Size Whys

A Little Bit More

Once you think about it, it probably comes as no surprise that a reduction in the size of appendages (arms, legs, ears, wings, even bills) reduces heat loss. It also follows that the reverse is true; having large appendages improves heat loss. Known as Allen’s Rule (remember A for Appendages), this general rule states that bird and mammal species living permanently in cooler climates tend to have smaller external appendages than their counterparts living in warmer climates. The Arizona Jackrabbit has enormous ears, ears of the Jackrabbit from Oregon are smaller, the Snowshoe Hare’s are smaller yet while the Arctic Hare’s, the most northern species, has the smallest ears of all. In the jackrabbit of the Southwestern U.S., ear length may be almost 25% of the total body length. The Arctic Hare of the far North, on the other hand, has an ear that represents only 12% of its total body length.

The second general rule illustrated in the poster was formulated by a German zoologist in 1847. Now known as Bergmann’s Rule (remember B for Body), it states that overall body size tends to be greater for species and races of birds and mammals living permanently in colder climates than those living permanently in warmer ones. Heat is given off over a warm-blooded animal’s entire body. You might think at first that this means that the bigger the body, the more heat is lost, since there is more total surface to the animal. The catch is that as an animal’s size increases, its volume increases more quickly than its surface area where heat is lost. Therefore, a larger animal may have more surface area for losing heat than a smaller animal, but it has considerably more volume or mass for holding on to that heat. If you want to get technical, volume varies as the cube of an animal’s length; surface varies only as the square of that length. So, if an animal doubles in length (2X), its surface increases 2X2, or 4 times; but its volume increases 2X2X2, or 8 times!

Activities

Big vs. Small

Objectives: See how volume affects heat loss/retention

Materials: Materials: 2 Ice cubes, 2 plastic plates, 2 glasses (different sizes), coffee cup, spoon, microwave/stove

Both Allen’s Rule and Bergmann’s Rule deal with heat loss/retention in mammals and birds. This is an incredibly important component of survival as heat is generated by the foods these animals eat and any reduction in heat loss translates into fewer calories needed. Although the size differences that we’re talking about may seem trivial at first, they can make the difference between life and death for some species.

Here are a few simple exercises that your students can try that should help them understand the general principal at work here.

Ice Cube melt

  1. Remove two, identically sized ice cubes from the freezer. Crush one into small chunks and leave the other ice cube intact.
  2. Ask your students which of the two they think will completely melt the fastest.
  3. Place all of the crushed cube on plate A and the intact cube on plate B, then time the melting process
  4. Write down the time required for the crushed pieces to completely melt and also write down how long it took for the intact cube to completely melt – there should be a marked difference

(The greater surface area of the crushed cube allows it to equalize (warm up) to the room’s temperature)

Hot water cool-down

  1. Place a coffee cup filled with water in a microwave and heat the water above room temperature (not too hot!)
  2. Take the cup out and use a plastic spoon to remove a teaspoon of the hot water. Place the spoon, still full of water, on a plastic plate
  3. Ask your students which of the two, the cup of water or the spoon of water, will cool more quickly
  4. Wait several minutes and then place a thermometer (or use a finger) in the cup and in the spoon to note (feel) the temperature of each. Again, there should be a marked difference

(the greater surface area of the spoonful of water allows it to equalize (cool down) to the room’s temperature)

Cold water warm-up

  1. Fill two glasses of water (one large, one small) with the same cold water from a refrigerator
  2. Place the two glasses next to each other in an obvious place in the room and insert a thermomenter in each
  3. 3. Ask your students which of the two, the large glass or small glass, will warm the quickest
  4. Periodically, note the temperatures of each over the next 20-30 minutes

(the greater surface area of the smaller glass of water allows it to equalize (warm up) to the room’s temperature

In all three of the mini-experiments it should be apparent that increased surface area, as compared to volume, has a marked effect on temperature equilibrium.

Key Concepts

Structures and Functions

Questions

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Filed under: Ecology