Phys104 - How Things Work
University of Maryland, College Park
Spring 2013, Professor: Ted Jacobson

Notes, Demos & Supplements

Please refer to notes from 2008,9,10 for many details about the material.
Here I will try to elaborate topics not adequately covered in my previous notes or
in the textbook. (Actually, I will often get carried away and write much more...)

crib sheet for exam1

crib sheet for exam 2
article about the electric power grid

Tuesday 5/7


Trichroic prism assembly sometimes used (instead of color filters over individual pixels) to split light into three color components for separate detection by camera, copier, or scanner:

Photoelectric effect: ejection of electrons from atoms by absorption of photons. This exhibits quantum physical behavior, since it requires a certain minimum energy per photon. This is illustrated with the demo P2-03 above. UV is absorbed by glass, and the ejection of the electrons from the charged zinc plate requires UV photons... (Even the fact that glass absorbs completely UV photons but passes visible ones that are maybe a factor of two lower in frequency shows that there is something "quantum" going on in the absorption process. This is an illustration of a "wave acting like a particle". Conversely, a particle can act like a wave:

Electron diffraction: We can produce a beam of electrons in a tube like K1-12. It's fun to see the electrons deflected by a magnet. Actually what we see is the light emitted by nitrogen when the electrons collide with nitrogen. Those electrons are certainly particles, but in demo P2-13 they behave like waves: the are sent through a layer of graphite (like pencil lead), which looks like layers of chicken wire, made from nothing but carbon atoms, in random orientations. Just as we saw with light wave interference from a diffraction grating or the surface of a CD or DVD, the electrons are being diffracted from the graphite. Each electron exhibits wave interference with regard to the probability of landing somewhere on the phosphorescent screen!
That means that each electron somehow doesn't have a definite location, but passes by many carbon atoms "at once". I showed that the diffraction angle, and hence the wavelength of the electron/wave, is smaller for higher energy electrons. In fact, the wavelength is inversely proportional to the velocity, a fact that is directly related to Heisenberg's uncertainty relation. The velocity is proportional to the square root of the kinetic energy E, hence wavelength ~ 1/sqrt[E].

X-rays: see textbook

CT (Computed tomography)

MRI (Magnetic resonance imaging)

NYTimes on X-rays from scotch tape; and in Nature Magazine, with a video;  development of portable X-ray imaging devices

Thursday 5/2


- how a LASER works

- how a light emitting diode (LED) works: it's a junction between two materials in which the ground state of electrons have unequal energies. By placing a voltage difference across the junction a current can be induced to flow across the junction from the higher to the lower ground state energy side. This is sort of like a river flowing over a waterfall. The energy difference for each electron is released in a transition to the lower energy, with emission of a photon. The rate of light emitted is determined by the voltage difference. This is a very direct, super efficient way to convert energy to light.

- a Laser Diode is a special sort of LED, for which the electrons that have flowed across the junction remain in the excited energy level for a relatively long time. Then if the junction is contained by some kind of reflecting surface photons can bounce back and forth ans stimulate the downward transitions of the population of excited electrons, all with the same wavelength and direction, and phase. That is, the diode becomes a laser! Then the light must somehow escape. For images of the architecture channeling the light away from the junction see for example

- run in reverse, an LED is a photo-diode, which absorbs photons and converts the energy into driving a current across an energy increase junction. So this is a photon detector that turns light into an electrical current. This is how electronic cameras sense light. Photo-diodes can detect photons with up to 90% efficiency. By comparison, the human eye has 1-5% efficiency, and photographic film has 2% efficiency.

- Charge coupled device (CCD):
In a camera, a planar array of photodiodes collects light and converts it into stored electrons in individual "buckets", one per pixel. To read out the information in the array the contents of the buckets is systematically shifted from one row to another, and out the bottom row, by a sequence of voltage changes.
See for an animated image. For color images, either a color filter screen is placed over pixels, or the light is split into three color types and projected onto three different CCDs. For a scanner, the CCD is not a planar array, but just a linear array of photodiodes that is swept across the image to be scanned.

