Chapter 18, Problem 36A

Animals lose heat through the surface areas of their skin. A small animal, such as a mouse, uses a much larger proportion of its energy to keep warm than does a large animal, such as an elephant. Why is the rate of heat loss per unit area greater in a small animal than a large one?

To determine

To Explain: The smaller animals lose more heat.

Explanation of Solution

Introduction:

Animals generally lose some amount of heat to keep themselves warm.

In case of smaller animals, the surface area to volume ratio is more as compared to the larger animals. So, smaller animal’s rate of heat loss per unit area is more than that of larger animals. Go down the scale, surface area to volume ratio increases.

For example:

A sphere of radius 10 cm and 0.1 cm

Area to volume ratio will be

  $\frac{\text{surface area}}{\text{voume}}\text{=}\frac{{\text{4πr}}^{\text{2}}}{\frac{\text{4}}{\text{3}}{\text{πr}}^{\text{3}}}\text{=}\frac{\text{3}}{\text{r}}$

For radius 10 cm, surface to volume ratio will be 0.3 m-1

and for radius 0.1 cm surface to volume ratio will be 30 m-1

From this example, one can conclude that as the scale decreases, the surface area to volume ratio increases.

Conclusion:

Smaller animals can lose more amount of heat due to its high surface area to volume ratio.