The Energy Budget Concept

12.1 The Energy Budget Concept

The question of whether or not an animal can maintain its body tempera- ture within acceptable limits can be stated in another way which makes it more amenable to analysis. It can be asked whether heat loss can be bal-

anced by heat input and production at the required body temperature. We are well prepared to describe heat inputs and heat losses for a system, so the problem is easily solved, at least in principle. An equation stating that heat inputs minus heat losses equals heat storage for a system is called an energy budget equation. As an example of an energy budget, consider

a representative unit area of the surface of an animal that is exposed to the atmosphere. The energy budget of this surface is the sum of the heat

inputs and losses. Thus:

186 Animals and their Environment

where

is the flux density of outgoing, emitted radiation from the surface, M is the rate of metabolic heat production per unit surface area,

is the flux density of absorbed radiation,

is the latent heat loss from evaporation of water,

H is the rate of sensible heat loss, G is the rate of heat loss to the substrate by conduction, and q is the rate of heat storage in the animal per unit surface area.

Initially, we concern ourselves only with steady-state conditions for which the heat storage rate q is zero. The rate of heat storage is equal to the heat capacity of the animal multiplied by the rate of change of body temperature, so if the heat storage rate is zero, the rate of change of body temperature must also be zero. For simplicity, we also assume G = 0.

The emitted radiation and sensible heat [H -

terms both involve the surface temperature of the an- imal. It is always possible to set a value for surface temperature which balances Eq. (12. but that temperature may be too high or too low for the animal to remain alive. If body temperature and metabolic rate are specified, then Eq. (12.1) can be used to find environments that are ener- getically acceptable

and that will balance the energy budget). On the other hand, we could measure or estimate

and and com- pute M. Knowing M, we can specify food needs for thermoregulation in

a given climate. Equation (12.1) is not very useful as it stands because of its strong dependence on surface temperature, a quantity that is hard to estimate, or even to measure. Body temperature, at least for endotherms, is easily estimated since it is under tight metabolic control. This fact can be used to eliminate surface temperature from the energy balance equation. Fig- ure 12.1 shows the assumptions we make about the source (M) and sink

of heat, and the resistances to heat flow from the body core to the environment. In a nonsweating animal, much of the latent heat loss is through breathing, or

and the remainder is from beneath the coat, which generally has a much higher resistance than the tissues. It is therefore

to lump latent heat loss with metabolic heat production and place them at the body core. Later we do a more complete analysis which does not restrict the location of the latent heat loss. It is often useful to combine coat and tissue conductance into a whole body conductance:

Since all of the heat the body core flows through we can write

where is the specific heat of air. Equation (12.1) can now be rewritten explicitly showing the surface temperature dependence:

The Energy Budget Concept

F IG URE 12.1. Diagram of heat production and loss in an non-sweating animal.

By combining Eq. (12.3) and Eq. we can eliminate the sur- face temperature and have an energy balance equation in terms of body temperature and whole body conductance.

Before proceeding with the derivation of the energy balance equation, we briefly consider an algebraic manipulation which linearizes the surface emittance term, where surface temperature is raised to the fourth power.

+ AT, where AT - Now the binomial

can be written as

expansion is used to obtain:

A calculator can be used to verify that the in Eq. (12.5) with powers of AT greater than one are negligibly small for values of AT up to tens of degrees. Therefore

The approximation is almost exact if, instead of using the cube of the air temperature, the cubed average of surface and air temperature is used.

can be approximated as

Using this approximation, the surface term in Eq. (12.4) can

be written as:

Here we have defined a radiative conductance. For an animal in an en- closure the net exchange of thermal radiation between the walls of the enclosure and the animal is directly proportional to the difference be- tween wall temperature and animal surface temperature and also directly proportional to the radiative conductance. This conductance therefore allows the combination of thermal radiative exchange with convective

Animals and their Environment

heat exchange in a convenient way and also linearizes the energy balance equation. From Eq. (12.6) it is seen that

Values for (with set to 1) are tabulated in Table A.3 for temperatures between -5 and 45°C.

With these changes and substitutions, the energy balance equation now becomes:

where

Finally, making use of Eq. (12.3) to eliminate surface temperature the energy budget equation for an animal is obtained in terms of body temperature:

One final simplification allows the energy balance equation to be writ- ten in a particularly useful form. Animal metabolism is often studied inside chambers where air and wall temperatures are equal, where the

density of shortwave radiation is negligible, and where wall sivities are high. Such a chamber could be called a blackbody enclosure. If the radiation balance equation (Eq. (1 1.14)) is looked at for an animal in such an enclosure, it is seen that

We call the temper- ature of such a blackbody enclosure the operative temperature, with the symbol

Later we relate the operative temperature to outdoor radiation and temperature conditions, but for now the use of operative temperature allows us to eliminate radiation terms from the energy balance equation.

The operative temperature form of Eq. (12. with some rearrangement of terms is:

The second equation, in resistance form, is the more familiar but we continue to use conductances here. For now

can be thought of as the air temperature of a normal room in which the air and wall tempera- tures are equal. Equation (12.1 1) simply shows the relationship between temperature, resistance, metabolic rate, and latent heat loss for an animal.

It is extremely useful for analyzing interaction, but before going farther we need to consider some aspects of animal biology

to get values for M,

E, and

Metabolism