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ExampleFinalQ-10 - Geology 351; Final Exam Review Example...

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Geology 351; Final Exam Review Example Questions Some calculus questions 9.8 Consider example problem 9.8 in the text (page 171). The basic relationship is 3 20 zkW Q km = . This tells you that heat is being generated at a certain rate per cubic kilometer. This rate varies with distance above the base of the crust (z). The crust in this example is assumed to be 30km thick. There are some typical questions that can be asked about Q. Q gives us an amount of power per unit volume. So we might ask what the amount of heat energy per unit time would be for a certain specified volume. Since the heat generation rate varies with z, this is not a simple Q times volume answer. One way is to add up a lot of little volumes. Each little volume generates a different amount of heat since it lies at a different depth. So the total heat generated over a certain interval would be 1 n i i qQ = z = Δ . Now, a question you could be asked is how to express this sum as an integral? The integral is identical to this sum in a sense, except that we let our little volume element shrink to 0. i) What would that integral be? ii) Express that integral in definite form where the integration takes place from a range of distances z 1 to z 2 above the base of the crust. iii) Then you would be expected to evaluate that integral. If we wanted to calculate the total heat generated by a column of crust extending from the base of the crust to the surface - what would that be? 9.9 Since the Earth is an oblate spheroid, accurate estimate of its volume should take this into account. The Earth is not a perfect sphere but is flattened at the poles by about 21 km. The distance from the Earth’s axis of rotation to the surface at varying positions from pole to pole, varies from 0 to r e
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ExampleFinalQ-10 - Geology 351; Final Exam Review Example...

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