Phys104 - How Things Work
University of Maryland, College Park
Fall 2009, Professor: Ted Jacobson

---

Friday 12/11

P4-01 GEIGER COUNTER

Uranium ore, origin in supernovae

U-238 and U-235, the need to enrich proportion of U-235 for reactors (3-4%) or bombs (90%). Centrifuges.

Relative ease of separating Plutonium-239 for bombs. North Korean bombs used plutonium. Iran presumably has plutonium.

Fusion/hydrogen/thermonuclear bomb

Fallout

EMP - electromagnetic pulse from nuclear detonation. A student asked about this. (See http://en.wikipedia.org/wiki/Electromagnetic_pulse)

---

Wednesday 12/09

MRI

Binding energy

Fission and Fusion

alpha, beta, and gamma decays

Americium-241 and smoke detectors

Uranium-235 reactors and bombs

Plutonium-239 bombs

---

Monday 12/07

P2-02 PHOTOELECTRIC EFFECT IN ZINC - ARC LAMP

- X-ray absorption for imaging involves primarily the photoelectric effect, in this case ejecting a tightly bound
electron from an inner shell of a larger atom.

- I demonstrated another version of the photoelectric effect with the above demo. In the demo, UV photons have
enough energy to eject excess electrons from the negatively charged zinc plate, but when a plate of glass is placed
in the way, the ejection stops, since the glass absorbs the UV photons. This demo shows that 1) photons can eject electrons
from a material, and 2) ejection requires a photon of sufficient energy: the photon energy (Planck's constant h times the
frequency) must be greater than or equal to the energy it takes to pull the electron away from the zinc.

- electron-volt: 1eV is the difference of energy of an electron corresponding to a voltage difference of one volt.
The energy of different photons:  red light: 1.6 eV, blue light 3 eV, UV 7 eV (for example), X-ray 87,000 eV typical in medical
imaging. (Terminology: 1000 eV = 1keV, kilo-electron-volt.)

- radiation therapy: use of radiation to kill tumor or cancer cells. Requires higher energy photons than those used for imaging,
since the imaging ones get absorbed too much, eg 90% absorbed going through a patient's leg. Instead use ten times higher
energies, e.g. 1,000,000 eV = 1,000 keV = 1MeV. These don't interact by photoelectric effect, but rather by
Compton scattering: collision of photon & electron, in which a photon comes out, altered in energy, along with the electron.
When this happens, it can release enough energy to break apart molecules and damage DNA. Since cancer cells are
not as good at repairing their DNA, and also they replicate faster, this selectively damages the bad cells.
These colisions are rare events, so the photons mostly go all the way through a patient's body, only occasionally interacting.
But they are equally likely to interact anywhere along the beam, so they can damage healthy tissue as well as the target. To deal
with this a beam is sent from a large number of different angles, with all the beams intersecting at the target, so that the target
receives much more radiation overall than the healthy tissue.

- How do you get 1 MeV photons?

-- One way is, like in an X-ray tube,  to accelerate electrons and smash them into a durable target. But this requires larger,
more expensive equipment, because of the much higher energy. Still, it's done.

-- Another method is to use photons that come out of a nuclear decay. Photons that come from nuclear  decays are called gamma rays.
An example uses cobalt-60: a nucleus with 27 protons and 33 neutrons. One of the neutrons can decay, turning into a proton, an
electron, and a neutrino. This is called beta decay. The electron and neutrino escape the nucleus, but the proton remains, and the
nucleus becomes nickel-60, with 28 protons and 32 neutrons. But it is an excited state of this nucleus, not the ground state!
It very rapidly makes two transitions to get to the ground state, emitting gamma ray photons of energies 1.33 MeV and 1.17 MeV.
It is these that are used in the radiation therapy. The electron that was emitted is easily blocked so is kept away from the body,
and the neutrino goes through anything. (I didn't say this in class, but neutrinos can go through the whole earth without interacting.
In fact trillions of neutrinos per second that originate in nuclear reactions in the sun pass through your body every second.)

- half-life:  Radioactive decay is a random event.  A neutron is by itself, rather than in a nucleus, undergoes beta decay with a
half-life of about 10 minutes, i.e. half the neutrons will decay in a time span of 10 minutes. But a neutron in cobalt-60 takes
longer to decay: Half of the cobalt-60 atoms in a given sample will undergo beta decay to nickel-60 in about 5.27 years.
(To make cobalt-60, cobalt-59 is exposed to neutrons in a nuclear reactor.)

- proton therapy: a method of radiation therapy where the beam is not photons, but rather protons. The advantage is that
the protons, being massive, will keep going in a straight line and gradually slow down as they go through the body, and the key thing
is that they only really damage DNA in the last few millimeters before coming to rest. So, by adjusting the initial velocities of the
protons, the radiologist can arrange for them to come to rest at a particular location within the body, and so to target the tumor or cancer.
The protons start with kinetic energies in the range 70-250 MeV, which means they are moving fairly cose to the speed of light.
To get them going that fast requires an accelerator called a cyclotron. The whole set-up is extremely costly. The one recently installed
at the University of Pennsylvania cost around $150 million dollars.
See http://www.proton-therapy.org/howit.htm, and http://en.wikipedia.org/wiki/Proton_therapy

---

Friday 12/04

L5-01 OPTICAL BOARD - TOTAL INTERNAL REFLECTION

POWERFUL GREEN LASER POINTER

P3-31 X-RAY TUBE

- a bit more about laser diffraction, and colors produced by diffraction

- demo L5-01 of total internal reflection; worked great with the laswer pointer as light source

- more explanation of optical fibers, digital pulse transmission, dispersion, and signal amplification

- X-rays (see section 16.2), showed X-ray tube; how X-rays are generated, and how they interact with electrons in atoms

---

Wednesday 12/02

M1-22 LASER DIFFRACTION - GRATINGS

L5-02 TOTAL INTERNAL REFLECTION IN LONG TANK

Special equipment ordered

A CD, A DVD, AND A VINYL RECORD

POWERFUL GREEN LASER POINTER

- structure of CD's and DVD's; 0 vs. 1 coded in change of reflected intensity; number of lines:
 on CD with line spacing of 1.6 microns, and 3.6 centimeter from inner to outer edge of disk, have
(3.6 x 10^-2 m)/(1.6 x 10^-6 m) = 22,500 lines in all. Actually, it's one long spiral.

- "burning" a CD: laser light heats up and transforms dye from transparent to cloudy.

- diffraction: effects from wave nature of light

- size of bits on disk set by limit of resolution of the light, which is set by laser wavelength

- optical read-out system

- laser diffraction: when coherent light reflected from many parallel scattering sources, one gets near perfect
cancellation of all the light due to destructive interference, except at special angles for which the path
length differences from one source to the adjacent one are exactly one wavelength, or two wavelengths,
etc. So narrower source spacing implies wider diffraction maximum. Also longer wavelength implies
wider diffraction maximum. I demonstrated this with a green and an orange laser on the same
diffraction grating. [Mathematical detail: The sine of the angle for the first diffraction maximum is
equal to the ratio (wavelength)/(source spacing).]

- Compared vinyl record, CD, and DVD line spacings using diffraction:
Side 2 of the original Miles Davis album, Kind of Blue, plays at 33 revolutions per minute
for 20 minutes, so makes about 660 revolutions, so has 660 grooves. The grooves extend
about 7.5 cm from inner to outer edge, so the line (groove) spacing is about 7.5cm/660 lines
= 0.0114 cm/line, or 114 microns/line. The vinyl record spacing is 114/1.6 = 71 times larger
than the line spacing on a CD with 1.6 micron spacing, so the first diffraction spots are at an
angle roughly 71 times wider. In the other direction, the line spacing on a DVD is 0.74 microns,
a little less than half that on a CD, so the first diffraction spots would be at an angle about twice
as wide as for the CD. I showed this by reflecting the green laser pointer off the disks onto the
wall of the lecture room.

- total internal reflection: when light hits an interface where it travels faster on the other side, it
partially reflects, and partially refracts (goes through with a bend) closer to the surface. If the angle
of the incident light is sufficiently shallow, the refracted light can come ut parallel to the surface.
If the incident beam is any shallower, there is no refracted light: the light experiences total internal reflection.
I showed this with demo L5-02.

