where g is the acceleration due to gravity, p is the fluid density, a is the thermal ex- pansion coefficient, AT is the temperature difference across the fluid layer, d is the thickness of the layer, n is the viscosity, and k is the thermal diffusivity. (a) Show that the Rayleigh number is dimensionless! (b) Broadly speaking, the Earth's mantle is divided into two parts, the upper mantle, from the surface (ignoring the crust for the moment) to a depth of 670 km; and the lower mantle, from a depth of 670 km to 2900 km. All else equal, would the mantle be more likely to convect as two separate layers (upper and lower mantle), or as one layer? Why?

where g is the acceleration due to gravity, p is the fluid density, a is the thermal ex- pansion coefficient, AT is the temperature difference across the fluid layer, d is the thickness of the layer, n is the viscosity, and k is the thermal diffusivity. (a) Show that the Rayleigh number is dimensionless! (b) Broadly speaking, the Earth's mantle is divided into two parts, the upper mantle, from the surface (ignoring the crust for the moment) to a depth of 670 km; and the lower mantle, from a depth of 670 km to 2900 km. All else equal, would the mantle be more likely to convect as two separate layers (upper and lower mantle), or as one layer? Why?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

(e) The Sun has a surface temperature of 5770 K, a radius of 6.96 × 10° km, an average distance from Earth of 1.496 x ix 10* km, and radiates e/m radiation into space isotropically. Earth is a sphere with a radius of 6378 km, and on average absorbs 30 percent of the sunlight that shines on it, with the rest reflected back into space. Both the Sun and Earth are opaque to e/m radiation of all wavelengths, so intensity I = oT“, where o is the Stefan-Boltzmann constant and T is Kelvin temperature. Calculate the temperature (in Kelvins) of Earth.
In Joule's experiment, if a 10.0 kg mass falls a distance of 1.0 m, and the paddle is immersed in a 0.5L beaker of mercury, what is the rise in temperature of the mercury, given that its mass density is 13.5 g/cm and its specific heat capacity is 138 J/(kg C)?
The next four questions use this description. Our Sun has a peak emission wavelength of about 500 nm and a radius of about 700,000 km. Your dark-adapted eye has a pupil diameter of about 7 mm and can detect light intensity down to about 1.5 x 10-11 W/m2. Assume the emissivity of the Sun is equal to 1. First, given these numbers, what is the surface temperature of the Sun in Kelvin to 3 significant digits? What is the power output of the Sun in moles of watts? (in other words, take the number of watts and divide it by Avogadro's number) Assuming that all of the Sun's power is given off as 500 nm photons*, how many photons are given off by the Sun every second? Report your answer to the nearest power of 10 (e.g. if you got 7 x 1024, give your answer as 25).
A cylindrical surface of radius 15 cm and length 0.8 m maintained at a temperature of 140°C is continuously emitting radiations. If the emissivity of the surface is 0.93. (consider: Stefan's constant σ = 5.67 x 10-8 W/m2T4) Calculate the rate of heat energy radiated in Watts =
Show that the surface temperature, T, of a rotating spherical body at a distance R from the Sun falls as the inverse square root of R. Knowing that a spacecraft in Earth orbit prior to orbital insertion towards the Sun reached a stable temperature of 260K, find the constant of proportionality in the relationship between R and T, where T is in kelvin 3. and R is in astronomical units.
Needs Complete typed solution with 100 % accuracy.
type answer
The goal in this problem is to find the growth of an ice layer as a function of time. Call the thickness of the ice layer L. (a) Derive an equation for dL/dt in terms of L , the temperature T above the ice, and the propertiesof ice (which you can leave in symbolic form instead of substituting the numbers). (b) Solve this differential equation assuming that at t = 0 , you have L = 0. If you have studied differential equations, you will know atechnique for solving equations of this type: manipulate the equation to get dL/dt multiplied by a (very simple) function of L on one side, and integrate both sides with respect to time. Alternatively, you may be able to use your knowledge of the derivatives of various functions to guess the solution, which has a simple dependence on t. (c) Will the water eventually freeze to the bottom of the flask?
100 Mll, N 8.6.E (a) Calculate the equilibrium temperature of a meteoroid of mass M, density p, and albedo A in the vicinity of the Earth. (b) Evaluate your result for a chondrite with M = 10° g, p = 2.5 g cm-3, and albedo A = 0.05 and for an achondrite with M = 10° g, p = 3 g cm and albedo A = 0.3. -3
1. (1) Use the Maxwell speed distribution function F(v) for an ideal-gas particle to derive the most probable speed v*, average speed u = (v), root-mean-square speed vyms = V(u2) = 3K5", where mis the mass of the ideal-gas particle, kg is the Boltzmann m constant, and T is the temperature. (1I) prove that Vrms >i >v*. (III) Rewrite the Maxwell speed distribution function F(v) as a function related to and v*, i.e., F (, v*). How much percentage do ideal-gas particles distribute at v*±(0.5% v*), v±(0.5% v*), and vms±(0.5% v*), respectively? (IV) Use the Maxwell velocity distribution function f (T) to determine the average velocity of the ideal gas (ī).
An explorer is standing in a cave. It emits a sound which echoes back to it 20 s later. If it is 5 ° C, determine the depth of the cave.
The tube shown has a uniform wall thickness of 12 mm. Take P= 18 kN. F H E 28 KN P 28 KN 125 mm 75 mm Determine the point where the neutral axis intersects line AB. The point where the neutral axis intersects line AB is mm above point A.