What is the relationship between metabolic rate per kg of body weight and size?
The smaller the animal, the higher the rate. This is because heat loss is proportional to the animal's free body surface ('free' means exposed to the environment). If the body temperature is to remain constant, as it does in homeotherms, then heat loss from the animal must be equalled by its heat production. Therefore, heat production is proportional to the animal's free body surface, which in turn is proportional to the square of the linear dimensions of the animal.