- Total internal reflection

- fiber optic communication

Tuesday 4/30

- 4-cone color perception of birds

- diffraction gratings explained again. Emphasized that closer spacing of lines makes for wider spacing of diffraction pattern. So diffraction turns a small, repeated distance int a large distance. Used this to show the difference in spacing between the lines on a vinyl record, a CD, and a DVD. Here are the numbers (in class I confused the line spacing with the wavelength):

- disc formats, laser wavelengths, and capacities:

capacity per layer
wavelength in vacuum
wavelength in plastic
length of pits
between tracks

100,000 nm
700 MB
780 nm (IR)
503 nm
830 nm
1600 nm
4.7 GB
650 nm (red)
420 nm
400 nm
740 nm
25 GB
405 nm (violet)
261 nm
140 nm
320 nm

- showed electron micrograph of vinyl grooves and explained how this encodes the sound and how it is read out. Stereo records have two channels in one v-shaped groove: the two diagonal directions of motion correspond to the two channels. 

- red photon energy calculation, in J and eV (see 4/25 notes). Visible light photon energy ranges from 1.6-3.1 eV.

- "electron-Volt" eV is a useful unit of energy for photons. Photons can come from atomic or chemical energy level transitions, and these are associated with potential energy changes of the order of volts, and they can be induced by or can produce visible photons. This is why visible photon energies are in this range.

- fluorescent lamps. The important mercury transition to its ground state is is a photon of wavelength 254 nm, and energy 4.9 eV. This is beyond the visible, in the ultraviolet (UV) range. It is absorbed by glass. Isn't that remarkable, that a photon quite similar to visible ones is absorbed, while visible light is transmitted. This is because the visible photons don't have adequate energy to induce electronic transitions in the glass, but UV ones do. This in itself illustrates quantum behavior. Otherwise, I discussed aspects of the fluorescent lamp more or less as in the textbook. Note that with the diffraction grating last week we looked at the fluorescent lamps in the room and saw that although they appear white, their spectrum is NOT full of all colors, but rather has content something like this:

compact fluorescent spectrum
This combination of frequencies produces in the three cone types of our retina a similar response to what a full spectrum of white light would produce, illustrating again in what sense we are all color blind: we can't distinguish light with some very different spectral content.

LASER light: characterized by the fact that all the photons have nearly the same:
i) wavelength
ii) direction
iii) phase (they oscillate in step)

How to produce laser light: first we must take note of the fact that photons can be created in two ways when an atomic transition occurs frmo a higher to a lower energy level: 1) spontaneous emission, and 2) induced, or stimulated emission. Spontaneous emission occurs just because the accelerating electron radiates. It happens at a random time and the photon can come out in any direction. Induced emission, by contrast, occurs when an incoming photon interacts with the excited electron. That interaction shakes the electron. If the incoming photon has just the right frequency so that its energy matches the transition energy, then it can induce the excited electron to make a transition, and in the process the new photon that is generated is more likely to be an identical copy of the incoming photon than anything else. So induced emission can "clone" the photon.

Thursday 4/25


- more on the colors that arise from the optical activity (rotation of polarization vector) when light passes through the Karo Syrup. Different frequencies rotate by different amounts, so they exit the second polarizer with different intensities. As that polarizer is rotated, the intensity mix is changed and the perceived colors change.

- color perception:
explained more or less as in textbook. Going deeper, the relative intensity of response of two pairs of cones define axes in a "color space" in which all the perceptual colors can be mapped. The Chromaticity Diagram below illustrates a way of representing this space. The perimeter represents spectral colors, and is labeled by the corresponding wavelength. The line across the bottom is called the line of purples. The actual colors you see in this diagram are not completely correct because in fact any display with three types of colored pixels can only generate perceived colors inside the triangle whose vertices correspond to those pixel colors.  
                    gamut diagram

color "blindness": in the most common form, the "red" and "green" cones are closer in their spectral response than in "normal" vision. This leads to a different set of color responses.

- diffraction grating: This is an amazing but simple device. The plastic film gratings I handed out have 13,200 parallel lines per inch, which is about 5,000 lines per cm, or 0.5 lines per micron. That is, the lines are separated by 2 microns. That's too small to see. The lines in some gratings are grooves, while some are just variations in properties that affect transmission of light. The key thing is that when light passes through one of these gratings, it emerges as from line sources spaced 2 microns apart. The original light falling on the grating is generally coherent, that is, the waves are "in step" across the surface of the grating. The light of a given wavelength emerges on the other side of the grating only at those special angles for which the
waves from adjacent lines are in step, otherwise they all add destructively and cancel each other out. To be instep, the path length difference from adjacent lines must be a whole number of wavelengths. For example, for green light of wavelength 0.5 microns, the smallest such angle (besides zero) would satisfy sin(theta) = 0.5/2 = 1/4, so it would be theta = 14.5 degrees.

