On The Earth Considered As A Heat Engine

81 GEOPHYSICS. G. F. BECKER ON THE EARTH CONSIDERED AS A HEAT ENGINE By George F. Becker UNITED STATES GEOLOGICAL SURVEY, WASHINGTON Prented to the Academy. Decmber 4. 1914 Imagine that the earth solidified in such a way that fluid equilibrium were perfectly preserved and that the exterior were perfectly smooth,presenting an ideal equipotential surface of uniform temperature. Suppose that the only differences between different portions of this surface. were in the diffusivity (that there are large variations in the diffusivities of different rocks, the published determinations clearly show). For simplicity's sake, suppose that a certain square area had a uniformdiffusivity smaller than that of the surrounding surface. It is evident that this square would cool more slowly than the adjacent portions, and by reason of the slower escape of heat it would develop a slight relative elevation-provided indeed that the material of the globe contracted in cooling as almost all substances actually do. Furthermore, the relative contraction of the surrounding mass would bring to bear a pressure on all four sides of the square, and this pressure would extend downward as far as the difference of temperature was sensible. Such a pressure might even suffice to rupture the rock within the square. Indeed the order of magnitude of the difference in temperature needful to induce rupture is easily estimated. Let M be the Young's modulus of the rock composing the square, P the lateral pressure on any face and e the elongation. Then by definition Me = P or e = P/M. The crushing load for the best granite is about 1000 kilograms per square centimeter, and the average Young's modulus found by H. Nagaoka1 for 5 granites is 25 X 1010 dynes or 254800 kg. per square centimeter, only about half as great as that given by Everett for glass. This would indicate at the breaking point e 0.004, very nearly. N