Page 1
PTYS 214 – Spring2011
Homework #4 – Due Tuesday, Feb. 15
Class website: http://www.lpl.arizona.edu/undergrad/classes/spring2011/Pierazzo_214/
Useful Reading: class website “Reading Material” http://www.geology.sdsu.edu/how_volcanoes_work/Heat.html
http://csmres.jmu.edu/geollab/fichter/PlateTect/heathistory.htmlhttp://en.wikipedia.org/wiki/Radioactive_decay
Announcements
Page 2
Summary
Solar flux decreases as radiation spreads out away
from the Sun
Planets are exposed to some small amount of the total solar radiation
A very small portion of that radiation can be used by photo-(autotrophs/heterotrophs) (e.g. photosynthesis)
Other biota (chemo-) can eat energy-rich organic molecules from photo-autotrophs or each other
Page 3
Energy/food chain Photosynthesis
Respiration Solar Radiation
Page 4
Stellar spectrum and life
Photosynthesis requires visible radiation (0.4-0.7 microns)
Photosynthesis can be inhibited by UV radiation (UV-B)
Organisms have to protect themselves from UV but have to be able to absorb visible radiation at the same time
Page 5
Earthquakes
Volcanoes
Are there other sources of energy?
Page 6
Earth is geologically active
Earthquakes, volcanoes and the slow motion of the continents (plate tectonics) do not depend on the energyfrom the Sun
There should be an internal heat source!
Page 7
Heat Flow from Earth’s Interior
Heat coming from the Earth’s interior amounts to about 3.8×1013 W for an average heat flow of 0.075 W/m2
Page 8
Source of Energy in the Earth’s Interior
1. Radioactive decay (dominant)
2. Energy remaining from accretion
3. Energy released from Earth’s differentiation
Page 9
1. Radioactive decay
Process in which an unstable atomic nucleus loses energy in the form of particles or electromagnetic waves and transforms towards a more stable nucleus (also known as fission)
Unstable: nucleus has an unbalanced number of protons and neutrons
Stable: balanced number of protons and neutrons
Energy is released during radioactive decay
Page 10
Nuclides Atomic species characterized by the number of protons Z and
neutrons N in the nucleusSome nuclides are stable, others are not
Isotopes: Nuclides with the same atomic number (Z), but different mass number (A=Z+N)
Example: 12C – 13C – 14C 12C: 6 protons, 6 neutrons – Stable13C: 6 protons, 7 neutrons – Stable14C: 6 protons, 8 neutrons – Unstable
Half-life - T½: amount of time it takes for one-half of the radioactive atoms in a sample to decay
Page 11
Chart of Nuclides
C
Identifies the nuclear (stable
or unstable) behaviour of
nuclides
Page 12
Typical natural radioactive decay
A=Z+N
Page 13
238U 234Th + 4He
New nuclide: Z-2 and N-2 particle speed ~10,000 miles/sec (kinetic energy)
Beta Decay 234Th 234Pa + e
neutron to proton: Z+1proton to neutron: Z-1
Alpha Decay α
β
Page 14
Radioactivity on Earth
Slowly decaying (large half-life) radioactive isotopes are a constant heat supply for the Earth
Important natural radioactive elements on Earth are238U (92 p, 146 n) L½ ~ 4.5 billion years235U (92 p, 143 n)L½ ~ 0.7 billion years40K (19 p, 21 n) L½ ~ 1.25 billion years232Th (90 p, 142 n) L½ ~ 14 billion years
They are still around today, after 4.6 billion years
Page 15
2. Accretional Heat
Accretional heating occurs in forming planets as a result of the transfer of kinetic energy of objects striking the surface of the proto-planet
Once the planet is formed, it will start cooling down by slowly losing its accretional energy over geologic time
Page 16
Infrared
Remaining dust and grains grow to clumps (D ~10 m)
Clumps grow into planetesimals (D ~5 km)
Planetesimals grow into planets
Tremendous amount of energy is released when planetesimals run into each other – ACCRETION
Giant Molecular Cloud becomes gravitationally unstable – formation of the proto-sun
Nebular hypothesis
2mv2
1KE
Page 17
How much energy is in impactor?
Let’s consider an impactor with radius ~50 km that collides with Earth at 20 km/sec
How much energy will it release? Assume:
Density 3 g/cm3 = 3000 kg/m3
Mass = Density× Volume
KE = 3.11026 J
Convert (J) to TNT using1 Mton TNT (trinitrotoluene) = 4.1841015 J
E (Megaton TNT) = ???