- optical fiber: these use the principle of total internal reflection to make a "light pipe" that
keeps the light inside the fiber. This year's Nobel Prize in physics went 1/2 to the guy who
discovered that by (a) purifying the glass and (b) giving the glass a variable index of refraction,
decreasing toward the outside of the fiber, the light could be guided with little loss for long distances
in the fiber. Repeating Monday's post: For a very brief description of the Nobel Prize topics see:
http://nobelprize.org/nobel_prizes/physics/laureates/2009/speedread.html
For a more extended explanation for the general public see:
http://nobelprize.org/nobel_prizes/physics/laureates/2009/info.pdf

---

Monday 11/30

- reviewed essentials of lasers

- LED's (light emitting diodes): These generate the light in modern computer displays, for example, as well as
solid state laers (see below). They are made by forming a junction of two materials. I explained the principle
with a waterfall analogy: the ground state of the conduction electrons on one side of the junction is at a
higher energy level than the ground state on the other side, so when a current flows across the junction,
the downstream electrons can drop to a lower level and emit the energy difference in the form of a photon (light quantum).

- laser diode: This is the kind of laser that is in a laser pointer, or a DVD player, for example. It is an LED with
the characteristic that the downstream electrons survive long enough in the excited state to produce a
"population inversion" that can play the role of the laser medium. Also there are mirrors or reflective
crystal boundaries that confine the radiation into a resonant cavity to allow the laser amplification process to happen.
For pictures see the wikipedia article http://en.wikipedia.org/wiki/Laser_diode. For images of the architecture
channeling the light away from the junction see for example 
http://content.answers.com/main/content/img/CDE/LASDIODE.GIF
and
http://www.shorelaser.com/Laser_Operation.html

- photo diode: run an LED backward: absorbing a photon can produce a conduction electron, hence a current.
These are used in digital cameras, camcorders, video cams, DVD players, etc, etc.

- CCD (charge coupled device): Half of this year's Nobel Prize in physics was for the invention of the electronic
light image sensor array called a CCD. This is a planar array of "buckets" each of which uses a photo diode to
collect an amount of charge proportional to the amount of light that it absorbed. The charge is read out by
shifting the charges from one row to the next by manipulating the voltages on the buckets, and shifting sideways
to read out the last row. See http://en.wikipedia.org/wiki/Charge-coupled_device for an animated image showing
how this can work. For a scanner the CCD is not a planar array but just a linear array of photodiodes.
To make color detection there are either color filters over the different detectors, to "see the image through three
sets of color filters", or the light is split into three colors before being sent to three different CCDs.
I didn't say this in class, but another technology used for imaging is a CMOS (complementary metal oxide semiconductor -
I don't know why they called it this) array, in which each pixel is addressed and read out locally, without the
"bucket brigade" method used by CCDs. A remarkable thing is that a photodiode can detect 90% of the photons
(in a certain frequency interval) that strike it, compared with a human eye or photographic film that detect
a few percent. For a very brief description of the Nobel Prize topics see:
http://nobelprize.org/nobel_prizes/physics/laureates/2009/speedread.html
For a more extended explanation for the general public see:
http://nobelprize.org/nobel_prizes/physics/laureates/2009/info.pdf

- Digital music storage: A sound wave pressure is sampled 44,100 times per second, which is twice the
maximum frequency a human can hear. This suffices to reconstruct any signal a human can percieve.
The pressure (or other signal) at one of those sample times is quantified as a binary number with 16 bits (0 or 1).
2¹⁶ = 65,536, so the pressure change is assigned an integer between -32,767 and + 32,768.
One byte is 8 bits, so that means that each sample uses 2 bytes of data.

Binary numbers use 2 rather than 10 as the "base". The digits in each place are thus either 0 or 1, and the places,
from right to left, are for 1, 2, 2²=4, 2³=8, etc. For example, the binary number 101 means 1x4 + 0x2 + 1x1 = 5.
With this scheme, every number can be written with nothing but 0's and 1's.

How many megabytes (million bytes, MB) of data is needed for a minute of stereo music? Each channel requires
(44,100 samples/second)(2 bytes/sample)(60 seconds/minute) = 5,292,000 bytes/min = 5.3 MB/min,
so both channels together take about 10.6 MB. (This is something like 10 times the size of an mp3 file,
since the latter is a "compressed" format that sacrifices some of the data by some kind of filtering that takes
into account the sensitivity of the human ear.) An hour of music would require 635 MB, and a 74 minute
playing time would require 783 MB.

Notes:
1) In digital parlance, "mega" usually means not 1,000,000 but rather 2²⁰ = (2¹⁰)² = (1024)² = 1,048,576, about
5% more than a million! With this meaning, the 783 MB would be referred to as about 747 MB.
See http://en.wikipedia.org/wiki/Mebibyte

2) There is some redundancy in the data storage, for error correction, so more data is needed. For music data errors
are not a disaster, so there is little error correcting redundancy. For software for which each bit is crucial, there
are error correction schemes that use more data.

Next time: 1) how the data is stored on the disk and read out; and 2) optical fibers.

---

Friday 11/27 - no class, Thanksgiving break

---

Wednesday 11/25

Independent study:
a. Read "Reperesenting Sound: Analog & Digital" on pp. 405-406.
b. Read pp. 489-492 "Digital Recording" and "The Structure of CD's and DVD's"
Be sure to try to answer all three "Check your understanding"'s, in these sections, and then look up the answers.

---------------------------------
As an interesting optional project, if you can get your hands on a balloon and a compact or not compact
fluorescent bulb (removed from it's fixture) over the break, then rub the balloon on your hair or on a carpet
or something, and hold it near the bulb in a very dark room. If you can see the bulb light up, try to explain
to yourself and your friends and/or family what happened!

---

Monday 11/23

P3-67 FLUORESCENCE OF LAUNDRY SOAP

M4-02 NEWTON’S RINGS - PROJECTION

P3-71 VISIBLE LASER

- repeated the role of the uncertainty principle in producing a ground state of atoms (see notes below).

- fluorescence demo using laundry soap and UV emitting "black light"

- inteference fringes: colors of soap film & oil slicks, Newton's rings. (See textbook, and demo description).
Also mentioned anti-reflective coatings, and dichroic filters that produce colored light from white light by interference.

- laser (light amplification by stimulated emission of radiation).
The three distinguishing qualities of laser light: all the photons have nearly
(i) the same wavelength
(ii) the same direction of propagation
(iii) the same phase (oscillating in step with each other).
This allows the laser light to travel in a very straight line, and to be very narrowly focused, and to exhibit very dramatic interference effects.
(See textbook for explanation of how lasers work.)

---

Friday 11/20

N2-02 DIFFRACTION SPECTRA - THREE SOURCES - EXPENDABLE GRATINGS

N2-21 PRISMATIC SPECTRUM OF MERCURY - SUPERPRESSURE LAMP

M7-34 ROTATION OF POLARIZATION - POLAROID AND WAX PAPER

M8-01 POLAROIDS AND KARO SYRUP

P3-53 ATOMIC ENERGY LEVEL MODEL

depolarization with scattering in waxed paper (M7-34)

rotation of polarization, dependence on frequency (M8-01)

bee vision of polarization; and apparently my statement that humans cannot see polarization effects
with the naked eye is wrong - there is a very faint effect that can be perceived:
http://en.wikipedia.org/wiki/Haidinger%27s_brush

I found in Wikipedia an article about tetrachromacy, i.e. four-color vision.
Apparently most birds have it, and some humans may have it!

