Surface/Volume: How Geometry Explains Why Grain Elevators Explode, Hummingbirds Hover, and Asteroids are Colder than Ice

Description

This book explains that diffusion, osmosis, dissolution, evaporation, and heat loss all preferentially affect small bodies due to their high surface/volume ratios. Because surface area increases as the square of length, but volume (and mass) increase as the cube, large objects have low surface/volume ratios and small objects have high surface/volume ratios. This simple physical constraint governs much of the physical world. It accounts for why the Earth has active volcanoes, but the Moon does not, why the human brain has numerous folds, why deciduous trees lose their leaves every Fall, and why nanoparticles of gold melt at surprisingly low temperatures. It is a phenomenon well known to every scientist, but this book is the first comprehensive treatment of this effect. Introduction Other Books by Alan E. Rubin Contents 1 A Truncated History of Geometry References 2 Middle-School Math 2.1 Geometric Forms 2.2 Plane and Solid Geometry 2.2.1 Squares and Cubes 2.2.2 Circles and Spheres 2.3 The Ratio of Surface Area to Volume Reference 3 Asteroids, Moons, Planets, and Meteorites 3.1 Inventory of the Solar System 3.2 Surface/Volume Effects in the Inner Solar System 3.3 Meteorite Strewn Fields 3.4 Chondrules 3.5 Aqueous Alteration of Chondritic Meteorites 3.6 Cosmic Spherules References 4 Geologic Processes 4.1 Extrusive and Intrusive Igneous Rocks 4.2 Permeability of Sandstones 4.3 Erosion and Weathering References 5 Geometry of Life 5.1 Metabolism 5.2 The Surface/Volume Ratios of Mammals and Birds 5.3 Muscles and Wings 5.4 Formidable Formicidae or the Mighty Ant 5.5 Biological Rules of Thumb 5.5.1 Bergmann’s Rule 5.5.2 Allen’s Rule 5.5.3 Hesse’s Rule 5.6 Gigantothermy 5.7 The Impossibility of King Kong (But Not Dinosaurs) 5.8 Thermoregulation of Insects 5.9 The Risk of Animal Dehydration 5.10 Krill 5.11 Sponges 5.12 Leaves and Trees 5.12.1 Leaves 5.12.2 Deciduous Trees 5.13 Human Anatomy 5.13.1 The Brain 5.13.2 The Respiratory Tract 5.13.3 The Gastrointestinal Tract 5.14 Human Anatomical and Behavioral Responses to Extreme Temperatures 5.15 Frostbite 5.16 Bacteria 5.17 Oxygen Diffusion Through Red Blood Cells References 6 Biochemistry 6.1 Protein Folding 6.2 A Summing Up References 7 Chemical Reactions 7.1 Elementary Chemistry 7.2 Chemical Properties of Water 7.3 Dissolution 7.4 The Effort to Reduce Sodium in Food 7.5 Sugar and Candy Making 7.6 Evaporation 7.7 Osmosis 7.8 Grain Elevators References 8 Ecology 8.1 Wildfires 8.2 Coral Reefs References 9 Manufacturing 9.1 Artificial Bones 9.2 Artificial Lungs 9.3 Aerogel and Stardust 9.4 Giant Telescope Mirrors 9.5 Nanoparticles References Epilogue Index