In the case of animals, metabolic heat is generated by the burning of fuel at a rate dependent upon the type and morphology of the animal and the conditions of its immediate thermal environment. The concept is readily extended to the case of an urbanized area and its environs. In particular, published data for population (P), area (A), and regional rates of anthropogenic heat release (Q) - in units of {power} - are employed to explore, theoretically and empirically, the relationships among (A), the population density (P/A), and the per capita rate of release (Q/P). These explorations yield three relationships:
(i) the population of any region (with modifications for islands) is proportional to the radius of its area when that area is assumed to be circular, which is to say the square of a population is linearly related to its area;
(ii) for a particular class of populated area - such as a city, an industrialized region, or a nation - the product (Q/P)(P/A)0.5 is quasi-constant; and thus
(iii) within each of those classes the area-specific regional metabolic rate (Q/A) is proportional to the square root of population density (P/A)0.5. The last two relationships are hypothesized to be a reflection of the fact that individuals in densely populated places increasingly share energy, as in multi-story, shared-wall buildings and mass transportation.