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

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 * velocity2

•  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/s2) and Z is the elevation measured from some reference datum

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.

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 = 4.184 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.

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

Vpillow= 4/3r3 ~ 4 (100 cm/m)3 ~ 4 x 106 cm3 If the density of basalt is 3 g/cm3, then the mass is ~12 x 106 g; consider Vwater ~ 4 x 109 cm3 (10 times the radius of pillow) #

qwater = qrock = Cp T

(4 x 109 g * 1.0 cal/g/°C) * (Tfinal - 0°C) = (12 x 106 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!

Quick Example: MORB eruption at ridge crest depth

MORB pillow

Sea Water

0

200

400

600

800

1000

1200

1.0 1.5 2.1 3.1 4.6 6.7 9.8 14.4 21.1 30.9 45.3 66.3 97.0

dT (°

C) S

ea W

ater

Radial Distance (m)

T (°C) Sea Water - MORB Pillow (1 m radius)

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

10.0

5.0 6.0 7.0 8.0 9.0 10.0 dT

(°C

) Sea

Wat

er

Radial Distance (m)

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.

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

Heat Flux = Thermal Conductivity * T

Thermal Conductivity = K; rocks have very low values and thus deep heat has been retained!

Heat Flux by Conduction

Where K is the thermal conductivity, t is time, d is the distance between Thot and Tcold, and A is the cross-

sectional area.

convection in the mantle

models

observed heat flow warm: near ridges cold: over cratons

from: http://www.geo.lsa.umich.edu/~crlb/COURSES/270

from: http://www-personal.umich.edu/~vdpluijm/gs205.html

Convection Examples

Rayleigh-Bernard Convection

Earth’s Geothermal Gradient A

ppro

xim

ate

Pres

sure

(GPa

=10

kbar

)

Average Heat Flux is 0.09 watt/meter2

Solar Heat flux is 1370 W/m2 Geothermal gradient = T/ z

20-30°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 1018 times tar at 24°C !

note continuity of blue slab to depths on order of 670 km

blue is high velocity (fast) …interpreted as slab

from: http://www.pmel.noaa.gov/vents/coax/coax.html

examples from western Pacific

Cartoon of Earth’s Interior

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

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: 238U, 235U, 232Th, 40K, and 87Rb all have t1/2 that >109 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 26Al 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

Rates of Heat Production and Half-lives

Heat Production through Earth History

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) = 105 Pa

Force = mass * acceleration = kg*(m/s2) = kg m s-2 = N

Pressure = Force / Area

P = F/A = (m*g)/A and (density) = mass/volume (kg/m3)

P (in Pa) = (kg * m/s2)/m2 = kg/m1s2 = kg m-1 s-2 = Nm-2

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/cm3 (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