 32◦C. The radiative heat loss is 63 Cal/hr.
If the radiating surface is warmer than the skin surface, the skin is heated by radiation. A person begins to feel discomfort due to radiation if the temperature difference between the exposed skin and the radiating environmentexceeds about 6 C◦. In the extreme case, when the skin is illuminated bythe sun or some other very hot object like a fire, the skin is heated intensely.
Because the temperature of the source is now much higher than the temperature of the skin, the simplified expression in Eq. 11.5 no longer applies.
11.7 Radiative Heating by the Sun
154
Chapter 11 Heat and Life FIGURE 11.2 Radiative heating by the sun.
rotation further reduces the intensity of solar radiation at the surface. However,in dry equatorial deserts, nearly all the solar radiation may reach the surface.
Because the rays of the sun come from one direction only, at most half the body surface is exposed to solar radiation. In addition the area perpendicular to the solar flux is reduced by the cosine of the angle of incidence(see Fig. 11.2). As the sun approaches the horizon, the effective area for theinterception of radiation increases, but at the same time the radiation intensitydecreases because the radiation passes through a thicker layer of air. Still, theamount of solar energy heating the skin can be very large. Assuming that thefull intensity of solar radiation reaches the surface, the amount of heat Hr thatthe human body receives from solar radiation is Hr 1150/2 × e × A cos θ Cal/hr
(11.6)
Here A is the skin area of the person, θ is the angle of incidence of sunlight, and e is the emissivity of the skin. The emissivity of the skin in thewavelength region of solar radiation depends on the pigmentation. Dark skinabsorbs about 80% of the radiation, and light skin absorbs about 60%. FromEq. 11.6, a light-skinned person with a skin area of 1.7 m2, subject to intensesolar radiation incident at a 60◦ angle, receives heat at the rate of 294 Cal/hr.
Radiative heating is decreased by about 40% if the person wears light-coloredclothing. Radiative heating is also reduced by changing the orientation of thebody with respect to the sun. Camels resting in the shadeless desert face thesun, which minimizes the skin area exposed to solar radiation.
155
11.8
Evaporation eccrine glands in the palms of the hand and the solesof the feet are stimulated by elevated levels of adrenaline in the blood, whichmay result from emotional stress.
The apocrine sweat glands, found mostly in the pubic regions, are not associated with temperature control. They are stimulated by adrenaline in theblood stream, and they secrete a sweat rich in organic matter. The decomposition of these substances produces body odor.
The ability of the human body to secrete sweat is remarkable. For brief periods of time, a person can produce sweat at a rate up to 4 liter/hr. Such ahigh rate of sweating, however, cannot be maintained. For longer periods, upto 6 hours, a sweating rate of 1 liter/hr is common in the performance of heavywork in a hot environment.
During prolonged heavy sweating, adequate amounts of water must be drunk; otherwise, the body becomes dehydrated. A person’s functioning isseverely limited when dehydration results in a 10% loss of body weight. Somedesert animals can endure greater dehydration than humans; a camel, forexample, may lose water amounting to 30% of its body weight without seriousconsequences.
Only sweat that evaporates is useful in cooling the skin. Sweat that rolls off or is wiped off does not provide significant cooling. Nevertheless,excess sweat does ensure full wetting of the skin. The amount of sweatthat evaporates from the skin depends on ambient temperature, humidity,and air velocity. Evaporative cooling is most efficient in a hot, dry, windyenvironment.
There is another avenue for evaporative heat loss: breathing. The air leav ing the lungs is saturated by water vapor from the moist lining of the respiratory system. At a normal human breathing rate, the amount of heat removedby this avenue is small, less than 9 Cal/hr (see Exercise 11-9); however, forfurred animals that do not sweat, this method of heat removal is very important. These animals can increase heat loss by taking short shallow breaths Chapter 11 Heat and Life
By evaporative cooling, a person can cope with the heat generated by mod erate activity even in a very hot, sunny environment. To illustrate this, we willcalculate the rate of sweating required for a person walking nude in the sun ata rate of 3 mph, with the ambient temperature at 47◦C (116.6◦F).
With a skin area of 1.7 m2, the energy consumed in the act of walking is about 240 Cal/hr. Almost all this energy is converted to heat and delivered tothe skin. In addition, the skin is heated by convection and by radiation fromthe environment and the sun. The heat delivered to the skin by convection is
H c K cAc(Ts − Ta) For a 1-m/sec wind, K c is 13 Cal/m2-hr-C◦. The exposed area Ac is about 1.5 m2. If the skin temperature is 36◦C,
H c .50 × (47 − 36) 215 Cal/hr As calculated previously, the radiative heating by the sun is about 294 Cal/hr. The radiative heating by the environment is
H c KrAre(Tr − Ts) 6 × 1.5 × (47 − 36) 99 Cal/hr In this example, the only mechanism available for cooling the body is the evaporation of sweat. The total amount of heat that must be removedis (240 + 215 + 194 + 99) Cal/hr 848 Cal/hr. The evaporation of about1.5 liter/hr of sweat will provide the necessary cooling. Of course, if theperson is protected by light clothing, the heat load is significantly reduced.
