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

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

Energy/food chain Photosynthesis

Respiration Solar Radiation

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

Earthquakes

Volcanoes

Are there other sources of energy?

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!

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

Source of Energy in the Earth’s Interior

1. Radioactive decay (dominant)

2. Energy remaining from accretion

3. Energy released from Earth’s differentiation

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

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

Chart of Nuclides

C

Identifies the nuclear (stable

or unstable) behaviour of

nuclides

Typical natural radioactive decay

A=Z+N

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

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

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

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

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

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

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

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

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?

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?

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

ActivitySolvents for life

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

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

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?

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

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

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

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

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