Esci 2201 Exam 3 Study Guide L22/23

Know what happens to the volume of adiabatically rising/sinking mantle and how work done by the material and its internal energy vary

1. As material (an isolated system) rises, it expands due to reduced pressure. 2. Work is done by the material to expand (dW = PdV) 3. Work comes from internal energy (dU) of the material since no heat enters the system (adiabatic), and T decreases

Rayleigh-Bénard Convection cells have aspect ratios (L/D) =

1.1-15

asthenospheric mantle relaxation time

1000 years

Last glacial period

115,000-11,700 years ago

Clausius-Clapeyron Slope (dP/dT)

= Change in Entropy/ Change in Volume = L/ (Temp change in volume) The slope of a reaction in P-T space • It is related to entropy and volume changes associated with the reaction. (L = T dS) at a constant temperature dV with increasing P is negative; positive slope results when L is negative (release of latent heat; exothermic), and vise versa. Both quantities need to be negative for slope to be positive. (exothermic)

Glacial Isostatic Adjustment

= Elastic response of the lithosphere (instantaneous) followed by viscous response of the mantle (time delayed)

Stress Relaxation

A decrease in stress when the strain is held constant for a given period of time in a visco-elastic(maxwell) body.

Entropy

A measure of disorder • Determined by the amount of heat introduced to the system divided by temperature

Thermal convection in the solid mantle occurs because

Actual temperature gradient (geotherm) is larger than the adiabatic gradient - i.e., superadiabatic • Rayleigh number is large > Rac

Why is convection the dominant form of heat transfer in the asthenosphere

Because silicates are poor conductors, convection dominates heat transfer in the asthenosphere.

Maxwell Body

Both viscous and elastic.

What drives convection?

Convection arises because fluids expand and decrease in density when heated. • Mass motion is driven by internal buoyancy. • But viscous forces oppose fluid motion, so there is a competition between viscous and (thermal) buoyancy forces.

The D" (D double-prime) layer

Core-mantle boundary zone - Lower viscosity (lower seismic velocity) than overlying lower mantle - Variable thickness - Source of plumes

Viscosity decreases exponentially with T and

Increases exponentially with P

Decay (relaxation) of the deflection of the surface has what paramters.

Initial deflection exponential model of inverse relaxation time * time

Maxwell Body with constant strain

Instant stress increase with the elastic portion, then the viscous portion increases in strain. over time stress relaxes, spring part goes back to normal but the dashboard still retains some stress from deformation.

Maxwell Relaxation time

Larger viscosity means larger time. Meaning system stays elastic for much longer

Lithosphere has high viscosity and low E

Practically always elastic

superadiabatic

T gradient is greater than adiabatic (superadiabatic). Extra contraction and expansion lead to gravitational instability and convection, driving towards adiabat (i.e., reducing temperature difference ).

- the first law of thermodynamics.

The total energy of an isolated system is constant/conserved but there can be a change in internal energy, dU, if the energy is transferred as work

Postglacial rebound refers to vertical movements in response to melting and unloading.

Uplift rate of the ground and gravity anomaly

mantle convection cells

Whole mantle: 1.6 - 3.3 upper mantle: 6-14

Viscous deformation

constant yielding due to stress

For dQ (heat gain or loss) to be zero,

dS (entropy) is zero unless we are at absolute zero temperature!

Change in internal energy = difference between heat gained or lost (dQ) and the work done by the system (dW = PdV

dU=dQ - dW =dQ - PdV For adiabatic process/isolated system, dQ is zero.

thermal diffusion time =

d^2 / k

when seismic waves propagate through the mantle, it behaves mainly

elastically

convection only occurs if Ra is

greater than 1000

the mantle is viscous on a

long time scale

For vigorous convection

rise time must be <<< than diffusion time

the mantle is elastic on a

short time scale

Because of heating from the core, cooling at the surface, and radiogenic heat production, the mantle's temperature gradient is

super-adiabatic.

Geothermal gradient must be _______ for convection to occur.

super-adiabatic.

Rayleigh Number

td / tr = Ra The time scale of thermal diffusion relative to convection • Convection only occurs if Ra is greater than ~1000 (critical Rayleigh number, Rac; dependent on geometry and d) • Increase d, larger Ra (more unstable) à larger planet is more unstable à convection slide 4 for equation

• Be familiar with the parameters that the adiabatic temperature gradient depends on.

thermal expansion * temperature/ (density *heat capacity)

rise time of the mantle varies with mantle viscosity, the temperature difference, and the layer/mantle thickness.

tr = D/v = n /( pga (change in Temp) D )

For the mantle to convect it must be

viscous

Quaternary/Pleistocene Glaciation

• 2.58 Ma to present; the Ice Age by geologists • Alternating series of glacial and interglacial periods (currently interglacial)

adiabatic

• Heat does not enter or leave a system (no conductive heat transfer) • It involves a volume change (via compression or decompression) and therefore T change (change in internal energy)

The lithosphere's rigidity does not allow Rayleigh-Bénard convection

• It prevents the development of smaller cells with aspect ratio of 1- 1.5 under large/major plates. • It results in cells with smaller aspect ratio under small plates

Positive Clapeyron slope

• Slab is denser than ambient mantle (promote subduction) • Plume is less dense than ambient mantle (promote upwelling)

Negative Clapeyron slope

• Slows subduction and plume upwelling