3
sphere R3
4πV
Page 18
Accretion We still see the evidence of
these early, huge collisions on the surface of the Moon
There are a few craters on the Earth’s surface as well
Manicouagan, 100 km
Meteor Crater, 1.2 km
Page 19
Iron (dense!) from impactors follows gravity and accumulate towards the core
Lighter materials, such as silicate minerals,migrate upwards in exchange
Result: A differentiated Earth & generation of energy!
Early Earth heats up due to radioactive decay and impacts
Enough energy is quickly accumulated that most of Earth becomes mostly molten
3. Internal Energy from Differentiation
Page 20
Radioactive decay, accretion and sinking of heavy metals provide energy in the Earth’s interior (internal energy)
Internal energy is the driver of volcanism, earthquakes and plate tectonics in general
Tectonics constantly brings “fresh” rocks and volcanic gases to the surface where they can react with chemicals in the ocean releasing energy for life
Summary
Page 21
Earth, Mars and Venus: have adequate sources of energy for
photosynthesis
probably had similar delivery of organic molecules by comets and asteroids
Why did life originate and evolve only on Earth?
Page 22
Need for a LiquidLiving systems need a medium in which molecules can
dissolve and chemical reactions can take place
In any living system H2O:
a) Dissolves organic molecules (hydrogen bond)
b) Transports chemicals in and out of the cell
c) Directly participates in metabolic reactions
CO2 + H2O CH2O + O2
Why water?
Page 23
Element Parts per million
Hydrogen 750,000
Helium 230,000
Oxygen 10,000
Carbon 5,000
Neon 1,300
Iron 1,100
Nitrogen 1,000
Silicon 700
Magnesium 600
Sulfur 500
All Others 500
Elements in the Universe(by weight)
Water, H2O
O
HH
Ammonia, NH3
HHH
N
Ethane, C2H6
H
H
HH
HC
C
Methane, CH4
H
HHH
C
Page 24
ActivitySolvents for life
Page 25
Activity: Solvents for life
Solvent liquid over most of Earth’s surface temperature range:Water
(also acetic acid, and hexadecane barely!)
What if cells had methane or hexadecane instead of water? On Earth, cells would be quickly desiccated with methane,
mostly solid with hexadecane
What is more important, large boiling-freezing temperature difference or temperature difference within Earth’s range?
Both! - Range of temperatures: higher chances for liquid phase,
and thus cell survival - Within Earth’s range: necessary for the survival of the cell
Page 26
Why water? Water is liquid over a broader range of temperatures and
within Earth’s surface temperature range a) Broader temperature range – water stays liquid under
climate changes b) Higher temperature range – water allows faster rates of
chemical reactions, but not hot enough
to break important carbon bonds
Other substances are liquid at temperatures that are problematic for biochemical reactions
Page 27
Three states of water On Earth water can be present in all three states (phases):
ice (solid), liquid water (liquid), water vapor (gas)
Pressure and Temperature control which phase is the dominant in a particular planetary environment
We already discussed Temperature What about Pressure?
Page 28
What is Pressure?Pressure is a force applied on a surface in the
direction perpendicular to that surface
where F – force; A – area
Units: 1 Pa = 1 N/m2
A
FP
Page 29
Saturation (Phase) Curve: line along which two phases are inequilibrium (liquid to vapor Condensation = Evaporation)
Triple Point: temperature and pressure at which three phases (gas, liquid, and solid) of a given substance can coexist in thermodynamic equilibrium
Critical Point: liquid and vapor phase cease to exist
Phase Diagrams
Boilin
g
Freezin
g
Page 30
Temperature and Pressure identify the phase of any
substance Conditions (1) – solid phase Conditions (2) – liquid phase Conditions (3) – gas phase
We can make a liquid boil by either:
a) increasing temperature (at constant pressure) or
b) decreasing pressure (at constant temperature)
1
2
3
Page 31
H2O
CO2
It is not possible to get liquid water to be stable under 0.006 atm pressure (average surface pressure on Mars is 0.007 atm)
It is not possible to get liquid CO2 under 1 atm pressure (surface pressure on Earth – dry ice) 1
atm
Mars
Earth
Page 32
Another H2O advantage: Ice floats!
Most substances are denser as solids than as liquids
Ice is less dense than liquid water, which is why ice floats
The ice crust acts as a blanket, decreasing heat escape from the liquid water body below
Lakes and oceans do not freeze out completely!
Life can survive glaciations