Energy

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Energy

• kinetic energy
• bulk motion a moving car, orbiting planet E
  ½mv2
• thermal energy E 1.5 kT
• potential energy
• lifting a rock up a hill increases its potential
  energy E mgh
• Rolling it down the hill decreases its potential
  energy

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What is temperature?

• temperature is a measure of thermal kinetic
  energy of matter.
• absolute zero when matter has no thermal energy
  it is as cold as it can be zero Kelvin or T 0
  K.
• When water ice has enough thermal kinetic energy
  to go from solid to liquid, T 273 K. When
  liquid water gains enough thermal energy to boil,
  T 373 K.
• Large changes in temperature are often
  associated with physical, chemical and nuclear
  reactions.

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Atomic Theory

• The idea that matter is made up of many many
  particles, the so called atomic theory, is at the
  heart of our understanding of temperature.
• Temperature can be thought of as the average
  thermal energy of the molecules

solid
liquid
gas
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Kinetic Theory
Every once in a while we get a collision of the
molecule on the wall. This pushes on the wall -
adding up all the pushes gives pressure
What will happen to the number of collisions if
the temperature increases?
It will go up - in other words the pressure
increases as the Temperature increases.
What if the box is made smaller (so that the
density increases) What happens to the number of
collisions then?
It will go up - in other words the pressure
increases as the density increases
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Temperature
Heat
Heat is the flow of energy between two (or more)
substances.
Temperature is the amount of energy in the
molecules of the substance
Temperature is an intrinsic property of the
material and can be measured in Kelvin.
We cant measure heat, only the temperature
change heat flow causes
Temperature does not depend on how many molecules
you have, only the energy per particle.
More molecules will transfer heat more efficiently
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Heat Transport

• Conduction
• a hot metal rod transfers energy to your hand via
  conduction.
• energy transferred without moving the molecules
• important for metals (where electrons within the
  metal transfer the energy)
• Convection
• a boiling pot of water transfers heat from the
  bottom of the pot to the air above via convection
  
• moves molecules (either individually or in large
  groups)
• Radiation
• the hot filament of a light bulb provides light
  and heat via radiation.
• doesnt require matter at all.

• conduction example
• convection example.
• radiation example the hot filament of a light
  bulb provides light and heat via radiation.In
  all cases matter/energy is conserved if you
  include whats carried away heat and light.

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Review of Energy

• Energy is conserved
• Kinetic Energy Energy of Motion
• Potential Energy Energy of Position
• Kinetic Theory Atoms are tiny elastic
• Temperature is the average kinetic energy of the
  atoms
• Pressure is the number of collisions
• a cold, dense gas can exert the same pressure as
  a warm, less dense gas
• In stars, the inward pull of gravity balances the
  outward push of thermal pressure.
• Heat energy can be transported by Conduction,
  Convection, and Radiation

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Energy Concept Test
As a satellites orbit decays, it plunges toward
the earth. Describe what happens to the total
energy, the kinetic energy, and the potential
energy of the satellite.
The potential energy decreases steadily as the
satellite gets closer to the earth, while the
kinetic energy increases steadily as the
satellite moves faster and faster. If we neglect
friction and other losses of energy, all the
potential is converted to kinetic and so the
total energy remains constant.
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What is matter?

• matter is the amount of stuff protons, neutrons,
  electrons.
• How do you measure the stuff?
• By the gravitational attraction it exerts on
  other matter (gravitational mass)
• By its resistance to changes in motion (inertial
  mass)
• In general, the inertial mass is the same as the
  gravitational mass, both are measured in kg

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Conservation of Mass?

• Physical and chemical reactions appear to
  conserve mass the amount of inertial mass before
  the reaction is the same as after the reaction.
• However, nuclear reactions show that what is
  conserved is matter energy. You can convert
  mass to energy

E mc2
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Atomic matter
Atomic number number of protons. All atoms of an
element have the same atomic number
In a neutral atom, the number of electrons equals
the number of protons. Every proton has a 1
charge, and every electron a -1 charge. Ions are
formed by adding or removing electrons, never
protons
Atomic Weight the number of protons and neutrons
(electrons weigh almost nothing).
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Atomic matter and the periodic table
Isotopes of an element have the same atomic
number but different atomic weights. They differ
only in the number of neutrons.
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States of matter
When thermal motions are very large (hot), the
electrons fly away from the nucleus. This state
is a plasma.
When thermal motions are moderate (warm), the
electrons are bound to the nucleus, but atoms
cannot bind to form molecules. This is atomic
gas.
When thermal motions are low (cold), the
electrons are bound to the nucleus and most atoms
are bound together in molecules. This is
molecular gas.
At high pressure, warm and cold atoms and
molecules condense to form liquids and solids.
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Johannes Kepler (1571-1630) first law

• 1. The orbit of a planet about the Sun is an
  ellipse with the Sun at one focus

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Keplers 2nd and 3rd laws

• 2. A line joining a planet and the Sun sweeps out
  equal areas in equal times.

• 3. The square of a planets sidereal period is
  directly proportional to the cube of its orbits
  semi-major axis.

P2 (in earth years) a3 (in au)
It takes as much time to go from C to D as from A
to B
planets move faster closer to the sun
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Newtons First Law

• An object will continue in a state of rest or a
  state of straight motion in the absence of any
  force.
• An object will not start moving by itself
• An object will not stop moving by itself
• Why did Aristotle and friends think every object
  would naturally become stationary?
• Because they didnt know about friction, the
  force that acts to slow things down
• This implies that the planets are being acted on
  by a force, since they are not moving in a
  straight line or remaining at rest.

