forms of energy - uta · forms of energy • energy ... • kinetic energy: associated with the...
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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
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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
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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.
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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.
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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
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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)
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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.
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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!
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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.
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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
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Convection Examples
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Rayleigh-Bernard Convection
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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 !
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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
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Cartoon of Earth’s Interior
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From: "Dynamic models of Tectonic Plates and Convection" (1994) by S. Zhong and M. Gurnis
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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
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Rates of Heat Production and Half-lives
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Heat Production through Earth History
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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
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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