- atoms are microscopic antennas that can emit and absorb electromagnetic waves.
That's because they have electrons that can move around and accelerate. To illustrate the peculiar nature of atomic antennas  we looked at N2-02. Using diffraction gratings, we compared the full spectrum of white light from an incandescent bulb with fluorescent lights, and with mercury and cadmium vapor lamps. The vapor lamps showed discrete spectral colors, while the fluorescent light showed a set of 4 or 5 smeared colors. The discrete spectra are a sign of discrete structure in atoms, unique to each type of atom. That structure can be understood only with quantum mechanics. In fact, even the existence of a stable, lowest energy state of hydrogen would be impossible to explain with the physics we've discussed so far. Why? The electron would just radiate electromagnetic waves and spiral into the proton in a nanosecond! The fact that this doesn't happen can be traced to the Heisenberg uncertainty principle: the more certain is the position of a particle, the more UNcertain is its velocity. An electron could minimize its electric potential energy by getting closer to the nucleus without limit. However then its velocity, and therefore its kinetic energy, would become very uncertain, hence potentially very large. The ground state is the "happy medium" achieved by minimizing the sum of the potential and kinetic energies.

- With more electrons the structure of the ground state of the atom depends on another quantum phenomenon: the Pauli exclusion principle: no two electrons can be in exactly the same "state", which refers to both the position of the electron and its spin. There are just two distinguishable spin states along any axis, up and down. In the helium ground state, the two electrons have the same spatial localization, but opposite spins. And so it goes. Higher energy states of atoms have a discrete level structure.

- When an atom makes a transition from a higher to a lower energy level, it emits light in the form of a packet of light energy called a photon. Energy is conserved, so the energy of the photon is the difference of the atomic energy levels. A single photon behaves in some respects as a particle, but it can also behave as a wave. This is an aspect of the wave-particle duality of quantum mechanics.
A photon also has a frequency f, related to its energy E by E = hf, where h is Planck's constant, 6.6 x 10^-34 J-s.

- As an example, consider a "red" photon, with wavelength 660 nm = 6.6 x 10^-7 m. The corresponding frequency is f = c/wavelength = (3 x 10^8 m/s)/(6.6 x 10^-7 m) = 3/6.6 x 10^15 Hz. The corresponding energy is hf =
(6.6 x 10^-34 J-s)(3/6.6 x 10^15 Hz) = 3 x 10^-19 J. That's a tiny energy, the energy of one photon of red light. It's interesting to measure this energy in a different unit, namely the potential energy change of an electron moved across a potential difference of one volt: 1 eV = (1.6 x 10^-19 C)(1 J/C) = 1.6 x 10^-19 J. So the red photon has an energy equal to 3/1.6 eV = 1.9 eV. That means that the electron energy level difference in an atom that produces a red photon would be around 1.9 eV, and the potential difference would be around 1.9 V.

Tuesday 4/23


- how polarizing filters work, illustrated with M7-05.

- how LCD's (liquid crystal displays) work. See also the homework assignment, and the diagram below.
- note the computer display is linearly polarized...and polarized sunglasses can block its light 100%, but only when the glasses are rotated at 45 degrees. I think it's no accident that the polarization angle for displays was chosen as 45 degrees, so as not to be blocked completely by polarized sunglasses.

- someone asked if a privacy screen uses polarizing filters. According to this no, but I'm not sure.

- polarized sunglasses are oriented to block horizontal polarization. That's because light that reflects off a horizontal surface is preferentially horizontally polarized.

- optical activity of sugar syrup: the molecules of sugar have a "handedness", i.e. a twisting sense, as does DNA. (I mentioned that the origin of the handedness of life on earth is not known, but there are theories...) See Thursday 4/25 for explanation.

- circular polarization
: M9-03. Used in modern 3D movie technology. An older generation method used perpendicular linear polarizers, one for the image projected for each eye. But this doesn't work well unless the head is held at just the correct angle. If instead right and left circular polarization is used, then the held can be tilted and it still works just as well. I didn't explain how glasses that pass only right or only left circular polarization work. Ask me if you want to know...(or it may be written in last year's notes.)

- circular polarized light is emitted along the axis of rotation of a circling charge. It is also possible to convert linearly polarized light into circularly polarized light, and vice versa. Ask me if you want to know how.

- refraction: when electromagnetic waves travel through transparent matter, the speed is slower than the speed of light. This speed change generally depends on the frequency of the light, a phenomenon called dispersion. The ratio of the speed of light in vacuum c to the speed in a material v is called the refractive index n = c/v.

