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Test Exam SOLUTIONS Introduction to Earth System Science (Part: R. Malservisi, Solid Earth Part) December 13, 2007 [8:15-10:00] Question 1: Gravitational attraction and secular cooling of the planet are the 2 principal sources of energy for the solid part of the Earth system, describe at least two sources of heat. Radioactive elements; Primordial Heat (the heat accumulated by the gravitational collapse and collisions during the planet formation; Latent heat for the solidification of the internal core The solar radiation is a wrong answer! We have seen that it would influence only the top few cm to m depending on the temporal scale we are looking at! The only importance of the solar radiation on solid Earth behavior is in the climate control and hydrological cycle since these can affect the erosion rate and weathering. As we said in class the interface between atmosphere and solid Earth can play an important roleon shaping the outer part of the solid planet but only in this way the solar radiation is important! Question 2: Describe 3 methods of heat transport. Which methods are relevant for the solid part of the Earth system? Radiation, Conduction, Advectionand Convection Radiation transfer heat through electromagnetic waves (so does not need a medium) Conduction is mainly active in solids and is transfer of heat through contact of molecules or atoms that exchange their vibrations. Advection transfer of heat through the motion of heated material Convection a special case of advection (thus transfer of heat through the movement of heated material) but due to changes in density of the material due to the different temperature. It happen only in fluids (both liquids and gases) Conduction is going on too in fluids but if the velocity of the motion is slow compared to the velocity of diffusion it will play an important role (in general for high viscous fluid this can be the case) Also the solids can have fluid like behaviour and for long time scale can flow (the example I did for the glass of a church or the bench in marble). In particular the mantle on geological time scale is flowing (even if it is solid, s waves can travel along the mantle). So for Solid Earth are important both conduction and convection (the second probably more important than the first). In case of erosion or faulting we have also movement of material not due to density changes so advection is important too. Question 3: What is heat advection? Make an every day life example. Make an example of advection in the solid Earth system. See above. Esample in every day life putting ice in a cooler, bringing a bottle of hot water in a cold bed to warm it up Examples for solid Earth, erosion and sedimentation in a basin, normal and thrust faulting, dike ingection Question 4: Equation (1) describes the heat conduction in a solid. T 2T A (1) 2 t t c p Write the equation for the steady state case WELL SORRY FOR THE TYPO!!! Almost everyone found it the correct equation is T 2T A 2 t z c p T Steady state means that there is not change with time so 0 this leave the t 2T A correct equation to be: 0 2 In the case of (1) it would be z c p 2T A T 0 2 but if 0 t c p t so it must be without heat generation 2 T A must be 0 0 t2 c p But it is not correct, my fault! Write the equation in the case the heat generation is equal to 0 and describe it by words. Heat generation =0 means A=0 so the equation became: case of the wrong equation 1: T 2T 2 (2) or in t z T 2T 2 (3) t t Equation 2 can be described as a Spatial 1-D equation for which the rate of change of the quantity T with the time is proportional to a constant call diffusivity and to the curvature (second derivaty) of the field of T in the space. This means that biggest is the change of the gradient of T respect to the space variable z faster the quantity T will change. It make sense if you think to a diffusion process biggest is the gradient of the concentration faster the concentration will change. Question 5: How is equation 1 called in case of no heat generation? Which processes can it describe? Make at least 2 examples of applicability of the equation. (3) does not have a specific name (it is even not a partial differential equations! (2) is called diffusion equation and describe any phenomena related to diffusion as chemical diffusion, diffusion of a pollutant, thermal diffusion, scarp erosion processes… Question 6: Describe the difference between relative and absolute dating and make 2 examples. Relative dating does not give as a number for the date, only if something is younger or older than the other. Absolute dating I assign to the date a number of time before present. If everyday when I go home I put my used bus ticket in a box. Every time I put it above the tickets that are already on the box. Without to look at the date printed on the ticket I know that the ticket at the bottom is older than the ticket at the top but I do not know how much older RELATIVE dating. But If I look at the date printed on the ticket at the bottom I can tell when I started to do this game ABSOLUTE DATING For geology relative dating is in general related to stratigraphy (deeper strata are older) while absolute dating with some quantitative method as radioactive decay or counting tree rings or corals ring, snow layer etc… Question 7: The following table gives the half-life of some of the isotopes used in geological darting. Parent Daughter t1/2 238U 206Pb 232Th 208Pb 87Rb 87Sr 40K 40Ar 235U 207Pb 4.47 b.y 14 b.y 48 b.y 1.28 b.y 707 m.y 14C 14N 5,730 y Useful Range >10 million years >10,000 years 100 - 70,000 years Type of Material Igneous & sometimes metamorphic rocks and minerals Organic Material Why cannot the C14 be used to date very old rocks? The half life of C14 is too short to date anything older than ~70000yr The heat generated within the Earth in the early stages after its formation was dominated by the decay of potassium (K) isotope while it is currently dominated by the decay of Uranium (U) isotope. Can you explain why? The half life of K is much shorther so even if at the beginning I had more K than U now the majority of K is consumed. Extra question, answer only if you have time! The Earth system must be studied on temporal and spatial scales that cover different order of magnitude. Explain the max spatial and temporal scale. Make the example of 2 processes: one that must be studied on a long temporal scale and one that must be studied on a short temporal scale. Quantify the typical time scale you must usefor those 2 processes in seconds. The largest spatial scale we can study on the planet Earth is on the full planetary scale thus ~20000 km The max temporal scale is related to the age of the planet ~4.5 bilion years So a process like differentiation tht started at the beginning and is still going on is a long temporal scale process Geological processes like mountain formations can also be considered long (order of 10-100 Milion years) A short time process can be an earthquake or a landslide (from few seconds to few minutes) To quantify the number in second I need to know how many seconds there are in a day (86400) or in a year (~31000000) So the age of the Earth in seconds will be: 4.5 109 yr x 3.1 107 ~ 12 1016s so of the order of 1017s