Endothermy, size and heat loss
Mammalian origins and defining features, the cost of endothermy, and the surface-area-to-volume ratio: why small mammals lose heat faster and have a higher metabolic rate per kilogram.
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Mammals are synapsids; a group called the cynodonts are thought to be their ancestors, and the earliest known mammal fossils are from the early Jurassic, about 205 million years ago. Today there are about 5,200 species.[1]
Defining features include hair made of keratin, mammary glands, sweat glands, a muscular diaphragm and, like birds, a four-chambered heart. Two of the three middle-ear bones, the malleus and incus, evolved from jaw bones.[1][2]
Mammals are endotherms: they keep a relatively constant body temperature. Hair traps a boundary layer of air close to the body, and humans have sweat glands over most of the body surface.[1][7]
Endothermy is expensive. Human males have a basal metabolic rate (BMR) of 1600–1800 kcal/day and females 1300–1500 kcal/day, while an ectotherm such as an alligator has a standard metabolic rate of about 60 kcal/day.[7]
For a sphere, surface area = 4πr² and volume = (4/3)πr³, so SA : V = 3/r: bigger bodies have less surface per unit volume. Doubling body size increases body mass about eight times. Smaller endotherms therefore lose heat faster for their mass and have a higher BMR per kilogram: a mouse uses far more oxygen per gram than an elephant.[7]
Sea mammals reduce heat loss with blubber: a Weddell seal of 400–600 kg can carry up to 240 kg of it.[6]
Try it: Modelling body size and cooling
You need
- Three beakers of different sizes (e.g. 100 ml, 250 ml and 600 ml), same glass type
- Hot water at about 50–55 °C (prepared by the teacher)
- Three thermometers or temperature probes with data logger
- Measuring cylinder, ruler, stopwatch
- Heat-proof mat
Safety
Only the teacher pours the hot water; keep it below 55 °C. Stand beakers on a heat-proof mat away from the bench edge. Report breakages; do not pick up broken glass by hand.
What to do
- Fill each beaker to the same fraction of its height with water at about 50 °C, measuring the volume of water in each.
- Estimate the surface area of water and glass in contact with the air and bench for each beaker (treat it as a cylinder: 2πrh + πr² for sides and base, plus πr² for the top), and calculate SA : V.
- Start all three readings together. Record the temperature of each every minute for 15 minutes, stirring gently before each reading.
- Calculate the mean cooling rate (°C per minute) for each beaker over the first 10 minutes.
- Plot cooling rate against SA : V. Describe the pattern.
- Repeat with one beaker wrapped in cotton wool or fleece as a model of fur or blubber, and compare.
What happens, and why?
Heat is lost through the surface, but the heat stored depends on the volume. The smallest beaker has the largest SA : V ratio, so it cools fastest, like a small mammal that must burn more energy per kilogram to stay warm. The insulated beaker cools more slowly, as hair and blubber slow heat loss. Different starting temperatures, evaporation from the open top and the glass itself all add uncertainty.[7][1][6]
Play: Heat in, heat out or mammal feature?
Does it mainly keep heat in, make an animal lose heat faster, or is it a defining mammal feature not about heat?
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Other ages: Ages 6–7 · Ages 10–11