- When waves encounter an interface between two media in which the wave speed is different, they partially reflect, and partially transmit. The transmitted wave direction is bent at an angle if the incoming wave is not perpendicular to the surface.

- someone asked me what determines how much reflection there is from an interface between two media. For waves traveling perpendicular to the interface, the fraction of reflected wave energy is, to a good approximation, (speed difference/speed sum)^2. For example, for glass, the refractive index is about 1.5, so the speed is 2/3 c. Thus (speed difference)/(speed sum) = (1-2/3)/(1+2/3) = (1/3)/(5/3) = 1/5, so the fraction of reflected energy is (1/5)^2 = 1/25 = 4%.

- how rainbows form. One very important point not really explained in the textbook is the fact that there is a special angle (relative to the incoming sunlight indirection) at which the light emerging from a spherical water droplet is concentrated. That is in fact the maximum angle at which light can emerge. See the neat applet below for a good demonstration. Grab the incoming ray with your cursor and move it from the center of the droplet upwards, until the angle of exit stops growing and starts shrinking. That's the rainbow angle.

Thursday 4/18


- the electromagnetic wave spectrum:
Electromagnetic waves cover a huge range of frequencies, essentially an infinite range: Our eyes are sensitive to a narrow band from maybe 380nm to 780 nm, just one "octave"
(factor of two) in frequency. Why the visible band? Because that's where the light is! Look at the solar spectrum below.


- sunlight: emitted by the surface of the sun, which is hot thanks to the nuclear fire within. I explained the various features of the following graph which shows the energy flux of sunlight, in units of watts per square meter per nanometer of wavelength interval, vs. wavelength on the horizontal axis. Photosynthesis extracts energy from sunlight, so plants exploit the region of maximum energy. Animals need to see plants, and predators, and prey, (and also to get around!) so they are sensitive to the same region of the spectrum in general. Some animals can see infrared (snakes, piranhas, moquitoes,...) but, in general, longer wavelength vision is more susceptible to thermal noise, which may be why it is not exploited much by animals.


- amazing and essential fact: the electric and magnetic fields from different sources combine simply by vector addition at each point in space at each time. (The is called superposition of the fields.) In particular, electomagnetic waves don't "bump into each other", they don't mess each other up, they just pass through each other. But when they are at the same location, their fields combine. This is why transmitters and receivers need to be tuned to particular frequencies. That way, when waves of different frequencies are combined, it is still possible to pick out the part that has a particular frequency range.

- Bluetooth: uses the band 2.4 - 2.480 GHz, which is also used for some cordless phones, baby monitors, wifi, etc. To avoid interference problems bluetooth uses "spread spectrum frequency hopping", switching between 79 frequencies 1600 times per second.

- AM (amplitude modulation) and FM (frequency modulation).
AM and
AM and FM both require a range of frequencies to transmit a given signal; this range is called the bandwidth. FM is more robust since frequencies are more stable under the distortions of strength than is AM. Also the bandwidth of FM is much greater, so it can transmit much more information about the sound.

- Microwave ovens:
: generate 2.45 GHz waves with a magnetron. See picture here:
We covered how they heat food, and how the magnetron works. These are also explained in the book.

- polarizing filters: they pass one linear polarization and absorb the perpendicular one. Will demonstrate more on Tuesday.

Tuesday 4/16



- Electric fields E come from two different sources: charge, and changing magnetic fields B (magnetic induction). Magnetic fields come from moving charge, or current. James Clerk Maxwell, Scottish physicist, realized in the early 1860's that the electromagnetic theory would be inconsistent with conservation of charge unless, similar to magnetic induction, a changing electric field would induce a magnetic field. (I'm not sure how he actually thought about this, but this is how it is viewed now.)

- It was hard to notice experimentally that a changing E makes B in settings where the changes are not so rapid. The difference between the "strength" of electric induction and magnetic induction can be traced to the speed of light: Notice from the electric and magnetic force laws, F_elec = qE and F_mag = qvB_perp, that the units of E and vB are the same, where v is a speed. Let's use the letter c for a special speed relevant to changing fields, which turns out to be the speed of light, 3 x 10^8 m/s.  Magnetic induction tells us that a changing B makes an E. To match the relation of units we could guess that a changing E/c makes a cB, or, equivalently, a changing E/c^2 makes a B. The division by c^2 makes the effect of the change of E very small unless the change of E is happening fast enough for the light travel time to be relevant.

