Latent Heat Exchange

12.3 Latent Heat Exchange

Evaporation of water from the respiratory tract and from the result in latent heat loss from the animal. The total latent heat loss, needed for the energy budget equations, is the sum of the respiratory and skin latent heat losses. Respiratory loss is a direct result of the air exchange for breathing. Skin water loss was already treated in detail in Chs. 6 and 7.

In respiratory evaporation, air is breathed in at ambient vapor pressure and breathed out at the saturation vapor corresponding to the temperature of the nasal passages. In most species the nasal passages are maintained at about body temperature. Since increased metabolic heat production results in increased oxygen consumption, and this increases breathing rate, it would seem reasonable to compute respiratory latent heat loss as some fixed fraction of metabolic heat production. Taking into account the

concentrations of inhaled and exhaled oxygen and water vapor, and the heats of combustion and evaporation we can write:

Mh

where and are expired and inspired vapor pressure, and are the corresponding oxygen concentrations, is the latent heat of vaporization for water (44

is the atmospheric pressure, and is the heat produced per mole of oxygen consumed (480

The difference in oxygen concentration between inhaled and exhaled air is around five percent or 0.05

To get an idea of the magnitude of respiratory latent heat loss, assume air is breathed out at

and has a vapor pressure of 1

when it is breathed in. From Table A.3, the exhaled vapor pressure is 5.3

0.1 M . Some animals with small nasal passages exhale air at temperatures well below body temperature. Figure 12.3 compares exhaled air temperatures for several bird species with values for humans and for kangaroo rats. The

Substituting these values into Eq. (12.15) gives

Latent Heat Exchange

10 20 30 Air Temperature (C)

F I GURE 12.3. Temperature of exhaled air as a function of air temperature for several species

Schmidt-Nielsen, 972).

exhaled air temperature for the kangaroo rat is lower than air temperature, and approaches wet bulb temperature.

The appropriate value of for animals which exhale air at temper- atures lower than body temperature is the saturation vapor pressure at exhaled air temperature from Fig. 12.3. To see how effective this is for water conservation, compute

for the kangaroo rat at From Fig. 12.3,

= 2.1 If the other values are as in the previous example, then

C, so

0.02 M, rather than 0.1 M. This is only 25 percent of the respiratory water loss per unit area of a human

under similar conditions. The resulting water conservation is important for survival of kangaroo rats in their arid habitat.

7. The general equation is

Cutaneous latent heat loss is discussed in Chs. 6 and

where

and are the conductances to vapor through the skin, coat, and boundary layer, and and

are the vapor pressures at the subcutaneous (saturated) evaporating surface, and in the atmosphere. For animals with moist skins (earthworms, snails, and amphibians) and

are large so the controlling conductance for water loss is the boundary layer conductance. For nonsweating animals,

is often so

Animals and their Environment

small that effects of g,, and g,, are negligible by comparison, as shown in Ch. 7. Table 7.2 gives some animal

conductances. Table 12.1 gives a more extensive listing. Note that species living in arid environ- ments tend to have the lowest vapor conductances. Little is known about the variability of these numbers or their dependence on environmental moisture or temperature. Much additional research is needed in this area. Accurate estimates of skin-diffusive conductance are important, both for accurate energy budget predictions and for water budgets of animals. The importance of skin water loss is illustrated by the fact that it accounts for 75 percent or more of the total water loss even for the desert tortoise (Schmidt-Nielsen, 1969).

To illustrate the magnitude of we find the rate of water loss for a camel under circumstances similar to those for which

was found. If skin temperature is

= 5.9 Assuming = 1 and using the skin conductance for camel

then

Table 12.1 gives J

5.9 - 1 W = 44000

mol

6.9 - .

101 m 2 The effect of coat and boundary layer conductance have been ignored,

mol

but their effect is small when the skin conductance is so low. If we assume and M

= 5 The latent heat loss is larger than this value and, in fact, makes up about 58 percent of the total. The total latent heat loss is around 20 percent of M. These percentages are probably fairly typical for resting endotherms that are not

50 then

heat-stressed. For poikilotherms under similar conditions one typically assumes M

E. As the animal becomes heat-stressed, latent heat loss increases, gen- erally by some active process such as sweating or panting. There is no general approach to the calculation of latent heat loss under these con- ditions since animal responses are so varied. The approach would need to be fitted to the particular species being studied. In Ch. 13 we look at

T A BLE 12.1. Skin conductance to vapor for non-heat stressed animals

mmol white rat

10.6 gopher snake 1.0 human

5.4 chuckawalla 0.34 camel

3.2 desert tortoise 0.34

white footed mouse 3.0 Birds

spiney mouse

2.8 sparrow

budgerigar 4.9 caiman

Reptiles

zebra finch 4.1 water snake

village weaver 3.3 pond turtle

3.1 box turtle

poor-will

roadrunner 2.4 iguana

painted quail 2.1

Latent Heat Exchange 193

latent heat loss by sweating, but do not otherwise treat water loss under heat stress.

Example 12.1. White crown sparrows migrate over long distances. In flight, both water and energy are expended. If an average sparrow weighs

27 g, and can store 4 g of fat and 4 of water (including the water obtained from metabolism), will its range be limited by stored energy or stored water? Assume the metabolic rate for flight is

and the energy content of fat is 40

10" C, 38" C , and =

Also assume

Solution. The energy-limited flight time is equal to the total energy available divided by the rate of energy consumption. The rate of energy consumption is

= 50 M 300 From Eq.

Assuming

0.009 m 2 . The energy limited flight time is

the sparrow area is A

0.1 x

4g x 40000

x 0.009m 2

Water loss is from the and from the respiratory tract. The vapor pressure of the air is given, and the vapor pressure at the evaporating surfaces is e, (38)

6.63 Assuming a flight altitude of m, then = 89 Again we ignore effects of coat and boundary layer on vapor conductance, and use the sparrow skin conductance from Table 12.1. Using these numbers, the rate of skin water loss is

s Equation (12.15) can be used to get the respiratory water loss. The in-

89 m 2

spired air is at the vapor pressure of the atmosphere and the expired air is saturated at the expired air temperature. From Fig. 12.3, the sparrow expired air temperature at 10°C ambient is 21°C. The saturation vapor pressure is 2.49

The rate of respiratory water loss is therefore

2.49 rnol

x 0.05 m 2 s The total rate of water loss is the sum of respiratory and

loss, or 0.00045 rnol

0.22 mol. The water limited flight time is

The stored water is 4 g

0.22 rnol

2 = 54321 s 0.00045 15 x 0.009m With this set of assumptions, it appears that water and energy are about

equally limiting. The assumptions were not arbitrary, but were taken from literature on white crown sparrows, so the conclusions are probably not far off. It should not be a surprise that the two limitations would be that

194 Animals and their Environment

well matched, since any unnecessary weight would also limit the range of the bird.