GEOL 212 Study Guide - Final Guide: Thermodynamics, Solid Nitrogen, Advection
26 Dec 2017
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Surface to volume ratio: size matters because surface area and volume scale up at different rates: surface area: a = 4 r2, volume: v = 4/3 r3. If we scale an object like a sphere up proportionally, its surface area scales to the 2/3 power of its volume. Thus: a sphere with a 1 km radius has a surface area of 12. 57 km2 and a volume of 4. 19 km3. It"s surface to volume ratio is 3 km-1. If we double the radius, we get a = 50. 27 km2, v = 33. 51 km3and a/v of 1. 5 km-1. Assuming that heat is distributed uniformly inside the volume, then the larger sphere should take twice as long to cool as the first. A/v ratio is 3. 55 times that of earth. No surprise, then that the moon is colder internally than earth. Indeed: global mean heat flow for the earth is 87 2 mw/m2, global mean heat flow for the moon is 22-31 mw/m2.