Human color vision: a general experience of "color" corresponds to a given response intensity
of each of the three types of cone cells. Each type has a particular sensitivity to each frequency,
so is a kind of weighted sampler of the incoming light field.  So a "color" is characterized by three
numbers...or actually two, since the overall intensity doesn't correspond to a color change at all.
So that's why the colors can be laid out in a two dimensional pattern, as in the "color space" below.
(More often you see a "color wheel", which is a more symmetrical but I think somewhat less
well-founded representation...) Around the edge of the shape are the colors corresponding to a single
frequency of light, i.e. a pure spectral color, and are indicated by the corresponding wavelength, in
nanometers. All the other colors we can perceive are combinations of these, and fall within that
outer curve. But note, the computer screen you're viewing it with is generating
the image with a different relative intensity of each of three types of colored pixel. The colors that
are accurately represented by most modern (sRGB) computer displays are those in the black triangle.
Any set of three pixel types would correspond to some triangle, and no single set could faithfully
cover the whole color space. If the colors of the pixels are changed, then in the overlap of the
two corresponding triangles, the same set of color perceptions could still be reproduced using different
combinations of relative weights for the three pixel types.


http://en.wikipedia.org/wiki/SRGB

atomic spectra: N2-02. Students viewed these light sources though ahand held plastic sheet diffraction grating.
the mercury and cadmium lamps emit in a few discrete colors/frequencies. These are characteristic of
the electronic structure of the atom. We also saw how the spectra of fluorescent lights have a few distinct frequencies.
These come from different components of the coating of the tubes, which emit visible light when bombarded by
ultraviolet photons from mecury vapor in the tube.

quantum physics of spectra:
why don't the electrons in an atom simply radiate energy and crash into the nucleus, collapsing the atom?
This can only be understood using quantum physics. The essential element is the Heisenberg uncertainty principle.
The uncertainty in velocity is inversely proportional to the uncertainty in position. The electrons don't have enough
energy to collapse into the nucleus! If they became too localized near the nucleus, their velocity and hence their
kinetic energy would become very uncertain, in particular it could be very large. So if their energy is strictly limited,
they cannot get too close. In the ground state of the atom, they are in their lowest energy configuration, as close as
they can get. If an electron absorbs some energy by colliding with another electron, or absorbing some light, for example,
then it has extra energy, and since it is accelerating can radiate, shaking off the extra energy and settling back into its
lowest energy state in the atom. 

Each kind of atom has its own characteristic patterns of electron vibrations, with corresponding energies.
When an electron changes from one pattern to another of lower energy it gives off the energy difference in the form of a
"packet" of light, called a photon. The energy of the photon is equal to the frequency of the photon times Planck's constant.
Hence, each atom has its own characteristic frequencies of light it emits. 

Fluorescent lights explained. (See textbook.)

---

Wednesday 11/18

M7-34 ROTATION OF POLARIZATION - POLAROID AND WAX PAPER

M7-05 ROPE AND COOKIE COOLERS

VIDEO CAM TO SHOW DIGITAL WATCH DISPLAY

polarization of electromagnetic waves (including light)

illustration with M7-05: grill reflects one linear polarization and transmits the perpendicular one

crossed polarizers block everything

visible light polarizing filters absorb rather than reflect the light they don't pass.

light from a bulb is unpolarized, or rather is a superposition (linear combination) of all different polarizations,
since it is generated from zillions of randomly oriented accelerating electrons. putting it through a polarizing filter
we can produce light of one polarization.

polarized sunglasses & polarization of reflected light

Liquid crystal displays (LCD): Looked at my wristwatch through polarizing filter: all appears black when
filter is rotated a certain way. The display is a sandwich of two crossed polarizers, with a mirror behind.
Light coming in that makes it through the first would be blocked by the second, except that in the sandwich there is a
liquid crystal which rotates the polarization by 90 degrees, so when the light reaches the second polarizer,
it can pass, hit the mirror, reflect, pass through the polarizer again, get rotated back by 90 degrees, and
exit the top polarizer. So the dial there appears somewhat light. To make a patch of the display appear black,
a voltage is applied across the gap between the two polarizers, which reorients the liquid crystal molecules
in that patch so that they no longer rotate the polarization. For a diagram with explanation see last years notes:
search for 11/20 at http://www.physics.umd.edu/grt/taj/104a/104anotessupps.html

---

Monday 11/16

N1-41 RAINDROP RAY MODEL

LITTLE HEADPHONE SPEAKER, SIGNAL GENERATOR, AND RADIO

Rayleigh scattering - blue, red, and white sky
speed of light in matter
refraction & reflection at interfaces - A nice illustration of the same principle with waves on a rope is here:
http://www.surendranath.org/Applets/Waves/TwaveRefTran/TwaveRefTranApplet.html
When the applet opens, the "free end reflection" is selected. Change this to "thicker to thinner", and then "thinner to thicker",
to see how a reflected wave is generated when the rope thickness, and hence the wave speed, changes.]

rainbow - A good explanation of rainbows, including a very illuminating applet, is at this link.

---

Friday 11/13

Exam2

---

Wednesday 11/11

Review

---

Monday 11/9 

K8-51 MICROWAVE OVEN

K8-52 MICROWAVE MAGNETRON

N1-05 SPECTRA - VISIBLE AND INVISIBLE

class taught by Prof. Greene.  He showed these power point slides.

	AM radio	FM radio	Cell phone	Microwave oven	Visible
frequency	550-1600 kHz	87-106 MHz	870-895 MHz	2.45 GHz	450-800 THz
wavelength	300 m (1 MHz)	3 m (100 MHz)	30 cm (1 GHz)	12 cm	0.6 microns (500 THz)
bandwidth	10 kHz	200 kHz	30 kHz

- how microwave ovens work

- thermal radiation; dependence of spectrum on temperature

- visible light wavelengths are around a million times shorter than cell phone wavelengths, and the frequencies are
correspondingly about a million times higher.

- visible spectrum is a tiny slice of a huge expanse of frequencies/wavelengths- see book or Prof. Greene's slides.

---

Friday 11/6

M9-03 CIRCULAR POLARIZATION - STICK MODEL

K8-42 RADIOWAVES - ENERGY AND DIPOLE PATTERN

K8-01 ELECTROMAGNETIC WAVE - MODEL

K8-03 LIGHT NANOSECOND

- linear & circular polarization - a very nice applet demonstrates this. Horizontal plus vertical polarization
combines to 45 degrees polarization when added in phase, and combines to circular polarization when added
one quarter of a cycle out of phase. In between yields elliptical polarization. To see this in the applet, set the
phase difference to 0 (45 degrees), 0.5 pi (clockwise circular), -0.5 pi (counter clockwise circular).

- relation between E and B in plane waves: E = cB

- em waves carry energy

- AM & FM radio signals

- carrier frequency & bandwidths for AM, FM, cell phones

---

Wednesday 11/4

K3-03 DEMOUNTABLE TRANSFORMER - V VS N - PROJ METER

K7-61 TESLA COIL

K8-42 RADIOWAVES - ENERGY AND DIPOLE PATTERN

K8-01 ELECTROMAGNETIC WAVE - MODEL

K8-05 ELECTROMAGNETIC PLANE WAVE MODEL

- Discussed Table 13.1.1, sources of electric and magnetic fields.

- Discussed the purely theoretical nature of Maxwell's discovery that changing electric fields
  must be a source of magnetic fields, and that this leads directly to the existence of electromagnetic waves
  that travel at the speed of light.

- Explained induction in the Tesla coil demo, then in the transformer demo.

- Showed applet explaining the concept of electromagnetic radiation from accelerated charges.
  The key idea is that the change of the electric field travels at the speed of light.
  http://webphysics.davidson.edu/applets/retard/Retard_FEL.html
  The applet illustrates the concept that when a charge accelerates, distortions in the electric field
  lines propagate outward at the speed of light. These distortions amount to the electric part of
  electromagnetic waves. Try setting the demo button in the upper right on "inertial", with v=0.
  Then suddenly slide the slider to nonzero velocity, and watch the shift in electric field lines
  propagate outward. Notice that the kink becomes more and more perpendicular to the direction
  of propagation as it goes out. The kink represents a "sideways" electric field vector, showing
  the polarization of the wave. Next, set the button to "SHO", simple harmonic oscillator, and
  put the velocity slider on, say v = 0.7. (This is the speed in units of the speed of light, i.e. v = 0.7 c.)

- Used the wave models K8-01 and K8-05 to explain the nature of the electric and magnetic
  fields in an electromagnetic wave.

- Demonstrated em waves with K8-42, and pointed out that these waves carry energy.

---

Monday 11/2

K2-62 CAN SMASHER - ELECTROMAGNETIC

K2-43 LENZ’S LAW - PERMANENT MAGNET AND COILS

K2-02 INDUCTION IN A SINGLE WIRE

K2-61 THOMSON’S COIL

K2-44 EDDY CURRENT PENDULUM

RELAYS TO PASS AROUND THE ROOM

- This class was all about electromagnetic induction, and Lenz' law. See the demos for the topics covered.