- electromagnetic waves: since changing E and B can make each other, a pattern of changing fields can propagate through empty space without and charges present. Maxwell found that these waves exist and travel at the speed c mentioned above. The speed of light is also 30 cm/nanosecond, which is a nice, human scale way to think about the distance, but not the time. It travels 300,000 km in one second, which is a bit over 7 times around the equator of the earth and a bit under the distance from earth to moon (which varies between 357,000 and 406,000 km). It takes about 500s = 8.3 minutes to travel from the sun to the earth.

- Like for other waves, speed = wavelength x frequency.

- How can electromagnetic waves be generated? Similar to the generation of sound waves, something has to move around. Accelerating charge generates electromagnetic waves. This applet shows this nicely: 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. The changing E creates a changing B which creates a changing E, etcetera. 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.)

- Far from the source an electromagnetic wave becomes approximately planar. The electric and magnetic fields are perpendicular to each other, and perpendicular to the direction of propagation. The direction of the electric field is called the polarization. Showed two models of this. The electric field amplitude is c times the magnetic field amplitude, E = cB, in the wave. This means in fact that the two fields carry the same amount of energy in the wave.

- Touching a wire on a 9 volt battery to momentarily connect the circuit creates an electromagnetic wave that is picked up and amplified by the little AM radio receiver in demo K8-45.  Placing the receiver inside a conducting mesh blocks out the radio waves.

- The demo K8-42 shows the polarization properties of wave and antenna. The waves light up the light bulb when picked up by the antenna. This illustrates that the waves carry energy.

- Energy in electromagnetic waves: WAMU transmits at 50,000 W. A (dumb) cell phone transmits at maybe 50 milliwatts, i.e. 0.05 W = 1/20 W.

- Cell phones convert analog voice to a digital signal, and that and other data is sent in binary code. where the two alternatives are encoded as two different nearby frequencies. Old cell phones operated with just one pair of frequencies for transmission and one for receiving. In order to distinguish the two frequencies in a given amount of time they must be sufficiently different. This illustrates the importance of bandwidth, which is the range of frequencies used. A range is needed to convey information, and the wider the range the more information can be conveyed in a given amount of time.

- A student informed me that current technology is different. In fact, each phone uses many frequencies, splitting the signal into many parts, in order to make more efficient use of the available bandwidth.

Thursday 4/11



- J5-05 is a vivid demonstration of magnetic field line pattern. It also can be used to show something analogous to ferromagnetic domains.

- J5-51 is a device that measures magnetic field strength, which is measured in Tesla (T) or gauss. 1 T = 10,000 gauss. The earth's magnetic field is variable over the earth but around half a gauss. The way this device works is to exploit the Hall effect: So it is called a "Hall probe". An iphone has three perpendicular Hall probes in it, to measure three components of the local magnetic field vector. This is how the phone can detect its orientation.

- Showed K2-43.

- Alternating current (AC)

- transformers

- power transmission loss due to resistance of transmission wires. The loss minimized by using low current and high voltage. Why? The power wasted in heating the transmission lines is I^2 R, where I is the current in the lines and R is their resistance, so it is smaller for smaller currents (and very sensitive to the amount of current, since it grows as the square). The power conveyed by the transmission lines is the voltage across the lines, from one line to the other, times the current in the lines. For for a fixed power delivered, therefore, this voltage is inversely proportional to the current. Transmission line voltages can be very high, for instance 500,000 V. Transformers are used to step up the voltage from the power plant to the transmission lines, and then to step it back down for use, because very high voltages are unsafe to use. Transformers work using magnetic induction, hence need a time varying current. This is why AC current is essential to their operation.

- transformer: has primary and secondary coils, wrapped around an iron core that bends the magnetic field lines so they go around in a "circuit" through the two coils. The ratio of the number of turns of coil is equal to the ratio of the voltages, V_s/V_p = N_s/N_p. Voltages in an AC circuit are also called "emf", for "electromotive force". When there is a load connected to the secondary, it draws power, so that the transformer acts to hand off power from the primary circuit to the secondary.

The work done by the power supply on the charges in the primary coil is transferred via the magnetic field to the secondary coil, where the same amount of work is done on the charges there (aside from losses in the transformer). As with DC circuits, the instantaneous power is VI, where V is the induced emf (see p. 361), which plays the same role as the voltage. The power in the primary V_p I_p is approximately equal to the power in the secondary V_s I_s, so the ratio of the currents is I_s/I_p = V_p/V_s = N_p/N_s.
See the text for more on transformers.

