What is the physical basis of Bergmann’s and Allen’s rules?
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The Bergmannen Rule is about the allometric relationship between the body size and the ratio of volume to surface. The volume of a body increases by the third potency with increasing body size (length, width and height), but the surface grows only by the second potency (length and width only). With increasing body size, the ratio of the volume of a body to the surface increases more and more, i.e. in relation to the volume, the surface becomes smaller and smaller.
An example: A cube with an edge length of 1 cm has a volume of 1 cm3 (1 cm x 1 cm x 1 cm) and a surface of 6 cm2 (6 x 1 cm x 1 cm). The ratio of volume to surface is thus 1 : 6 = 0.167 (the surface is therefore greater than the volume). A cube with 10 cm edge length has a volume of 100 cm3 (10 cm x 10 cm x 10 cm) and a surface of 600 cm2 (6 x 10 cm x 10 cm), i.e. a volume surface ratio of 1.67 (the surface is therefore smaller than the volume).
The smaller the surface is, the smaller is the surface over which a body can radiate heat to its surroundings. In cold climates, it is cheaper if an animal is larger because it loses less heat than a small animal in relation to its volume (or its mass).
You can also study this experimentally. Take two potatoes that are almost round, but different sizes. Cook both and then plug a thermometer into both. Then you record the temperature for both ten minutes each minute. You can then apply the results graphically and see that the small potato cools faster than the large potato, although both had the same temperature at the beginning and the room temperature is the same for both.
The ratio of volume to body surface is also for Allen rule dictating. It is not about body size, but about body attachments (Eselsbrücke, not to confuse Bergmannschecund Allensche rule: Agreat rule – Anhangs). This means everything that stands out from the body, ears or arms and legs. Large body attachments increase the body’s surface and therefore promote heat dissipation. Conversely, small body attachments reduce the surface and minimize heat dissipation. This can be seen, for example, at the Fennek and at the Polar Fox. The Polar Fox has short legs and short ears to lose little heat. The fennek or desert fox is high-legged and has extremely large ears. He is also the smallest representative of the fox (here also the Bergmann rule applies).
The body shape is also important for the ratio of volume to body surface. The most efficient is the ball, it offers the largest volume at the smallest surface. Animals from cold climate zones are therefore generally also more stable (“spherical”), while related species from hot climate zones are slimmer.
The Bergmann rule and the Allen rule are two rules that are used in thermodynamics to describe the heat capacity of substances. The Bergmann rule states that the heat capacity of a substance is proportional to its density. This means that the denser is a substance, the more heat it must absorb to experience a certain temperature change. The Allenian rule states that the heat capacity of a substance is proportional to its molar mass. This means that the greater the molar mass of a substance, the more heat it must absorb in order to undergo a certain temperature change.
The Bergmann rule is based on the assumption that the heat energy that a substance absorbs is stored mainly in its volume. Since the density of a substance is proportional to its volume, it can be assumed that the heat capacity is proportional to the density.
The Allenian rule is based on the assumption that the heat energy that a substance absorbs is absorbed mainly by the molecules of the substance. Since the molar mass of a substance is proportional to the number of its molecules, it can be assumed that the heat capacity is proportional to the molar mass.
In general, however, the heat capacity of a substance depends on various factors, such as the type of bonds between its molecules, its structure and its state (solid, liquid or gaseous). Therefore, the Bergmannsche and the Allenian rule are only approximate points of reference and may differ in certain cases.
The Bergmann rule is not about density, but about the ratio of volume to surface of a body. The larger a body, the smaller its body surface becomes in relation to its volume, because the body surface increases with 2nd potency, but the volume with 3. potency.
The same applies to the Allenian rule. The ratio of body surface : body volume is crucial.
In this text the Orthography is correct. That’s what it was.
Thank you.