- Principle of operation of a transformer explained. The primary and secondary voltages are related by
 V_s/V_p = N_s/N_p, where V_s,p is the voltage across the pimary and secondary coils, and N_p,s is
 the number of turns in the two coils. This is true since each turn of wire contributes the same amount to the induced voltage.
 (I don't claim that this is a complete explanation.)

---

Friday 10/30

K1-03 FORCE ON CURRENT IN MAGNETIC FIELD

K2-01 EARTH INDUCTOR

K2-02 INDUCTION IN A SINGLE WIRE

K4-21 ST. LOUIS MOTOR

K4-41 MOTOR-GENERATOR PAIR

- This class focused on motors and generators, and induction. 

- This website illustrates very nicely how a "3-phase AC brushless motor" works:
   http://www.st.com/stonline/products/support/motor/tutorial/motor.swf
   Under the "Motor Type" tab at top in the middle, select "Asynchronous motor (indcution)".
   Then use the green arrow buttons in the lower left to step through the demonstration.

- This website explains much about the "Hybrid synergy drive" used in the Toyota Prius and other
   cars: http://www.hybridsynergydrive.com/en/start.html
   Run your cursor up to the words "Control panel" at the top and you get a list of topics.

---

Wednesday 10/28

J5-20 OERSTED EXPERIMENT - LARGE COIL AND COMPASS

K1-01 FORCE BETWEEN CURRENT-CARRYING WIRES

K1-03 FORCE ON CURRENT IN MAGNETIC FIELD

K1-05 FORCE BETWEEN CURRENT-CARRYING COILS

K1-12 CATHODE-RAY TUBE - DEFLECTION BY MAGNET

J6-04 LOW POWER - HIGH FORCE ELECTROMAGNET

ELECTROMAGNETIC BUZZER

-  parallel currents attract, antiparallel ones repel.

 - magnetic force on a moving charge, the so-called
   Lorentz force: the magnitude is F_magnetic = q v_perp B, where q is the electric
   charge, v_perp is the component of velocity perpendicular to the magnetic field, and
   B is the magnetic field strength. The direction of this force is perpendicular to both
   the velocity and the magnetic field. Between the two directions, it is the one your
   palm faces when your thumb points along v and your fingers point along B.

---

Monday 10/26

J7-01 LODESTONE

J5-04 MAGNETS

J7-13 CURIE POINT OF NICKEL

J5-05 MAGNET MODEL - FIELD LINES

J5-20 OERSTED EXPERIMENT - LARGE COIL AND COMPASS

K5-32 RESISTANCE VS DIAMETER AND LENGTH

K5-36 RESISTORS AT LN TEMPERATURE - LIGHT BULB INDICATOR

Electrical resistance of a wire

1) is proportional to length of the wire
2) is proportional to reciprocal of cross-sectional area of wire
         (see demo K5-32)

Resistance R of a material depends on temperature T. For conductors,
R increases with T, because electrons are deflected more often by
vibrations of the material. For semi-conductors, R decreases as T increases,
because more electrons are liberated to participate in the current (see demo K5-36).
For superconductors, the resistance is ZERO below some critical
temperature. So far the highest such temperature is 138K.

============================
MAGNETISM

Lodestone: naturally occurring magnetic material

Earth as a magnet

magnetic poles, dipoles, and impossibility of single isolated poles

magnetic polarization

All matter contains microscopic magnets (I'll explain what they are shortly),
but in most matter they all cancel each other out by opposite orientations.
In a few materials, called ferromagnetic, the micro-magnets "freeze"
into alignment with their neighbors, within magnetic domains. Normally these domains are
many, and their magnetization is randomly oriented, so there is no net magnetic dipole.
But if you place a magnet near such material, the domains aligned with the outside magnet
will grow, while the neighboring domains will shrink, thus producing an overall magnetization
of the material, which is therefore attracted to a magnet. We can "melt" the domains by raising the
temperature above a certain temperature, called the Curie point (see demo J7-13).

magnetic field: vector, determines the force at a given location on a magnetic pole, similar to electric field.
Magnetic field lines are curves aligned with the magnetic field vector at each point. They can be visualized
by displaying how little magets align (see demo J5-05).

key discovery of magnetism: In 1802, two years after Volta's invention of the battery ("voltaic pile"),
Romagnosi discovered that an electric current will make a magnetic needle deflect. Nobody noticed,
and it wasn't until 1820 when it was rediscovered by Oersted that it became widely known.
(See demo J5-20). This turns out to be the key to a complete understanding of magnetism and its
relation to electricity. It shows that magnetism is an electrical effect of moving charges...

---

Friday 10/23

K5-12 BATTERY AND CURRENT - WORKING MODEL

K6-03 SERIES AND PARALLEL LIGHTS - BATTERY AND CLIP-ON WIRES

K6-01 SERIES AND PARALLEL LIGHTS - TWO BULBS

Alessandro Volta's pile
The voltage of a battery is determined by the chemical potential energy difference of the
substances that react chemically in the battery. To make a larger voltage difference, you
can stack one on top of another. Volta's pile had many stacked layers of zinc and copper
plates, separated by cardboard soaked in brine (salt water).

batteries in series: like stairs

resistance & Ohm's law: V = IR

power in an electrical circuit P = VI

minimizing power losses in transmission lines: if transmission lines deliver a given power
P = VI to a load, that determines the product of V and I, but not V and I separately. To minimize
the power losses from resistance of transmission lines from the generating plant, the current in
those lines should be minimized (the power dissipated by the resistance is I² R). Thus losses
are minimized by transmitting the power at high voltage and low current.

AC: alternating current, DC: direct current.
Most, but not all, electric power transmission these days uses AC, but DC is also used.
The long distance transfer happens at very high voltage, 100kV (=110,000 V) and above.

bulbs in series and in parallel (see demo K6-01)
--------------------------------
Here are some notes that might help you understand the material:

Relations between voltage, current, resistance, and power

Definitions:
voltage: electrostatic potential energy per unit charge at a given location; SI unit: J/C = V = "volt"
current: charge per unit time flowing past a given point; SI unit: C/s = A = "ampere"
resistance: opposition to flow of current; SI unit: V/A = Ω = "ohm"
power: energy per time; SI unit: J/S = W = "watt"

Ohm's law, holds approximately in many situations: 

V= IR,

where V = voltage drop, I = current, R = resistance

Power: If charge q moves through potential drop V it loses energy qV. The energy might
wind up as heat, or might do work. If this happens in time t then the rate of energy use is
qV/t. Since q/t is the current I, the power P is

P =VI.

We can use Ohm's law to get different expressions for the power, in case it is being dissipated
by a resistance R:

P = I² R = V²/R.

Example of demo K6-01 SERIES AND PARALLEL LIGHTS - TWO BULBS:

A100W bulb generates more light than a 40W bulb at the same voltage (120V),
so evidently it has a lower resistance (since P=V²/R). If you connect these two bulbs
in parallel, so they have the same voltage across them, then the smaller
resistance bulb will be brighter. But if they are connected in series,
i.e. so the current goes through one and then the other, they have the same current.
Since P = I² R,  the smaller resistance bulb will be dimmer!

---

Wednesday 10/21

K6-03 SERIES AND PARALLEL LIGHTS - BATTERY AND CLIP-ON WIRES

J3-22 FARADAY CAGE - ELECTROSCOPE

K5-01 PIEZOELECTRICITY

J1-13 ELECTROSTATIC INDUCTION

SI unit of electric field: N/C, same thing as V/m

shielding of electric fields by a conducting enclosure (cf. demo J3-22)

charging by induction (cf.demo  J1-13).

electric current: SI unit A = C/s  "ampere".

drift velocity of charges in wire is very slow, e.g. less than 1 mm/s.

piezoelectric voltage generation, and spark discharge.

batteries: chemical potential energy

---

Monday 10/19

J3-01 EXISTENCE OF ELECTRIC FIELDS

electric field

electrostatic potential, a.k.a. voltage
analogy with height.

electric field = voltage gradient = voltage drop/distance.

strong electric field at a sharp point on a conductor:  charge gets backed into the
corner and concentrated, producing large nearby electric fields that can lead to
corona discharge. 

