## 9.2 Introduction

In earlier modules of the thermodynamics series, we considered the application of the First Law to biological systems (Stevenson 1977a and b) and the heat transfer processes which govern the energy balance of organisms (Stevenson 1978). The general heat budget equation for animals is $$$\Delta U = M + Q_a - Q_e - LE - C - G \tag{9.1}$$$ where3
• $$\Delta U$$ = change in internal energy ($$W m^{-2}$$),
• $$M$$ = metabolism ($$W m^{-2}$$ ),
• $$Q_a$$ = radiation absorbed ($$W m^{-2}$$),
• $$Q_e$$ = radiation emitted ($$W m^{-2}$$),
• $$LE$$= water vapor losses ($$W m^{-2}$$),
• $$C$$ = convection flux ($$W m^{-2}$$),
• $$G$$ = conduction flux ($$W m^{-2}$$).

Equation (9.1) is a complicated expression with many independent variables. Because biologists are interested in how animals modify their heat balance and why any particular behavior or physical characteristic of an animal influences this balance, they must find ways of analyzing the heat energy balance equation.

In this module we will discuss a model for which the animal’s temperature is not changing with time, that is the steady state assumption that $$\Delta U = 0$$. Porter and Gates (1969) presented the “climate space diagram” to visually display the range of environmental conditions an organism could survive. Subsequently, Monteith (1973) proposed another graphical method to represent the energy balance which we will consider briefly. The works of Hatheway (1978) and Porter et al. (1973) offer alternative methods for understanding an animal’s relationship to the physical environment.

1. In some of the biological literature the units of Equation (9.1) are cal cm-2 min-1, but we have adopted the mks system here.↩︎