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

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.

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

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

Temperature Heat

Temperature is the amount of energy in the molecules of the substanceTemperature is an intrinsic property of the material and can be measured in Kelvin.

Temperature does not depend on how many molecules you have, only the energy per particle.

Heat is the flow of energy between two (or more) substances.

We can’t measure heat, only the temperature change heat flow causes

More molecules will transfer heat more efficiently

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. – doesn’t require matter at all.

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

Energy Concept Test

As a satellite’s 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.

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

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

Atomic matterAtomic number: number of protons. All atoms of an element have the same atomic number

Atomic Weight: the number of protons and neutrons (electrons weigh almost nothing).

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 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.

States of matterWhen 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.

Johannes Kepler (1571-1630): first law

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

Kepler’s 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 planet’s sidereal period is directly proportional to the cube of its orbit’s semi-major axis.

It takes as much time to go from C to D as from A to B:

P2 (in earth years) = a3 (in au)

planets move faster closer to the sun

These two areas are the same

Newton’s 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 didn’t 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.

This is where the planet would move, if it were moving in a straight line

Force

This is where the planet does move, some force must be pushing it sideways

Newton’s 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

Newton’s 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

Rocket is pushed this way

Fuel is pushed this way

Gravity

Recall that this change in acceleration meant some force pointing inward This force is gravityWe 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

Acceleration and Gravity

Orbits and Gravity

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 Kepler’s 2nd and 3rd laws.

But how does gravity act on objects over such great distances?

Newton’s 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.

Gravity

• Because of Newton’s 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.

• 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.

Correcting Kepler

If there are two orbiting suns?Then they both orbit a common center of mass, somewhere between them.

Spring tides are the highest tides because the Sun and the Moon’s gravity are working together.Neap tides are lower than spring tides because the Sun’s gravity opposes the Moon’s gravity.

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 Earth’s rotation produces bulges slightly ahead of the Moon. Thus we experience about two high and two low tides every day.

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 timesIf you triple the distance, the intensity goes down by nine timesIf you quadruple the distance, the intensity goes down by sixteen timesIf you half the distance, the intensity goes up by 4 times.

Inverse Square Law

Waves

• 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

wavelengthLong wavelength

Short Wavelength

the electromagnetic spectrum

• E = hf

• E = hc/

• c = f

Hig

her

energ

yLo

wer

energ

y

104

10-2

102

10-4

1

10-6

10-8

10-10

10-12

Wavelength

Hig

her

frequ

en

cyLo

wer

frequency

Gamma rays

X rays

Ultraviolet

Visible

Infrared

RadioAM

FM

Mountain

Human

Pin head

virus

atom

nucleus10-14

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

SpectraThe area under the curve is proportional to the luminosity

The sun appears yellow because it emits more yellow light than any other kind.

As the temperature increases, the peak wavelength decreases

As the temp increases, the luminosity increases

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.

The electron jumps down to lower state emitting photons with an energy exactly equal to the energy difference between the two states of matter

What is it made of

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

Emission Spectra

Since different elements have different spectra, we can use the spectrum of a star to determine its composition.

H

H2

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

Incoming radiation is absorbed and the electron jumps to a higher energy state

The electron jumps down to its basic state, emitting a photon

Sometimes the electron goes down in steps, emitting lower energy photons than it absorbed.

Emission and Absorption of Hydrogen

Emission and Absorption linesLooking at the hot light source through cooler gas produces absorption lines.

If the cooler gas is hot enough and thin enough, it produces its own emission spectrum.

incident light is a continuous blackbody spectrum

The Solar SpectrumThe 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

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.

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.