Transcript Sun: Nuclear Powerhouse - Wayne State University Physics and

The Sun:
A Nuclear Powerhouse
26 July 2005
AST 2010: Chapter 15
1
Happy Sun
26 July 2005
AST 2010: Chapter 15
2
Why Does the Sun Shine?
The Sun gives off energy
The energy must come from somewhere
— there’s no free lunch
Conservation of energy is a fundamental
tenet of physics
Where does the energy come from?
Until the 20th century only 2 possibilities
were known:
Chemical reactions
Gravity
26 July 2005
AST 2010: Chapter 15
3
The Sun’s Energy Output
How bright is the Sun?
The Sun produces 4x1026 watts
The watt is the unit for the rate of
energy use, commonly seen on light
bulbs and appliances
Our largest power plants
produce around 5 x 109 watts of
power (5,000 megawatts)
Sun’s power = 8 x 1016 of these
power plants (10,000 trillion)
Anyway you look at it, the
Sun gives off a lot of energy
26 July 2005
AST 2010: Chapter 15
4
Is the Sun Powered by Chemical Reactions?
What are chemical reactions? Examples:
Rearrange the atoms in molecules, as in 2H2+O2
2H2O
This reaction combines hydrogen and oxygen (gases) to
produce water plus energy
Reverse the process: 2H2O  2H2 + O2
By adding energy, we can dissociate water into hydrogen
and oxygen
The energy factor is often left out of chemical-reaction
formulas, for convenience
If the Sun is powered by burning coal or oil, how long
could its fuel last?
Only a few thousand years!
A process that uses fuel more efficiently is needed —
something that gets more energy out of every
kilogram of material
26 July 2005
AST 2010: Chapter 15
5
Gravity Squeeze?
The Sun’s interior experiences contraction due to its
own gravity
This gravitational contraction converts gravitational
potential energy into heat energy
Drop a book  noise (gravitational potential energy turns
into sound energy)
A contraction of 40 m per day would account for the
Sun’s energy output
Efficiency ~ 1/10,000 %
Gravity could power the Sun for about 100 million
years
but the Sun is thought to be at least 4 billion years old!
So gravity cannot be the Sun's main energy source
although it did help ignite the Sun when it formed
26 July 2005
AST 2010: Chapter 15
6
Nuclear Physics and Theory of Relativity
To understand the way the Sun produces
its energy, we need to learn a little
about nuclear physics and the special
theory of relativity
Nuclear physics deals with the structure
of the nuclei of atoms
The special theory of relativity deals with
the behavior of things moving at close to
the speed of light
26 July 2005
AST 2010: Chapter 15
7
Converting Mass to Energy
Out of the special theory of relativity
comes the most famous equation in
science: E = m c2
This equation tells us that mass (m) is
just another form of energy (E)!
The c2 is the square of the speed of light
For example, 1 gram of matter is
equivalent to the energy obtained by
burning 15,000 barrels of oil
26 July 2005
AST 2010: Chapter 15
8
…But There Are Rules
We can’t simply convert atoms into energy
We rearrange the protons and neutrons in
nuclei to get a lower-mass configuration
The difference between initial mass and final
mass is converted to energy
Chemical energy comes from rearranging atoms
to configurations of lower energy (mass)
Nuclear energy comes from rearranging nuclei
to configurations of lower mass (energy)
In each case, we get out the energy difference
26 July 2005
AST 2010: Chapter 15
9
Elementary Particles
Particle
name
Mass
(MeV/c2)
Charge
(e)
Proton
938.272
+1
Neutron
939.565
0
Electron
0.511
-1
Neutrino
<10-6
0
Photon
0
0
26 July 2005
AST 2010: Chapter 15
5 particles play a
fundamental role
inside the Sun
Protons and
neutrons make
atomic nuclei
Electrons orbit
nuclei of atoms
Photons are
emitted by the
Sun
Neutrinos are
also emitted
10
Atomic Nucleus
Two ways to rearrange nuclei and get energy:
Fission
produces energy by breaking up
massive nuclei like uranium into smaller
nuclei like barium and krypton
is used in A-bombs and nuclear reactors
needs uranium-235 and plutonium-238
cannot occur inside the Sun: it has no
uranium or plutonium
Fusion
produces energy by fusing light nuclei
like hydrogen to make more massive
nuclei like helium
is used in H-bombs
can occur inside the Sun: it has lots of
hydrogen!!
26 July 2005
AST 2010: Chapter 15
11
How Does Fusion Work?
Nuclear fusion is a process by which two light
nuclei combine to form a single, larger nucleus
However, nuclei are positively charged
Like charges repel
Two nuclei naturally repel each other and thus
cannot fuse spontaneously
For fusion, electrical repulsion must be
“overcome”
When two nuclei are very close, the strong
nuclear force takes over and holds them
together
How do two nuclei get close enough?
26 July 2005
AST 2010: Chapter 15
12
Fusion Needs Fast-Moving Nuclei
Fast moving nuclei
can overcome the
repulsion
Low speed
They get a running
start
Lots of fast moving
nuclei implies high
temperatures
High speed
The core of the Sun
has a temperature of
15 million kelvin
26 July 2005
AST 2010: Chapter 15
13
Fusion Powers the Sun
Temperatures in the cores of stars are
estimated to be above the 8 million K
needed to fuse hydrogen nuclei together
Calculations have shown that the
observed power output of the Sun is
consistent with the power produced by
the fusion of hydrogen nuclei
The observed neutrinos from the Sun
produced are expected as one of the
byproducts of fusion reactions
We can, therefore, hypothesize: all stars
produce energy by nuclear fusion
26 July 2005
AST 2010: Chapter 15
14
Proton-Proton Chain
• Fuse two hydrogen
(H=1 proton) to make
deuterium (2H=1
proton+1 neutron),
neutrino, and positron
• Fuse one deuterium and
one hydrogen to make
helium-3 (3He=1
proton+2 neutrons) and
a gamma ray (energetic
photon)
• Fuse two helium-3 to
make helium-4 (4He)
and two hydrogen
H  H 2H  e  
2
26 July 2005
H  H 3He  
AST 2010: Chapter 15
3
He  3He  4He  H  H
15
Why a Complicated Chain?