The human body is indeed very well equipped to withstand heat. In controlledexperiments, people have survived a temperature of 125◦C for a period of timethat was adequate to cook a steak.
11.9 Resistance to Cold critical temperature.
This temperature is a measure of the ability of an animal to withstand cold.
Human beings are basically tropical animals. Unprotected, they are much better able to cope with heat than with cold. The critical temperature forhumans is about 30◦C. By contrast, the critical temperature for the heavilyfurred arctic fox is −40◦C.
157
The discomfort caused by cold is due primarily to the increased rate of heat outflow from the skin. This rate depends not only on the temperature butalso on the wind velocity and humidity. For example, at 20◦C, air movingwith a velocity of 30 cm/sec removes more heat than still air at 15◦C. In thiscase, a mild wind at 30 cm/sec is equivalent to a temperature drop of morethan 5 C◦.
The body defends itself against cold by decreasing the heat outflow and by increasing the production of heat. When the temperature of the body begins todrop, the capillaries leading to the skin become constricted, reducing the bloodflow to the skin. This results in a thicker thermal insulation of the body. In anaked person, this mechanism is fully utilized when the ambient temperaturedrops to about 19◦C. At this point, the natural insulation cannot be increasedany more.
Additional heat required to maintain the body temperature is obtained by increasing the metabolism. One involuntary response that achieves this isshivering. As shown in Table 11.1, shivering raises the metabolism to about250 Cal/m2-hr. If these defenses fail and the temperature of the skin andunderlying tissue fall below about 5◦C, frostbite and eventually more seriousfreezing occur.
The most effective protection against cold is provided by thick fur, feath ers, or appropriate clothing. At −40◦C, without insulation, the heat loss isprimarily convective and radiative. By convection alone in moderately moving air, the rate of heat removal per square meter of skin surface is about660 Cal/m2-hr (see Exercise 11-10). With a thick layer of fur or similar insulation the skin is shielded from convection and the heat is transferred to theenvironment by conduction only. The thermal conductivity of insulating materials such as fur or down is Kc 0.36 Cal cm/m2-hr-C◦; therefore, the heattransfer from the skin at 30◦C to the ambient environment at −40◦C through1 cm of insulation is, from Eq. 9.3, 25.2 Cal/m2-hr. This is below the basalmetabolic rate for most animals. Although body heat is lost also through radiation and evaporation, our calculation indicates that well-insulated animals,including a clothed person, can survive in cold environments.
As stated earlier, at moderate temperatures the amount of heat removed by breathing at a normal rate is small. At very cold temperatures, however,the heat removed by this channel is appreciable. Although the heat removedby the evaporation of moisture from the lungs remains approximately constant, the amount of heat required to warm the inspired air to body temperature increases as the ambient air temperature drops. For a person at anambient temperature of −40◦C, the amount of heat removed from the bodyin the process of breathing is about 14.4 Cal/hr (see Exercise 11-11). For awell-insulated animal, this heat loss ultimately limits its ability to withstandcold.
Chapter 11 Heat and Life
11.10 Heat and Soil
The surface soil is heated primarily by solar radiation. Although some heat is conducted to the surface from the molten core of the Earth, the amountfrom this source is negligible compared to solar heating. The Earth is cooledby convection, radiation, and the evaporation of soil moisture. On the average,over a period of a year, the heating and cooling are balanced; and therefore,over this period of time, the average temperature of the soil does not changeappreciably. However, over shorter periods of time, from night to day, fromwinter to summer, the temperature of the top soil changes considerably; thesefluctuations govern the life cycles in the soil.
The variations in soil temperature are determined by the intensity of solar radiation, the composition and moisture content of the soil, the vegetationcover, and atmospheric conditions such as clouds, wind, and airborne particles (see Exercises 11-12 and 11-13). Certain patterns, however, are general.
During the day while the sun is shining, more heat is delivered to the soilthan is removed by the various cooling mechanisms. The temperature of thesoil surface therefore rises during the day. In dry soil, the surface temperaturemay increase by 3 or 4 C◦/hr. The surface heating is especially intense in dry,unshaded deserts. Some insects living in these areas have evolved long legs tokeep them removed from the hot surface.
The heat that enters the surface is conducted deeper into the soil. It takes some time, however, for the heat to propagate through the soil. Measurementsshow that a temperature change at the surface propagates into the soil at arate of about 2 cm/h. At night, the heat loss predominates and the soil surfacecools. The heat that was stored in the soil during the day now propagates tothe surface and leaves the soil. Because of the finite time required for the heatto propagate through the soil, the temperature a few centimeters below the surface may still be rising while the surface is already cooling off. Some animalstake advantage of this lag in temperature between the surface and the interior of the soil. They burrow into the ground to avoid the larger temperaturefluctuations at the surface.
At the usual temperatures the thermal radiation emitted by the soil is in the infrared region of the spectrum, which is strongly reflected by water vaporand clouds. As a result, on cloudy days the thermal radiation emitted by thesoil is reflected back, and the net outflow of heat from the soil is reduced—this