---

Friday 10/16

J1-05 CHARGED BALLOONS

J1-12 INDUCTION - ELECTROSCOPE

J1-24 ELECTROSTATIC HAIR RAISING

J2-03 VAN DE GRAAFF GENERATOR WITH GROUND SPHERE

J2-14 LIGHTNING ROD SIMULATOR

- attraction of polarized neutral objects
- e.g., attraction of two neutral atoms to form a molecule: random polarizations of the atoms are correlated and they attract
- e.g. gecko feet: zillions of tiny hairs provide cotnact with walls or ceiling.
- artifical gecko feet material. The movie of ``gecko tape" I tried to show is here.

- van de Graaff generator
- corona discharge at a sharp point
- lightning rods

National Oceanic and Atmospheric Administration information on lightning:
http://www.nssl.noaa.gov/primer/lightning/ltg_basics.html
http://www.srh.noaa.gov/mlb/ltgcenter/whatis.html

---

Wednesday 10/14

J1-05 CHARGED BALLOONS

J1-21 ELECTROSTATIC ATTRAC AND REPULS - CHARGED CYLINDERS

K5-04 PIEZOELECTRIC GUN

- Balloon rubbed on hair sticks to wall.
- Nyon cords or glass tubes rubbed by silk repel each other.
- Glass tube rubbed by silk attracted to rubber cylinder rubbed by fur.
Conclusion: whatever it is, this force can be attractive or repulsive.

- Matter is made of atoms, which are made of a tiny nucleus, 100,000 times smaller than the atom
but containing virtually all of the mass of the atom. The rest of the atom is electrons in a "cloud"
whizzing around. The electrons are structureless particles, but the nucleus is composite, made of
protons and neutrons. Protons and electrons mutually attract, that's what holds an atom together.
But two electrons or two protons repel each other. This electric force law is summarized in Coulomb's law:

Electric force = k_C q₁ q₂/r²,

where the q's are the electric charges, r is the separation distance, and k_C is the Coulomb constant.
It looks a lot like the universal gravity force law of Newton, with charge in place of mass.

The big difference now is that unlike mass, charge can be negative.
The force is repulsive if q₁ q₂ > 0, attractive if q₁ q₂ < 0.
So ++ and -- repel, while +- or -+ attract (opposites attract).
Electrons have negative charge, protons have positive charge
(thanks to Ben Franklin's naming choice --- he didn't know about electrons).

SI unit of charge: 1 C (coulomb). Charge on an electron: -1.6 10^-19 C, charge on proton
+1.6 10^-19 C. Every electron has exactly the same charge, and every proton has exactly the
opposite charge! A normal atom is neutral: it has the same number of electrons and protons,
and the total charge adds to zero.

- Silk pulls electrons off glass: the glass becomes positively charged. Rubber pulls electrons off
fur: the rubber becomes negatively charged. For any two surfaces, one will hold onto electrons
more strongly than the other, so when you bring them into contact, some electrons will transfer.
E.g. rubber tires on the road pick up negative charge. How much charge can they pick up? It's
self-limiting: once the rubber picks up some extra electrons, those repel any new electrons so
the rubber no longer holds electrons more strongly than the road, so it stops  acquiring electrons.

- A sock charged out of a dryer has a charge of maybe 10^-7 C, or around 10¹² (a trillion)
extra elementary charges, not balanced by opposite charges. That sounds like a huge number,
and it is, but it is miniscule compared with the total number of charges in the sock which is
perhaps around 10²⁵.  So only one out of every 10¹³ charges is imbalanced. 

- So why does the balloon stick to the wall? Yes, it is charged negatively, but the wall is neutral,
so why should there be any net force at all? Why doesn't isn't the attraction canceled by the
repulsion?

- Answer: the wall is made of positive and negative charges. The negatively charged balloon
pushes the electrons in the wall a little bit away, leaving a slighly positively charged surface.
The balloon is attracted to the positive charges, and repelled by the negative ones. Since the
positive charge is a little closer, the attraction is a little stronger than the repulsion, so the
net effect is attraction. The separation of positive and negative charges is called
charge polarization.

---

Monday 10/12

H4-31 VIOLIN

H4-34 GUITAR AND OSCILLOSCOPE

H3-24 OPEN AND CLOSED PIPES

G2-01 MASS ON SPRING - HAND HELD

BOTTLES

- First, to clear up something I mentioned earlier, here is an animation showing how a
standing wave like on a string can be represented as a superposition of two oppositely
moving traveling waves.  Where the waves are both positive they add, where one is negative
they subtract. One of the black dots is at a node, always cancelling, and the other black dot
is at an antinode, with maximal excursion.

http://www.kettering.edu/~drussell/Demos/superposition/super3.gif

- Resonance: violin bow feeds energy into the string vibration at its natural frequency.

- Drum head overtones are not in a harmonic series

- Superposition of waves or signals: adding them together

- Wave interference: enhancing or cancelling of superposed waves  (constructive or destructive interference).

- Beats: two sound sources with nearby frequencies will combine to produce a sound
  with a pulsing magnitude. I showed how this can be used to tune a guitar. As an example,
  suppose you sound a 440 Hz string vibration and another, 441 Hz vibration. If they
begin in step, they will go out of step, since the first one takes 1/440 second to complete
a cycle, while the scond one takes only 1/441 seconds. As the cycles continue, the
two will get more and more out of step, until at some point they will be completely
opposed, at which point the superpositions of the sound they make will tend to cancel,
suppressing the loudness. After one whole second, the first one will have completed 440 cycles,
and the second one 411 cycles, so they are once again in step. So the beating itself completes
a cycle in 1 second, i.e. it ihas a beat frequency of 1 Hz. If the other string had a frequency
of 442 Hz, it would complete 2 cycles more per second than the first string, so the beat
frequency woudl be 2 Hz. In general, the beat frequency is the difference of the two
frequencies. Here is an applet demonstrating beats visually:

http://www.kettering.edu/~drussell/Demos/superposition/super4.gif

And here is one I showed in class, demonstrating beats with an audio signal:
http://qbx6.ltu.edu/s_schneider/physlets/main/beats.shtml


- I started to explain the Pythagorean comma and the relation to the 12 tone muscial
scale, but I wasn't very clear and didn't have enough time. Here follows
what I was trying to explain. (You are not responsible for this material except for the
nature of the intervals of an octave and a fifth. I include it just for your interest.)

Octaves, fifths, the Pythagorean comma, and equal termperament

A vibrating sring has overtones with frequencies that are an integer multiple of the fundamental,
f₁, 2f₁, 3f₁, 4f₁, ... The frequency of the first overtone is twice that of the fundamental, and the interval
between those two pitches is called an octave. Any doubling of frequency corresponds to an octave. But
what is the interval between the second harmonic 2f₁ and the third harmonic 3f₁? The frequency ratio is
3/2, and the interval is called a fifth.

Octaves and fifths are pleasing to hear, so it's natural (at least mathematically...) to repeat them and collect
the resulting notes into a scale, including any octave of any note, since octaves "sound the same".
So let's see what we get if we start adding notes by repeating octaves and fifths.

We begin with the octaves of the fundamental, f₁, 2f₁, 4f₁, 8f₁, ... We could also take the ones below,
for example (1/2)f₁, (1/4)f₁, (1/8)f₁, ... but I'll stick with the ones above here. Next I'll add (3/2)f₁,
the fifth above f₁. This note lies between f₁ and the first octave above that, 2f_1. Now a fifth above the
first one would have frequency (3/2)(3/2) f₁ = (9/4) f₁. This lies above the first octave, since 9/4 is
greater than 2. We can shift it down an octave by dividing its frequency by 2. This yields (9/8) f₁,
which lies between f₁ and the first octave 2 f₁. We could keep going, the next fifth would be at
(3/2)³ f₁ = 27/8 f₁, which shifted down below the first octave becomes 27/16 f₁, etc.

Now the question arises, can we ever stop?! What if we keep going up by fifths, do we ever get to some
whole number of octaves? Mathematically, the question is this: are there two whole numbers, n and m,
such that (3/2)ⁿ = 2^m? The answer is NO! The reason: 2 and 3 are relatively prime numbers.

So how close can we get? It turns out that the first time we get close enough for the human ear to hear
the pitches as purdy darn close is when n = 12 and m = 7:

(3/2)12 = 129.7,                27 = 128

The gap between 12 fifths and 7 octaves is called the Pythagorean comma.