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Newtons Second Law

• Objects accelerate more if they are pushed with
  bigger forces less massive objects accelerate
  more for the same force than more massive
  objects.
• In other words, F ma
• F is force
• m is mass, we can measure that in kg
• a is acceleration, the rate of change of speed.
• For example, if you are going 60 mph, and you
  slam on the brakes, and you stop in 5 seconds,
  your acceleration was -12 miles per hour per
  second.
• We usually measure acceleration in m s-2 (both
  time units the same)
• acceleration is not just speeding up and slowing
  down, changing direction requires acceleration as
  well

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Newtons Third Law

• For every action, there is an equal and opposite
  reaction.
• For example, if you step off a skateboard, you
  move forward and the skateboard moves backward
• This also allows rocket propulsion to work

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Gravity
Recall that this change in acceleration meant
some force pointing inward This force is gravity
We can show that this force is greatest for the
interior planets and weaker for the exterior
planets
In fact, it turns out this force obeys an
inverse-square law i.e. the force decreases as
the square of the distance. Thus if you double
the distance, the force decreases to 1/4. If you
triple the distance, the force decreases to 1/9
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Acceleration and Gravity
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Orbits and Gravity
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When Newton used his newly discovered calculus to
solve the his newly discovered law of gravity, he
found three kinds of solutions elliptical,
parabolic, hyperbolic.
He found that for the elliptical orbits, gravity
explained Keplers 2nd and 3rd laws.
But how does gravity act on objects over such
great distances?
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Newtons Law of Gravitation

• F GM1M2 / d2
• The gravitational force (F) on an object is
  proportional to the mass of the first object (M1)
  times the mass of the second object (M2) divided
  by the distance between them (d) squared.

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Gravity

• Because of Newtons third law, we know that
  gravity acts two ways. The earth exerts a force
  on you, you exert a force on the earth.
• Even though the forces are the same, the effects
  are different. The acceleration, remember is
  bigger for lighter objects. Since the earth is
  much more massive than us, we feel a big
  acceleration and the earth feels a smaller
  acceleration.

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Correcting Kepler

• If both the sun and planets exert a force on one
  another, then they are orbiting each other.
• Thus the focus of the ellipse is not the Sun,
  instead it is their center of mass.

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Spring tides are the highest tides because the
Sun and the Moons gravity are working together.
Neap tides are lower than spring tides because
the Suns gravity opposes the Moons gravity.
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Gravity causes tidal forces. The gravitational
force is greatest on the surface of the Earth
facing the Moon and weakest on the opposite side.
The result is two tidal bulges. The Earths
rotation produces bulges slightly ahead of the
Moon. Thus we experience about two high and two
low tides every day.
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Inverse Square Law
As you move away from a light source, the
intensity decreases as the square of the distance.
If you double the distance, the intensity goes
down by four times If you triple the distance,
the intensity goes down by nine times If you
quadruple the distance, the intensity goes down
by sixteen times If you half the distance, the
intensity goes up by 4 times.
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Waves
Short Wavelength
Long wavelength
wavelength

• All light waves travel at the same speed, c
  300,000 km/s
• Wavelength is the distance between two crests of
  the wave
• Frequency is the number of crests that pass by
  you in a second
• The longer the wavelength, the lower the
  frequency, the lower the energy of the photon

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the electromagnetic spectrum
10-14
Gamma rays
nucleus
Higher frequency
10-12
Higher energy
atom
X rays
10-10

• E hf
• E hc/?
• c ?f

virus
10-8
Ultraviolet
Visible
10-6
Infrared
Pin head
10-4
10-2
Human
FM
1
Radio
AM
Lower frequency
102
Lower energy
104
Mountain
Wavelength
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Two Laws of Radiation

• The hotter the material the more radiation the
  matter emits.
• This tell us that the sun, at about 6000 K, emits
  more radiation than the earth, at 300 K
• Something twice times as hot (its absolute
  temperature is twice as high) emits 16 times as
  much radiation
• The hotter the material, the higher the energy of
  the average photon and the higher the frequency
  of the radiation
• this tells us the sun emits mostly visible light
  and the earth emits infrared light

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Spectra
The sun appears yellow because it emits more
yellow light than any other kind.
The area under the curve is proportional to the
luminosity
As the temperature increases, the peak wavelength
decreases
As the temp increases, the luminosity increases
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Emission
The outgoing photon can only have certain
energies, corresponding to the energy difference
between different states. In other words, only
very exact wavelengths are emitted.
What is it made of
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Hydrogen Spectra
The spectra of radiation emitted by Hydrogen only
shows a few wavelengths, corresponding to the
energy difference between the electrons allowed
states
What is it made of
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Emission Spectra
H2
H
Since different elements have different spectra,
we can use the spectrum of a star to determine
its composition.
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Absorption
The incoming radiation is only absorbed if the
energy is the same as the difference in energy
between two states. In other words, only very
exact wavelengths are absorbed
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Emission and Absorption of Hydrogen
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Emission and Absorption lines
Looking at the hot light source through cooler
gas produces absorption lines.
incident light is a continuous blackbody spectrum
If the cooler gas is hot enough and thin enough,
it produces its own emission spectrum.
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The Solar Spectrum
The darkest lines were observed in the solar
spectrum by William Wollaston in 1802, but
Fraunhofer catalogued them 10 years later they
are now known as Fraunhofer Lines
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Just as the pitch of the train whistle tells us
whether the train is moving away or toward us,
the wavelength of light from a star or galaxy
tells us whether it is moving away or toward us.
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Summary

• Temperature can be determined from the wavelength
  peak of the emitted radiation
• Composition can be determined from the spectral
  absorption or emission lines of the object
• The speed of the object toward or away from you
  can be determined by the Doppler shift of the
  spectral lines.