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Igneous and Metamorphic Petrology: Overview of Fundamental Concepts. What role is played by energy in its various forms to create magmatic and metamorphic rocks? What is the source of internal thermal energy in the Earth? How does this drive rock-forming processes?
obvious from space that Earth has two fundamentally different
physiographic features: oceans (71%) and continents (29%)
work = Force x distance
Example: Pressure-Volume work in volcanic systems.
Pressure = Force/Area; Volume=Area x distance;
PV =( F/A)(A*d) = F*d = w
where g = acceleration of gravity at the surface (9.8 m/s2) and Z is the elevation measured from some reference datum
An increment of heat, Dq, transferred into a body produces a
proportional incremental rise in temperature, DT, given by
Dq = Cp * DT
where Cp is called the molar heat capacity of J/mol-degree
at constant pressure; similar to specific heat, which is based
on 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.
Thermal Gradient=DT between
adjacent hotter and cooler masses
Heat Flux = rate at which heat is
conducted over time from a unit
Thermal Conductivity = K; rocks
have very low values and thus
deep heat has been retained!
Heat Flux = Thermal Conductivity * DT
Thermal conductivity is a property of materials that expresses the heat flux f (W/m2) that will flow through the material if a certain temperature gradient T (K/m) exists over the material.
The thermal conductivity is usually expressed in W/m.K. and called l. The usual formula is:
f = l * T
It should be noted that thermal conductivity is a property that is describes the semi static situation; the temperature gradient is assumed to be constant. As soon as the temperature starts changing, other parameters enter the equation.
In case of changing thermal parameters, also the heat capacity C (J/K.m3) starts playing a role. The heat capacity is again a material property. It expresses the fact that for changing the temperature T (K) of a certain volume V (m3) of material energy E (J) must flow in or out. The heat capacity is usually linked to the density (kg/m3) of the material. The heat capacity is usually found in the textbooks a specific heat capacity Cp (J/K.kg), which must be multiplied by the density to get the full picture.
C = * Cp
When dynamic processes are involved, the change of temperature versus time, at known boundary conditions is determined by both thermal conductivity and heat capacity.
a = l / * Cp , where l is the thermal conductivity.
The thermal diffusivity a ( m2/s) is always encountered in the equations multiplied by the time t (s).
convection in the mantle
observed heat flow
warm: near ridges
cold: over cratons
Average Heat Flux is
Geothermal gradient = DT/ Dz
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 !
Approximate Pressure (GPa=10 kbar)
blue is high velocity (fast)
…interpreted as slab
note continuity of blue slab
to depths on order of 670 km
all from: http://www.geo.lsa.umich.edu/~crlb/COURSES/270
Force = mass * acceleration = kg*(m/s2) = kg m s-2 = N
Pressure = Force / Area
P = F/A = (m*g)/A and r (density) =mass/volume (kg/m3)
P (in Pa) = (kg * m/s2)/m2 = kg/m1s2 = kg m-1 s-2 = Nm-2
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