In equal tempered tuning, the gap is completely eliminated, in the sense that fifths are not used: the fact that
there are 12 fifths gives rise to the idea of equally dividing an octave into twelve intervals, each with frequency
ratio 2^1/12 = 1.05946... Each of these intervals is called an (equal tempered) half-step. Doing so makes it possible
to begin a scale on any note and have a completely equivalent set of intervals. But note that then no intervals
except the octave match exactly the simple integer ratios like the fifth: The equal tempered fifth is 2^7/12 = 1.49831,
wheras the perfect fifth is 3/2 = 1.500000.

---

Friday 10/09

Exam 1

---

Wednesday 10/07

review for the exam

---

Monday 10/05

H4-23 SOUND BOARD - TUNING FORK AND LECTURE TABLE

H4-34 GUITAR AND OSCILLOSCOPE

H3-24 OPEN AND CLOSED PIPES

G3-28 SUSPENDED SLINKY

H4-31 VIOLIN

H3-14 TWIRL-A-TUNE

G3-21 TRANSVERSE WAVES ON A LONG SPRING

HELIUM TO BREATHE AND TO PUT IN TUBE

- more on string waves; demonstration of string harmonics with demo G3-21

- to hear the sound well you need to move some air, which a string or a tuning fork by itself doesn't do very well.
  After hitting the tuning fork I placed it on the bridge of the violin and guitar and you could hear it much louder.
  Actually the guitar allowed you to hear the fundamental, but the violin body is so small that it could only resonate
   at the first harmonic above the fundamental (plus higher harmonics).

- what is a sound wave? longitudinal (along the direction of propagation of the wave) compression and rarefaction
   pattern moving through the air, making a pattern of over-pressure and under-pressure deviations from the average
   room pressure. The pressure variations are very small.

-  Human hearing: When variations in pressure hit your ear drum, they shake it, and it sends the sound on to your
   inner ear where it is picked up by the movement of tiny hairs connected to nerves.
  
      + Human hearing is extremely sensitive. An ear can pick up variations of pressure as small as one part in a
         billion. In terms of energy, the quietest sound that can be heard carries a power (energy per unit time) of
         10^(-16) watts  per square centimeter. An ear opening is smaller than a square centimeter, but then the ear
         itself probably gathers sound and funnels it in, so probably the minimum power you can hear is around
          10^(-16) W. That's really tiny. For instance, compare it to the power to raise one gram 1cm in 1 s,
         mgh/second = 10^(-3)kg (10 m/s^2)(10^(-2)m) = 10^(-4) W. So you can hear sound with a power that is
         one TRILLIONTH (10^(-12)) of this tiny lifting power rate!

      +  Humans can hear sound from 30 Hz to 20,000 Hz. Some other animals can hear much higher frequencies.
           Elephants can hear lower frequencies: http://www.lsu.edu/deafness/HearingRange.html

-  sound modes/harmonics in pipes. Good demo is the twirl-a-tune. An open end of a pipe is a pressure node: the pressure
   must match room pressure.
  
-  Example of demo H3-24 OPEN AND CLOSED PIPES. The open pipe has pressure nodes at both ends, whereas the
   pipe closed on one end has a pressure node at the open and and an antinode at the closed end. Therfore the half-closed
   pipe is like a pipe twice as long, open at both ends. So it's fundamental pitch has half the frequency, i.e. it's an octave
   below the open pipe. (You can hear this at the demo link.)

  

---

Friday 10/02

H4-34 GUITAR AND OSCILLOSCOPE

G2-01 MASS ON SPRING - HAND HELD

G3-28 SUSPENDED SLINKY

- Discussed the operating principles of clocks, as in the textbook.

- Guitar string as a harmonic oscillator: the period determines the pitch or frequency we hear,
   and the pitch is the same no matter what the amplitude of vibration is, so evidently it's a harmonic oscillator!

- Ubiquity of harmonic oscillators: for almost any system, iif you push it away from its equilibrium configuration,
  the restoring force will be proportional to the displacement, for sufficiently small displacements.
  The displacement of a guitar string, for example, is indeed small.

- A guitar string can vibrate with many different pitches. This is because the string can wiggle in so many ways.
   The lowest frequency vibration is called the fundamental mode, or sometimes just the "fundamental". The
    higher frequency vibrations are called harmonics, and they have frequencies that are multiples of the fundamental.
    In a given harmonic mode, the string is divided into a whole number of sections in which it vibrates in alternating
    directions. The sections meet at nodes where there is no vibration. The positions of maximum vibration are called
    antinodes. The fundamental mode of a guitar string has just two nodes, one at either end of the string where the
    string goes over the nut and the bridge. Normally when the string is plucked many harmonics are present simultaneously.
    You mainly hear the fundamental, but the combination of the different harmonics with the different weights gives the
    string its characteristic timbre, i.e. musical "tone quality". The combination of waves added together is called
    superposition of waves. You can selectively emphasize a specific harmonic by touching the string lightly where
    that harmonic would have a node, then plucking the string, and immediately withdrawing your touching finger. Then
     all harmonics that don't have a node where you touched the string will be suppressed.

-  The frequency or period of a guitar string in the fundamental mode is determined by the length, mass, and tension
   of the string. I explained how these affect the period, using the concept of restoring force and inertia. One thing
   worth spelling out here: why does increasing the length increase the period? Answer: the restoring force for a given
    transverse displacement is less for a longer string, since the string is stretched less. In the higher harmonic modes,
    the effective length of the string is just the distance between two adjacent modes. The period is decreased, since the
    restoring force is increased.
   
-   Sound waves, speed of sound at 0 °C and atmospheric pressure is about 331 m/s.

-  Wave speed = wavelength/waveperiod = wavelength x frequency. So, what's the wavelength of A 440 Hz
   (1 Hz = 1 cycle/s = 1 hertz)?
  Answer: wavelength = wavespeed x waveperiod = wavespeed/frequency =~ (330 m/s)/(440 cycles/s) = 3/4 m/cycle.

---

Wednesday 9/29:

G1-15 PENDULA WITH 4 TO 1 LENGTH RATIO

G1-33 MASSES AND SPRINGS WITH SPIDER

C8-01 GIANT PENDULUM

- oscillation: repeating motion around an equilibrium configuration

- amplitude: magnitude of largest displacement from equilibrium
- period: time for one complete cycle
- restoring force: force pulling back towards equilibrium
- harmonic oscillator: period is independent of amplitude. this happens
  if the restoring force is proportional to the diplacement away from equilibrium.
  An oscilator that is not harmonic is called anharmonic.

- Period determined by restoring force and the inertia (mass). Greater restoring force
produces greater acceleration and thus shortens the period; greater inertia implies
less acceleration (for the same force) and lengthens the period.

- pendulum:
1) almost a harmonic oscillator, as long as amplitude not too large.
(graph illustrating how the period of a pendulum depends on the amplitude)

2) period is independent of the mass! This is because the restoring force is due to gravity,
which is proportional to the mass, so the acceleration is independent of the mass
(just like for a falling object). Period of a pendulum of length L is 2pi times the square root
of L/g, (where g is the acceleration due to gravity).

---

Monday 9/27:

- reviewed entropy, second law, and first law, and principle of a heat pump

- Example: How much work must an ideally efficient refrigerator with inside temperature 270 K (-3 celsius)
do to pump 900 J of heat out of the fridge, if the room temperature is 300 K (27 celsius)? Answer: Since the
fridge is ideally efficient, that means that the next entropy change is zero. This allows us to figure how much
heat must go into the room:  the entropy increase of the room must equal the net entropy decrease of the
fridge:  Q_room/300 K = 900 J/270 K, hence Q_room = 900 J (300 K/270 K) = 1000 J.  So 1000 J goes into
the room, but only 900 J of that originated as thermal energy in the fridge. Energy is conserved, so the remaining
100 J must have come from somewhere, and that somewhere is the work done by the fridge condensor pump motor.
That is, 1000 J = 900 J + W, hence W = 100 J.

- Using a heat pump to heat a house: reconsider the previous example, but let the outside of the house in winter
play the role of the inside of the refrigerator. Then an ideal heat pump can transfer 900 J of heat from the outside
air at 270 K into the house, provided the pump consumes 100 J of work, and dumps a total of 1000 J into the
house.  This is really striking: instead of paying for 1000 J of heat coming directly from electric, gas or oil heaters,
one can (ideally --- not in the real world) get 1000 J for the price of 100 J of work, by moving the remaining 900 J
of thermal energy from the outside to inside.

