Forms of Energy. Energy: commonly defined as the capacity to do work (i.e. by system on its surroundings); comes in many forms

Transcription

1 Forms of Energy Energy: commonly defined as the capacity to do work (i.e. by system on its surroundings); comes in many forms Work: defined as the product of a force (F) times times a displacement acting over a distance (d) in the direction parallel to the force work = force * distance Example: Pressure-Volume work in volcanic systems. Pressure = Force/Area; Volume=Area x distance; PV =( F/A)(A*d) = F*d = w

2 Forms of Energy Kinetic energy: associated with the motion of a body; a body with mass (m) moving with velocity (v) has kinetic energy» E (k) = 1/2 mass * velocity 2 Potential energy: energy of position; is considered potential in the sense that it can be converted or transformed into kinetic energy. Can be equated with the amount of work required to move a body from one position to another within a potential field (e.g. Earth s gravitational field).» E (p) = mass * g * Z where g = acceleration of gravity at the surface (9.8 m/s 2 ) and Z is the elevation measured from some reference datum

3 Forms of Energy (con t.) Chemical energy: energy bound up within chemical bonds; can be released through chemical reactions Thermal energy: related to the kinetic energy of the atomic particles within a body (solid, liquid, or gas). Motion of particles increases with higher temperature. Heat is transferred thermal energy that results because of a difference in temperature between bodies. Heat flows from higher T to lower T and will always result in the temperatures becoming equal at equilibrium.

4 Heat Flow on Earth An increment of heat, q, transferred into a body produces a proportional incremental rise in temperature, T, given by q = Cp * T where Cp is called the molar heat capacity of J/mol-degree at constant pressure; similar to specific heat, which is basedon mass (J/g-degree). 1 calorie = J and is equivalent to the energy necessary to raise 1 gram of of water 1 degree centigrade. Specific heat of water is 1 cal /g C, where rocks are ~0.3 cal / g C.

5 Quick Example: MORB eruption at ridge crest depth MORB pillow Sea Water MORB pillow is 1 m in radius Assume that eruption T is 1180 C WATER is 10 m in radius Assume that ocean T is ~0 C Assume spherical volumes for both Calculate the temperature rise in the ocean for fixed volumes using specific heats from previous slide V pillow = 4/3 r 3 ~ 4 (100 cm/m) 3 ~ 4 x 10 6 cm 3 If the density of basalt is 3 g/cm 3, then the mass is ~12 x 10 6 g; consider V water ~ 4 x 10 9 cm 3 (10 times the radius of pillow) # q water = q rock = C p T (4 x 10 9 g * 1.0 cal/g/ C) * (T final - 0 C) = (12 x 10 6 g * 0.3 cal/g/ C) * (1180 C - 0 C) yields ~1 C increase in temperature of the surrounding water volume at a distance of 10 m from the pillow!

6 T ( C) Sea Water - MORB Pillow (1 m radius) dt ( C) Sea Water dt ( C) Sea Water Radial Distance (m) Radial Distance (m)

7 Heat Transfer Mechanisms Radiation: involves emission of EM energy from the surface of hot body into the transparent cooler surroundings. Not important in cool rocks, but increasingly important at T s >1200 C Advection: involves flow of a liquid through openings in a rock whose T is different from the fluid (mass flux). Important near Earth s surface due to fractured nature of crust. Conduction: transfer of kinetic energy by atomic vibration. Cannot occur in a vacuum. For a given volume, heat is conducted away faster if the enclosing surface area is larger. Convection: movement of material having contrasting T s from one place to another. T differences give rise to density differences. In a gravitational field, higher density (generally colder) materials sink.

8 Magmatic Examples of Heat Transfer Thermal Gradient = T between adjacent hotter and cooler masses Heat Flux = rate at which heat is conducted over time from a unit surface area Thermal Conductivity = K; rocks have very low values and thus deep heat has been retained! Heat Flux = Thermal Conductivity * T

9 Heat Flux by Conduction Where K is the thermal conductivity, t is time, d is the distance between T hot and T cold, and A is the crosssectional area.

10 from: models convection in the mantle observed heat flow warm: near ridges cold: over cratons from:

11 Convection Examples

12

13 Rayleigh-Bernard Convection

14 Earth s Geothermal Gradient Approximate Pressure (GPa=10 kbar) Average Heat Flux is 0.09 watt/meter 2 Solar Heat flux is 1370 W/m 2 Geothermal gradient = / z C/km in orogenic belts; Cannot remain constant w/depth. At 200 km, would be 4000 C! ~7 C/km in trenches Viscosity, which measures resistance to flow, of mantle rocks is times tar at 24 C!

15 examples from western Pacific blue is high velocity (fast) interpreted as slab note continuity of blue slab to depths on order of 670 km from:

16 Cartoon of Earth s Interior

17 From: "Dynamic models of Tectonic Plates and Convection" (1994) by S. Zhong and M. Gurnis

18 Earth s Energy Budget Solar radiation: 50,000 times greater than all other energy sources; primarily affects the atmosphere and oceans, but can cause changes in the solid earth through momentum transfer from the outer fluid envelope to the interior Radioactive decay: 238 U, 235 U, 232 Th, 40 K, and 87 Rb all have t 1/2 that >10 9 years and thus continue to produce significant heat in the interior; this may equal 50 to 100% of the total heat production for the Earth. Extinct short-lived radioactive elements such as 26 Al were important during the very early Earth. Tidal Heating: Earth-Sun-Moon interaction; much smaller than radioactive decay Primordial Heat: Also known as accretionary heat; conversion of kinetic energy of accumulating planetismals to heat. Core Formation: Initial heating from short-lived radioisotopes and accretionary heat caused widespread interior melting (Magma Ocean) and additional heat was released when Fe sank toward the center and formed the core

19 Rates of Heat Production and Half-lives

20 Heat Production through Earth History

21 Gravity, Pressure, and the Geobaric Gradient Geobaric gradient defined similarly to geothermal gradient: P/ ; in the interior this is related to the overburden of the overlying rocks and is referred to as lithostatic pressure gradient. SI unit of force is the Newton SI unit of pressure is the Pascal, Pa and 1 bar (~1 atmosphere) = 10 5 Pa Force = mass * acceleration = kg*(m/s 2 ) = kg m s -2 = N Pressure = Force / Area P = F/A = (m*g)/a and (density) = mass/volume (kg/m 3 ) P (in Pa) = (kg * m/s 2 )/m 2 = kg/m 1 s 2 = kg m -1 s -2 = Nm -2

22 Earth Interior Pressures P = Vg/A = gz, if we integrate from the surface to some depth z and take positive downward we get P/ z = g Rock densities range from 2.7 (crust) to 3.3 g/cm 3 (mantle) 270 bar/km for the crust and 330 bar/km for the mantle At the base of the crust, say at 30 km depth, the lithostatic pressure would be 8100 bars = 8.1 kbar = 0.81 GPa