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16 Νοε 2013 (πριν από 3 χρόνια και 7 μήνες)

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A group of particles move at many
different velocities

The Quiz


You are an astronaut floating in the vacuum of space,
about 100 feet from the space shuttle. You are out
there taking a picture of the Earth with your digital
camera. When you are finished you realize that the
jet pack you use to move around in space is no
longer working. You are stranded and everyone is a
sleep in the shuttle.


What must you do in order to get back to the space
shuttle? In explaining how you are going to get back
describe how Newton’s three laws of motion will
help you. All three are represented in this problem.

A balloon and the Sun

Magnetic lines of force trace out the magnetic field

Charged particles have similar force fields around them.
In this case the fields are electric fields.

When a charged particle, such as an electron, is accelerated rapidly
and for a very brief period of time, the distance field lines do not know
that the electron has moved, while the close by field lines point away
from the charge like normal. The kink that is produced in the field is
electromagnetic radiation (light). It moves out away from the electron
at the speed of light.

Imagine a charge being oscillated up and down
rapidly. There are now a series of kinks produced in
the electric field

A changing electric field produces a magnetic field. A
changing magnetic field produces an electric field. In this way,
the kink in the electric field, which is a change in the electric
field, produces a magnetic field. The resulting
electromagnetic wave is self propagating.

The electromagnetic wave propagates out into space
much like a water wave when a pebble is dropped in
a pond.

The wavelength of any wave (including EM waves) is the distance
from one point on the wave to the next point where the pattern
repeats. For instance, the distance from crest
-
to
-
crest

What we perceive as color is just the wavelength
of the EM wave.

Energy Conservation


Energy can be neither created nor destroyed.


The total energy is always constant. Energy
just changes form.



Potential Energy


Stored energy


Kinetic Energy


Energy of motion


Radiant Energy


Energy carried away by EM
wave


E
Total

=
E
Potential

+
E
Kinetic

+
E
Radiant




Let’s summarize what we know.


Particles in a gas are in motion with a large range of velocities


The gas motion can be characterized by the average kinetic
energy of the gas. This is also how temperature is defined


When a charged particle is accelerated, a kink forms in the
surrounding electric field which propagates outward from the
particle as a wave of electromagnetic (EM) radiation.


The radiant energy in the EM wave is inversely proportional to
the wavelength of the light. E =
hc
/
λ


Total energy is always conserved. It cannot be created or
destroyed but only change type between Potential, Kinetic or
Radiant.

In terms of energy conservation what must have
happened?

1.
The proton attracted the
electron and changed its kinetic
energy into potential energy

2.
The electron’s kinetic energy
was changed into radiant energy

3.
When the electron slowed to
nearly zero total energy
dropped to almost zero

4.
This can’t happen because
kinetic energy is always
conserved.

Which interaction produced the
shortest wavelength of light?

1.
Case A

2.
Case B

3.
Case C

The Sun is radiating.


The sun is radiating an enormous amount of energy
every second. ( Luminosity = 3.8 x 10
26

watts)


This radiation is produced by moving, free electrons
that are interacting with other charged particles.


The particles are all constrained to be within the Sun
because the force of gravity from the Sun’s mass is
pulling inward.


If this were all that is going on in the Sun;


What should we see happening to the Sun?

Please make your selection...

1.
The Sun should be
shrinking

2.
The Sun should be
expanding

3.
The Sun should
remain the same
size

Our Sun is NOT shrinking


The Sun’s particles are clearly converting their kinetic
energy into radiant energy.


In the process, the particles are losing kinetic energy.


This means that the average kinetic energy (or
temperature) should be decreasing with time.


IF the average kinetic energy decreases the particles
couldn’t hold up against the force of gravity. The Sun
would shrink.


Since it is not, we must conclude that some process
is generating energy inside the Sun in order to re
-
invigorate the particles. (Answer: Thermonuclear
fusion)

How can we measure the surface temperature of a
star?
(Note: temperature one of our stellar
parameters)


Measuring the average kinetic energy of a gas
on Earth is easy. You do it every time you read
a thermometer. But we can’t insert a
thermometer in the Sun or the other stars.


Energy conservation to the rescue. There is a
direct connection between the kinetic energy
of a gas and the radiant energy that the gas is
producing.

A radiating source produces many
colors of light.


A radiating source may look red, or orange or
yellow, BUT it is actually emitting light at many
wavelengths. You can see this when the light
is spread out into its components. Such as
when water droplets spread light from the sun
into a rainbow.


This can also be accomplished with a prism or
a diffraction grating.

A Spectrum


Top figure is
the velocity
histogram for
a gas.

Bottom figure
is the
intensity
verse
wavelength
plot for stars.


The relation between particle kinetic
energy and EM radiation


If you have a very large number of fast moving
electrons in a star then they will produce most of
their light with high radiant energy, or short
wavelength light.


If you have a cooler star (more slowly moving
electrons) they will produce mostly low radiant
energy light, or long wavelength light.



Result: cool stars look more red (long
λ
), hot stars
look more blue (short
λ
) .

Wien’s Law gives us the temperature
of the gas


T = (2.9 x 10
6
)/
λ
peak



When light is spread out into a spectrum (a rainbow) it
is possible to see which wavelength has the greatest
intensity. (
λ
peak
)


The average kinetic energy of the particles in a gas is
characterized by the peak in velocity histogram, the
radiation curve shows us the peak in radiation, which
comes from this average kinetic energy.


The light from a star can be used to find the surface
temperature.