- Efficiency and temperature difference: the greater then temperature difference, the more work must be done to
move a given amount of heat "uphill" to a higher temperature. That's why the most efficient heat pumps for
heating houses use not the thermal energy of the air, but the thermal energy of the ground. Even in dead of winter,
the ground a few feet down below the surface stays at around 50 Farenheit, or 10 celsius, or 283 K. Re-doing the
above calculation, with 270 K replaced by 283 K, we get Q_room = 900 K (300/283) = 954 J. So it only takes
954 J - 900 J = 54 J of work to pump the heat, rather than 100 J as before.

- Heat engines: If you run a heat pump backwards, you can take heat from a higher temperature body, let some of
it flow into a colder temperature body, and take the rest of it as work. A maximally efficient or ideal heat engine
is one that does not increase entropy, since then the minimum amount of heat is dumped, and so the energy
extracted as work is maximized. Example: a steamboat engine operates with steam at 500 K and dumps heat
into the air at 300 K. How much work can be obtained form 1000 J of steam heat, if the engine is ideally efficient?
Answer: The entropy increase of the air is equal to the entropy decrease of the steam: Q_air/300 K = 1000 J/500 K,
hence Q_air = 600 J. That is, just to satisfy the 2nd law, at least 600 J of heat must be dumped into the air.
Hence the maximum work that can be obtained from the 1000 J of heat is 400 J. Note that the higher the temperature
of the steam, the more efficient the engine can be, since for a given amount of steam heat, the entropy of the steam
decreases by less, so the heat dumped can be less. For example, if the steam operated at 1000 K, the minimum heat
dumped into the air would be given by Q_air/300 K = 1000 J/1000 K, so Q_air = 300 J, so in this case there would
be 700 J left over for work.

- Ideal heat pumps and engines and reversibility: If entropy increases in a process, then the time reversed process
would decrease entropy, in violation of the 2nd Law of Thermodynamics. So such a process cannot be reversed.
If on the other hand the entropy remains unchanged, then the process can be reversed. Hence an ideal heat
pump or engine is a "reversible" one.

- Internal combustion engines: I basically covered what is in the book. I also showed some diagrams and moving part
animations from a Wikipedia article, http://en.wikipedia.org/wiki/Internal_combustion_engine

---

Friday 9/25:

Demos:

I5-11 ADIABATIC PROCESS - AIR PISTON WITH THERMISTOR

I5-12 ADIABATIC EXPANSION OF AIR - FOG IN BOTTLE

I5-21 HEATING AIR BY COMPRESSION

- Heat flows naturally from hot to cold. Why? Increase of disorder, increase of entropy.

- How to make heat flow from cold to hot? Must do work, which ends up as extra entropy.

- How an air conditioner or refrigerator works.

- What determines the minimum amount of work required to pump a given amount of heat against the natural flow.


Supplement for Chapter 8:
Entropy change as a quantitative concept, and the efficiency of heat pumps and engines

As discussed in the textbook, entropy is a measure of disorder. When heat Q goes into a system in equilibrium
at a temperature T, the disorder increases. If the system is already very hot, it is already very disordered, so the
disorder increases less than it would if the same heat went into a colder system. Entropy gives a way of quantifying
the disorder: when heat Q goes into (or out of) a system at absolute temperature T, the entropy increases (or decreases)
by Q/T,

(1)     Entropy change =  Q/T = (heat into system)/(temperature of system)

This entropy change for a given heat transfer is inversely proportional to the temperature. For example, at twice the temperature,
the entropy change is half. With Q in Joules, and T in degrees Kelvin, the units of entropy are J/K.
The concept of entropy was originally formulated purely using the concepts of heat and temperature in this way.
The connection to disorder, which can be quantified using probability theory, came later. Since T is a measure of
the average thermal energy per particle motion, the entropy basically measures how many units of thermal energy there are.

Entropy increases when heat flows from a hotter body at temperature T_h to a colder one at temperature T_c < T_h, since then
Q/T_c > Q/T_h. The reverse direction, flowing from cold to hot, would decrease entropy. The "Second Law of thermodynamics"
states that the total entopy of an isolated system never decreases.

The maximum possible efficiency of a heat pump or heat engine is governed by the Second Law: to move heat from a cold
system to a hot one without decreasing entropy, a certain minimum amount of work must be done, which winds up as extra
thermal energy delivered to the hot system. Similarly, to generate work using heat in a hot system, a certain minimum fraction
of the initial heat must be discarded as heat in a colder system.  These limiting efficiencies can be determined with a bit of
analysis. I'll now show you the actual analysis showing how these limiting efficiencies can be determined. I do so because it's
pretty simple, and I think it's impressive how such a profound conclusion follows from a little bit of reasoning.

If a heat pump (refrigerator) moves heat Q_c from a cold system (the refrigerator) to a warmer system (the room),
that would violate the second law of thermodynamics unless the heat Q_h dumped into the room is greater than the
heat taken out of the fridge. Specifically, in order not to decrease entropy, it must be that

(2)     Q_h/T_h  ≥  Q_c/T_c,

hence

(3)     Q_h  ≥  Q_c (T_h/T_c).

The amount of heat is dumped is minimized when the entropy does not change at all, in which case the ≥ is replaced by =.
When the entropy does not increase, the heat pump is called ideal. In this case, since entropy did not increase, it
can also be run backwards without violating the second law, so it is reversible. The conclusion is that
the most efficient heat pump is a reversible one.

Now we can see what is the minimum amount of work W that a heat pump must do in order to transfer heat Q_c from
temperature T_c to temperature T_h. (This is given in the book by the otherwise mysterious formula (8.1.2), without
derivation there.) Since the total energy is conserved (the "First Law of thermodynamics") the total heat deposited in
the hot system at temperature T_h is the sum of the heat removed plus the work,

(4)     Q_h = Q_c + W. 

(This is different from (8.1.2) because the  textbook  seems to have taken -Q_c to mean the heat removed from the
hot object, rather than Q_c as done here.) Now (3) and (4) imply

(5)     Q_c + W  ≥  Q_c (T_h/T_c).

Subtracting Q_c from both sides we learn then

(6)     W  ≥  Q_c (T_h/T_c - 1) = Q_c (T_h - T_c)/T_c.

The lower limit on W occurs when ≥ is replaced by =, corresponding to no entropy change, i.e. an ideal
heat pump.  Note that the mimimum work required increases as T_h goes up: it take more work to run
a refrigerator in a hot room than in a cooler room (even neglecting the heat flow from the room through the walls
of the fridge).

Similar reasoning can tell us how much work W can be done if heat Q_h is provided to a heat engine (like a car motor),
if the motor heat is at temperature T_h and the engine dumps heat Q_c into the environment at the colder temperature T_c.
The dumped heat can't be zero, since that would mean entropy decreased, but it can be smaller than the suppled heat Q_h,
since T_c is less than T_h. Since we're starting with Q_h, and entropy must increase, the opposite of (2) must be satisfied,

(7)     Q_h/T_h  ≤  Q_c/T_c,

or

(8)     Q_h (T_c/T_h)  ≤ Q_c.

Once again energy conservation (4) holds, so we can replace the dumped heat Q_c in (8) by  Q_h - W,

(9)     Q_h (T_c/T_h)  ≤  Q_h - W.

A little algebra then yields

(10)    W  ≤  Q_h (1 -  T_c/T_h) = Q_h (T_h - T_c)/T_h.

The ideal case is when the entropy remains unchanged, so the engine is reversible. In that case, the amount of
work W you can get out of the input heat Q_h is given by (10) with ≤ replaced by =. Notice that if the environment
is at absolute zero of temperature, T_c = 0, then W = Q_h, i.e. all the heat goes into work! But in any other case,
some of the input heat is inevitably lost as dumped heat.

