Applications of the Energy Budget Equation

12.7 Applications of the Energy Budget Equation

We return briefly to the animal energy budget equation (Eq. (12.1 1)) to consider some applications. The metabolic rate, latent heat loss, body

temperature, and body conductance are primarily physiological, and have upper and lower bounds set by the physiological makeup of the animal. By

the limits of these variables, the extremes of environment can be predicted that can be tolerated by the animal. The combina- tion of minimum body temperature, maximum sustainable metabolic rate, minimum conductance, and minimum latent heat loss defines the lower lethal limit for the animal. The combination of maximum allowable body temperature, minimum metabolic rate, maximum conductance, and max- imum latent heat loss defines the upper lethal limit. The animal cannot survive extended periods of time in environments below its lower lethal limit or above its upper lethal limit. These limits define a kind of climate space in which the animal can reside. The climate space is a function of both air temperature and absorbed radiation.

In addition to being useful for predicting animal behavior, the energy budget equations can be used to predict the food energy required to main- tain a favorable body temperature. If the operative temperature of the environment is specified, and the body temperature and conductance are known, the energy budget equation can be used to compute the metabolic rate needed to balance the energy budget. This is just the metabolic re- quirement for thermoregulation, but other energy sinks are usually small compared to the requirement for thermoregulation.

Example 12.3. How much food is required for thermoregulation by a

1.5 kg rabbit in an environment with = O°C? Assume d =

0.1 m and

Solution. Since is given, there is no need to consider the radiative environment of the rabbit, but when considering both day and night con- ditions in a typical rabbit environment

are likely to be about the same. Equation (12.11) can be used to find M. We need to know the body temperature, the heat and vapor conductances, and the latent heat loss. We assume body temperature is 37" C, and that the combined respi- ratory and skin latent heat loss is 20 percent of the metabolic rate. There are three conductances for heat loss, the convective-radiative

and

the coat

and the tissue The convective-radiative conductance is the

The Transient State

sum of the forced convection conductance in Table 7.6 and the radiative conductance:

rnol

An estimate of the coat conductance can be obtained from Fig. 12.4 for rabbit. A mean conductance is around 0.045 rnol

. Correcting this

for wind effectsusing Eq.

gives:

= 0.045 x (1

x 1) =

0.05 rnol There are no data for rabbit tissue conductance in Table 12.2, but the numbers shown there suggest it might be around

0.5 rnol

. Substituting these values into Eq. (12.1 1) gives:

0.05 x 0.5 mol

0.05 0.046 + - 0.5 m 2 s

(37 C - 0 C) M(l - 0.2) =

From Eq. the area of a 1.5 kg animal is 0.13 m 2 , so the energy requirement of the rabbit is

The caloric content of glucose as 15.7 so a kilogram of glucose would last

15.7 x

2.05 x

or 24 days.

A kilogram of dry grass would last less than half that long because of inefficiencies in absorption in the digestion process. Efficiency factors are known for many animals and diets.