1. Physics of Earth's Evolution However the Earth came to its presently differentiated form, it must have obeyed our known physics: Conservation of energy and momentum The laws of thermodynamics The laws governing electromagnetism EPSC 666 November 4, 2009... Olivia

2. Energetics About 4.6 billion years ago, the primordial Earth condensed from a cloud of planetesimals with a composition not unlike that of the chondritic meteorites we find that have fallen to Earth. The gravitational potential energy available in this collapse could have brought the mass of Earth to a temperature exceeding 30000K –- a plasma primordial Earth?

3. Early Earth Early Earth surely didn't exist in a gravity- bound plasma state; internal temperature was probably pretty much as it is today – perhaps a little cooler, perhaps a little hotter. 26 Al  26 Mg (t ½ ~ 700k years;  1000K) The “Big Splat” (deep magma ocean) U, Th, K (long-lived; current sources)

4. Heat budget Losses: 1.Measured global cooling rate: ~30TW → 44TW* and probably higher during the ancient past. 2. Geomagnetic field loss (external): ~1 → 4TW Sources: 1. Radioactive decay: crust (6 → 9TW), upper mantle (12 → 21TW), lower mantle (3 → 14TW) 2. Entropy increase in mantle: (~3TW) 3. From core into mantle: ( > 8.6TW + ~1 → 2TW) 4. Remnant primordial gravitational energy: (~9 → 14TW) * In 2008, average rate of human energy consumption – all forms: 15 → 16TW New Theory of the Earth, Anderson, D.L, 2007, Cambridge

5. Earth model and T Mao, H-K and Hemley, R, 2007 www.pnas.orgcgidoi10.1073pnas.0703653104

6. Modes of cooling Inner core: conduction cooling, freezing surface (an interior source 40 K?) Outer core: very vigorous convection D'' layer (lowermost mantle): conduction Lower mantle ( > 660km depth): vigorous convection Upper mantle ( < 660km): convection Lithosphere ( upper 0 – 200km): conduction

7. Convection Convection continues to differentiate, to reorganize the Earth's mantle. Requirements for convection: Locally, the temperature gradient, dT(z)/dz, must exceed the adiabatic gradient: dT(z)/dz > g α P T / C P The observed “vigour” of mantle convection suggests that the adiabatic gradient must be “substantially” exceeded: The Rayleigh number, Ra, the ratio of bouyant to viscous forces: Ra ~ 10 6

8. Temperature Mao, H-K and Hemley, R, 2007 www.pnas.orgcgidoi10.1073pnas.0703653104

9. PREM Dziewonski and Anderson (1981)