---

Wednesday 9/23:

Demos:

I4-33 CRYOPHORUS

I4-19 CONDENSATION OF STEAM - SODA CAN COLLAPSE

THERMOMETER WITH LARGE DIGITAL READOUT, AND BEAKER OF WATER

- Why the ideal gas law holds: So, if a gas like air is almost all empty space, how can it exert a pressure?
Answer: zillions of collisions of the molecules. The molecules are tiny, but going really fast (eg about
500 m/s in room air) and there are zillions of them of order 10^25 in a cubic meter of air). Pressure
increases with the number of molecules, the speed of the molecules, and the mass of the molecules, the other
things being held fixed. There is a simple formula for the pressure in terms of the particle density rho_particle
and the temperature T, the ideal gas law:

p = k rho_particle T

where k = 1.38 x 10^(-23) Pa m^3/kg particle is a constant, called "Boltzmann's constant".
The pressure is the average force exerted by collisions of the molecules with the wall.
This is obviously proportional to the number of molecules per unit volume, i.e. the particle density.
The rate of collisions is proportional to the speed of the molecules v, and each molecule collision at the wall flips
velocity component perpendicular to the wall, so the acceleration is proportional to v, and therefore the force
is proportional to mv. Together the rate of collisions and the force per collision are thus proportional to mv^2,
twice the kinetic energy, whose average is proportional to the temperature.  Hence the pressure is also
proportional to the temperature.


-  Avogadro's principle:  The number of molecules in a (low density) gas is completely determined by the
volume, pressure and temperature of the gas, and in particular is independent of the type of molecule. This
follows directly fmor the ideal gas law.

- Because of Avogadro's principle, a helium balloon at room temperature and pressure has the same
number of molecules in it as an equivalent sized air balloon. Since each helium atom mass is only 4/28 = 1/7 of the
mass of a nitrogen molecule, the buoyancy force on the helium balloon is much greater than the weight of the balloon.

- Avogadro's principle was crucial in the development of chemistry, since it allows the proportional number of molecules
before or after a reaction to be assessed by measuring the macroscopic quantities: volume, pressure and temperature.

- Evaporation and condensation. Latent heat. Cooling by evaporation. Heating by steam condensation.

- Boiling.

---

Monday 9/21:

Demos:

I1-63 HYDROGEN EXPLOSION

I2-06 THERMOPILE WITH AUDIO OSCILLATOR

I4-52 CARBON DIOXIDE BALLOON ON LIQUID NITROGEN

I4-14 CHANGE OF STATE WITH BANG

- radiation from a hot source, ice and a body is different and depends on the temperature of the object

- most of the energy from an incandescent bulb is wasted in the infrared region of the EM spectrum

- what temperature is a measure of

-  specific heat (heat capacity)

-  latent heat

---

Friday 9/18:

Demos:

F2-12 HOT AIR BALLOON

I3-33 HELIUM BALLOON ON LIQUID NITROGEN

I1-11 THERMAL EXPANSION - BALL AND HOLE

I1-13 THERMAL EXPANSION - BIMETAL STRIP

I1-18 BIMETALLIC STRIP THERMOMETERS

I2-11 THERMOS BOTTLE

I2-22 THERMODYNAMICS BY TOUCH

I2-43 CONVECTION - HOT PLATE

- ideal gas law

- nice applet about the ideal gas law

- heat conduction, convection, and radiation

---

Wednesday 9/16:

Demos:

C7-17 SUPERBALL

I3-33 HELIUM BALLOON ON LIQUID NITROGEN

I3-12 WATER BAROMETER - CAN CRUSHER

- why doesn't the atmosphere fall down and collect on the ground?

- demonstration that air has very low density

- distance between air molecules roughly 10 times greater than size of a molecule

- atmospheric pressure

- absolute temperature scale

---

Monday 9/14:


Demos:

F1-01 FLUID PRESSURE VS. DEPTH

F1-04 EQUILIBRIUM TUBES

F1-06 WATER SEEKS ITS OWN LEVEL

F2-05 BUOYANCY - BOAT AND ROCK

F2-21 REACTION TO BUOYANT FORCE

HELIUM BALLOON

- pressure

- increase of pressure with depth

- Archimedes' principle

- air pressure

---

Friday 9/11:

Demos:

F1-11 HYDRAULIC PRESS

C6-11 SLIDING FRICTION - LECTURE TABLE AND FELT

RAMP, SKATEBOARD, AND LEAD BRICK

BICYCLE WHEEL

- mechanical advantage

- ramps

- friction

- wheels

- bearings

---

Wednesday 9/09:

Demos shown:
B3-13 PULLEY VS NO PULLEY

- universal gravity

- energy, force and work

- mechanical advantage

---

Monday 9/07: LABOR DAY

---

Friday 9/04:

- units. 1 kg = 1000 g, 1 g = mass of 1 cubic centimeter of water (at a standard temperature and pressure). Actually the
  kilogram is defined today in terms of a particular object: http://physics.nist.gov/cuu/Units/kilogram.html One day it will
  be defined in terms of the mass of some type of atom, once our ability to measure such things improves some.

- Newton's three laws

- vector notation

- units of acceleration, mass, and force

- gravitational force: peculiar property of being proportional to mass. Near surface of earth, F = mg,
  downwards, where g = 9.8 m/s^2 is the "gravitational acceleration".

- This arises from a universal law of gravitational attraction: any two masses, m1 and m2, separated
  by a distance d, exert a force of attraction on each other given by F = G (m1 m2)/d^2. Here G is a
  constant of nature, called "Newton's constant".  It is equal to the force in newtons between two masses
  of 1 kilogram each separated by a distance of 1 meter. The direction of this force is towards the attracting mass.
  The pull of the masses in the Earth adds up to a pull  toward the center of the Earth. The same law of attraction
  applies to the sun, the other planets, other stars, etc.

- How G is measured: one common method uses a little dumbbell hanging from a thin glass fiber and twisting back and forth
  in the presence of known masses. The gravitational force of the masses changes the twisting frequency. More recently,
   G has been measured (to somewhat lower accuracy) using a beam of atoms, exploiting the quantum mechanical
   wave-like nature of matter.

---

Wednesday 9/02:


Demos shown:

C8-21 ROCK AND WASTE BASKET

C3-05 INERTIA - PEN IN BOTTLE

C3-12 PENCIL AND PLYWOOD

C8-01 GIANT PENDULUM

A2-22 MAGNETIC VECTORS - LECTURE HALL

- More on inertia and mass

- definition and a bit of the origin/nature of the units of length (m), time (s) and mass (kg). For much more on this, see
  International System of Units (SI) This links to a website at NIST, the National Institute of Standards
  and Technology, located in Gaithersburg, Maryland. It has really nice brief summaries of the historical context
  of the SI base units, and their present definitions.

- 1 meter was originally defined as 1/10,000,000 the distance from the equator to
   the north pole. For history and later definitions see http://physics.nist.gov/cuu/Units/meter.html

- Newton's third law

- velocity & acceleration vectors

---

Monday 8/31:

Demos shown:
C8-01 GIANT PENDULUM
C3-04 INERTIA - LEAD BRICK AND HAND

- Introduction to the course: logistics, and topics.

- Energy: governs all of physics.  Amid all the transformations of nature, it changes from one form into another,
  but the total quantity of energy doesn't change, i.e it is conserved. (Analogy with money,

- Forms of energy: kinetic energy = energy of motion, and potential energy = energy of configuration.
  Potential energy has various forms, depending on the nature of the interaction that stores the energy:
  gravitational, electric, nuclear. Chemical energy is electric energy and kinetic energy, stored in the
  microscopic structure of chemicals.

- As time passes, energy changes from one form to another.  In general it spreads out into the environment,
   increasing in randomness. In the example of the pendulum, I transfer energy to it by lifting it up. That energy
   came from chemical energy in the food I ate. The plants got their energy from the sunlight. The swing of the
   pendulum slows down because some energy is transferred by rubbing at the pivot into heat, i.e. microscopic,
   disordered energy, and by collisions with air molecules, which also have disordered energy.

-  In general, the amount of disorder in the universe increases. This is known as the second law of thermodynamics.
   If you run a movie of the pendulum backwards in time, the pendulum will "spontaneously" start swinging, and its
   swing amplitude will increase with time. This will still obey the dynamical laws of physics, but there will be a "conspiracy"
   whereby the random, microscopic energy of molecules goes against the odds, and "gangs up"on the pendulum. This doesn't
   happen in nature, because, evidently, the world started out less disordered, and the disorder increases towards the future,
   rather than towards the past.

-  How do we describe what changes? For example, velocity. The rate of change of velocity is called acceleration.
   Acceleration is produced by force, "a push or a pull". The amount of acceleration of an object, when acted on by
   a certain force, depends on the mass of the object. The more mass, the less the acceleration. The resistance to
   acceleration is called inertia.

- Kinetic energy = 1/2 * mass * velocity^2

---