Test Exam SOLUTIONS
Introduction to Earth System Science
(Part: R. Malservisi, Solid Earth Part)
December 13, 2007 [8:15-10:00]
Question 1: Gravitational attraction and secular cooling of the planet are the
2 principal sources of energy for the solid part of the Earth system, describe at
least two sources of heat.
Radioactive elements;
Primordial Heat (the heat accumulated by the gravitational collapse and
collisions during the planet formation;
Latent heat for the solidification of the internal core
The solar radiation is a wrong answer! We have seen that it would
influence only the top few cm to m depending on the temporal scale we
are looking at! The only importance of the solar radiation on solid Earth
behavior is in the climate control and hydrological cycle since these can
affect the erosion rate and weathering. As we said in class the interface
between atmosphere and solid Earth can play an important roleon
shaping the outer part of the solid planet but only in this way the solar
radiation is important!
Question 2: Describe 3 methods of heat transport. Which methods are
relevant for the solid part of the Earth system?
Radiation, Conduction, Advectionand Convection
Radiation transfer heat through electromagnetic waves (so does not need a
medium)
Conduction is mainly active in solids and is transfer of heat through contact of
molecules or atoms that exchange their vibrations.
Advection transfer of heat through the motion of heated material
Convection a special case of advection (thus transfer of heat through the
movement of heated material) but due to changes in density of the material
due to the different temperature. It happen only in fluids (both liquids and
gases)
Conduction is going on too in fluids but if the velocity of the motion is slow
compared to the velocity of diffusion it will play an important role (in general
for high viscous fluid this can be the case)
Also the solids can have fluid like behaviour and for long time scale can flow
(the example I did for the glass of a church or the bench in marble). In
particular the mantle on geological time scale is flowing (even if it is solid, s
waves can travel along the mantle).
So for Solid Earth are important both conduction and convection (the second
probably more important than the first). In case of erosion or faulting we have
also movement of material not due to density changes so advection is
important too.
Question 3: What is heat advection? Make an every day life example. Make
an example of advection in the solid Earth system.
See above.
Esample in every day life putting ice in a cooler, bringing a bottle of hot water
in a cold bed to warm it up
Examples for solid Earth, erosion and sedimentation in a basin, normal and
thrust faulting, dike ingection
Question 4: Equation (1) describes the heat conduction in a solid.
T
2T
A
(1)
 2 
t
t
c p
Write the equation for the steady state case



WELL SORRY FOR THE TYPO!!! Almost everyone found it the correct
equation is
T
2T
A
 2 
t
z
c p
T
Steady state means that there is not change with time so
 0 this leave the
t
2T
A
correct equation to be: 0   2 
In the case of (1) it would be
z
c p
2T
A
T

0  2 
but if
0
t
c p
t
so it must be without heat generation
 2 T
A
must be
0
0
t2
c p
But it is not correct, my fault!
Write the equation in the case the heat generation is equal to 0 and describe it
by words.
Heat generation =0 means A=0 so the equation became:
case of the wrong equation 1:
T
2T
  2 (2) or in
t
z
T
2T
  2 (3)
t
t


Equation 2 can be described
as a Spatial 1-D equation for which the rate of
change of the quantity T with the time is proportional to a constant call
diffusivity and to the curvature (second derivaty) of the field of T in the space.
This means that biggest is the change of the gradient of T respect to the
space variable z faster the quantity T will change. It make sense if you think to
a diffusion process biggest is the gradient of the concentration faster the
concentration will change.
Question 5: How is equation 1 called in case of no heat generation? Which
processes can it describe? Make at least 2 examples of applicability of the
equation.
(3) does not have a specific name (it is even not a partial differential
equations!
(2) is called diffusion equation and describe any phenomena related to
diffusion as chemical diffusion, diffusion of a pollutant, thermal diffusion, scarp
erosion processes…
Question 6: Describe the difference between relative and absolute dating and
make 2 examples.
Relative dating does not give as a number for the date, only if something is
younger or older than the other.
Absolute dating I assign to the date a number of time before present.
If everyday when I go home I put my used bus ticket in a box. Every time I put
it above the tickets that are already on the box. Without to look at the date
printed on the ticket I know that the ticket at the bottom is older than the ticket
at the top but I do not know how much older RELATIVE dating.
But If I look at the date printed on the ticket at the bottom I can tell when I
started to do this game ABSOLUTE DATING
For geology relative dating is in general related to stratigraphy (deeper strata
are older) while absolute dating with some quantitative method as radioactive
decay or counting tree rings or corals ring, snow layer etc…
Question 7: The following table gives the half-life of some of the isotopes
used in geological darting.
Parent
Daughter
t1/2
238U
206Pb
232Th
208Pb
87Rb
87Sr
40K
40Ar
235U
207Pb
4.47 b.y
14 b.y
48 b.y
1.28 b.y
707 m.y
14C
14N
5,730 y
Useful
Range
>10 million
years
>10,000
years
100 - 70,000
years
Type of Material
Igneous &
sometimes
metamorphic rocks
and minerals
Organic Material
Why cannot the C14 be used to date very old rocks?
The half life of C14 is too short to date anything older than ~70000yr
The heat generated within the Earth in the early stages after its formation was
dominated by the decay of potassium (K) isotope while it is currently
dominated by the decay of Uranium (U) isotope. Can you explain why?
The half life of K is much shorther so even if at the beginning I had more K
than U now the majority of K is consumed.
Extra question, answer only if you have time!
The Earth system must be studied on temporal and spatial scales that cover
different order of magnitude. Explain the max spatial and temporal scale.
Make the example of 2 processes: one that must be studied on a long
temporal scale and one that must be studied on a short temporal scale.
Quantify the typical time scale you must usefor those 2 processes in seconds.
The largest spatial scale we can study on the planet Earth is on the full
planetary scale thus ~20000 km
The max temporal scale is related to the age of the planet ~4.5 bilion years
So a process like differentiation tht started at the beginning and is still going
on is a long temporal scale process
Geological processes like mountain formations can also be considered long
(order of 10-100 Milion years)
A short time process can be an earthquake or a landslide (from few seconds
to few minutes)
To quantify the number in second I need to know how many seconds there
are in a day (86400) or in a year (~31000000)
So the age of the Earth in seconds will be:
4.5 109 yr x 3.1 107 ~ 12 1016s so of the order of 1017s