The surface-to-volume ratio in thermal physics: from cheese cube physics to animal metabolism

The surface-to-volume ratio is an important quantity in thermal physics. For example it governs the behaviour of heating or cooling of physical objects as a function of size like, e.g. cubes or spheres made of different material. The starting point in our paper is the simple physics problem of how cheese cubes of different sizes behave if heated either in a conventional oven or in a microwave oven. The outcome of these experiments depends on a balance between heating and cooling with the surface-to-volume ratio (S/V) as the key parameter. The role of (S/V) becomes most obvious in studying cooling curves of differently sized objects like cubes or spheres, alone. Besides problems in thermal physics, the surface-to-volume ratio has many important applications in biochemistry, chemistry and biology. It allows us to draw general conclusions concerning the thermal and mechanical properties of different-sized animals, in particular their metabolism. Hence, this topic offers rich contexts for interdisciplinary teaching. An example presented in this paper starts in physics while studying thermal properties of cheese cubes and ends up in biology by discussing the differences in food intake of animals from small mice to huge elephants.