Fusion would be simpler if four protons would
collide simultaneously to make one helium
nucleus
That is simpler, but less likely
rare for four objects to collide simultaneously with
high enough energy
chance of this happening are very, very small
rate too slow to power the Sun
The proton-proton chain: each step involves
collision of two particles
chance of two particles colliding and fusing is much
higher
so nature slowly builds up the helium nucleus
26 July 2005
AST 2010: Chapter 15
16
Fusion and Solar Structure
Fusion occurs only in Sun's core
This is the only place that is hot enough
Heat from fusion determines the Sun's
structure
26 July 2005
AST 2010: Chapter 15
17
Heat from Core Determines Sun's Size
There is a force equilibrium inside the Sun,
called hydrostatic equilibrium, which is a
balance between
thermal pressure from the
hot core pushing outward
gravity contracting the Sun
toward its center
The nuclear-fusion rate —
how often fusion can occur
— is very sensitive to
temperature
A slight increase/decrease in temperature
causes the fusion rate to increase/decrease by
a large amount
26 July 2005
AST 2010: Chapter 15
18
Gravity and Pressure
Force equilibrium
Newton's 1st law states that an
object’s acceleration is zero if forces
on the object balance
Gravity tries to pull the 1/4 pounder
toward Earth’s center
Newton’s 3rd law implies that
pressure from the table opposes
gravity
Hydrostatic equilibrium in the Sun
The “cloud of gas” is like 1/4 pounder
Gravity pulls it toward the center
Pressure from below opposes gravity
The heat from fusion in the hot core
increases the pressure
Thus the energy output of the Sun
controls its size!
26 July 2005
AST 2010: Chapter 15
pressure
from
table
weight
from
gravity
pressure
from hot
gas
cloud
weight
from
gravity
19
Temperature and Pressure
The temperature of a gas
corresponds to the random
motion of atoms in the gas
The pressure of a gas is
the amount of force per
unit area on a surface in
contact with the gas
In general, pressure
increases with increasing
temperature
Balancing Fusion, Gravity, and Pressure
If the fusion rate increases, then
thermal pressure increases causing the star to expand
the star expands to a new point where gravity would
balance the thermal pressure
the expansion would reduce the pressure inside the core
the temperature in the core would drop
the nuclear fusion rate would subsequently slow down
the thermal pressure would then drop
the star would shrink
the temperature would then rise again and the nuclear
fusion rate would increase
stability would be re-established between the nuclearreaction rates and the gravity compression
26 July 2005
AST 2010: Chapter 15
21
Hydrostatic Equilibrium
The balance between the fusion rate, thermal
pressure, and gravity determines the Sun's size
Bigger stars have cooler cores
Smaller stars have hotter cores and, therefore, are
more compressed
26 July 2005
AST 2010: Chapter 15
22
Other Particles
Helium is not the only product in the
fusion of hydrogen
Two other particles are produced
Positrons
Neutrinos
26 July 2005
AST 2010: Chapter 15
23
Gamma-Ray Propagation in the Sun
The positrons emerging from the fusion reactions in
the core quickly annihilate the electrons near them
The annihilation produces pure electromagnetic
energy in the form of gamma-ray photons
These photons take about a million years to move
from the core to the surface
This migration is slow because they
scatter off the dense gas particles
The photons move on average about
only a centimeter between collisions
In each collision, they transfer some
of their energy to the gas particles
As they reach the photosphere, the gamma-ray
photons have become visible-light photons
because the photons have lost some energy in their
journey through the Sun
26 July 2005
AST 2010: Chapter 15
24
Neutrinos
These particles have no charge and are nearly
massless
They rarely interact with ordinary matter
Neutrinos travel extremely fast
at almost the speed of light if their mass is tiny
Neutrinos pass from the core of the Sun to its
surface in only two seconds
They take less
than 8.5 minutes
to travel from the
Sun to the Earth
26 July 2005
AST 2010: Chapter 15
25
Neutrino Abundance & Counting
The Sun produces a lot of neutrinos
In one second several million billion neutrinos pass
through your body
Do you feel them?
Not to worry!
The neutrinos do not damage anything
The great majority of neutrinos pass right through the
entire Earth as if it weren’t there
In principle, we can use the number of solar neutrinos
received on Earth to get clues about the Sun’s energy
output, but
neutrinos have a very low probability of interacting with
ordinary matter
they could pass through a light year of lead and not be
stopped by any of the lead atoms!
26 July 2005
AST 2010: Chapter 15
26
Detecting Neutrinos
Increase the odds of detecting neutrinos
by using a large amount of a material
that reacts with neutrinos in a
measurable way
A chlorine isotope changes to a radioactive
isotope of argon when hit by a neutrino
A gallium isotope changes to a radioactive
isotope of germanium
Neutrinos can interact with protons and
neutrons and produce an electron
The electron can be detected
26 July 2005
AST 2010: Chapter 15
27
Neutrino Detectors
Neutrino detectors use
hundreds of thousands of
liters of these materials in a
container buried under
many tens of meters of rock
to shield the detectors from
other energetic particles
from space called cosmic
rays
Even the largest detectors
can detect only a few
neutrinos per day
26 July 2005
AST 2010: Chapter 15
28