- DC motor; K4-21

- A generator is a motor run backward, and vice versa, K4-41

- Induction motor. See discussion in book, and

- Current hybrid motors use expensive permanent magnets. They might be replaced by induction motors, or partial induction motors, in the future:

Tuesday 4/9


- refrigerator flat magnetic sheets

- dysprosium becomes ferromagnetic at the temperature 85K. Liquid nitrogen boils at atmospheric pressure at 77K, so it's just cold enough to make dysprosium go ferromagnetic, see demo.

- ferromagnetic core is magnetized and turns a weak electromagnet into a super strong one! As soon as the current is switched off, the core is demagnetized.

- Lorentz force law, this time with a diagram showing FLorentz = q vperp B = q v Bperp = qvB sin(theta), where theta is the angle between v and B

- A current is induced in a conductor moving in a magnetic field.

- A current is induced in a conductor at rest in a changing magnetic field.

- A changing magnetic field induces an electric field. This is electromagnetic induction.

- Lenz' law: the effect of magnetic induction opposes the change that produced it.

- examples of Lenz' law: eddy current pendulum, and can smasher.

- reversals of the Earth's magnetic field.

Thursday 4/4



- magnetic fields are produced by moving electric charges.  In particular the field of a current in straight wire makes a pattern of circles around the wire. The curves that follow the direction of the field vectors are called field lines. (Bloomfield calls them flux lines, see Fig. 11.1.9.) The field of a current loop is shown in Fig. 11.1.11.

- Reciprocally, a moving charge in a magnetic field feels a magnetic force, called the Lorentz force, which is proportional to the charge, the magnetic field, and the component of velocity perpendicular to the magnetic field. In an equation: FLorentz = q vperp B. This is equivalent to
FLorentz = q v Bperp, where Bperp  is the component of the magnetic field perpendicular to the velocity. The direction of this force is perpendicular to both the velocity and the magnetic field, in the direction the palm of your right hand faces when your thumb points along v and your fingers point along Bperp.

- The magnetic properties of currents are extremely useful, because they allow an electric current to cause a mechanical motion. A cute example is the electromagnetic bell I demonstrated, or the relay switches I passed around. The bell works in a funny way: the ringer is a springy metal rod. When current flows to the electromagnet, it pulls the ringer so it strikes the bell. But when the ringer is pulled, that opens the circuit and thus turns off the electromagnet. Without the electromagnet pulling it away, the so the ringer springs back to its starting position, reconnecting the circuit, and turning on the electromagnet again for another cycle of motion.

- What metals are attracted to a magnet, and why? What is a permanent magnet? Are these examples of magnetism produced without currents? NO! Read on...

- an electron is a little magnet! Amazing fact that can only really be correctly described using quantum theory: an electron is perpetually spinning, and since it is charged, that means it is like a little current, which produces a magnetic dipole field. The amount of spin and the strength of the magnet is always the same. So, all matter is full of microscopic electron magnets. Also, electrons are orbiting atoms, which creates magnetic fields.

- In most matter, the fields of all these magnets cancel out. In some materials, notably (but not only) iron, nickel, and related "ferromagnetic" substances, the atomic structure favors aligning some electron spins with their neighbors, provided the temperature is low enough, below the so-called Curie temperature, for that material. This is a phase transition, analogous to freezing of a liquid into a solid. The spins align in clusters called magnetic domains, separated by domain walls.  But, unless the material is magnetized, the different domains are randomly oriented and their magnetic fields cancel out. 

- If a ferromagnetic material is placed in a magnetic field, the domains aligned with the field grow and the others shrink, and so the material becomes magnetized. It is then attracted to the region of stronger magnetic field. This can be thought of as being a result of stronger attraction of the closer, opposite pole of the magnet. But monopoles don't actually exist, and a correct explanation would be in terms of the current. If the external magnetic field is reversed, then the ferromagnetic material just magnetizes in the opposite direction, and is still attracted to the region of stronger field. That's why iron and steel are attracted to magnets, regardless or orientation.

- In demo J7-13 we saw how the ferromagnetic domains of nickel are "melted" above its Curie point. Once the domains are no longer there, the nickel is no longer attracted to the magnet. But when the nickel cools below its Curie temperature, the domains re-form, and it is again attracted to the magnet.

- If the external field is removed, most ferromagnetic materials would pretty much return to their original non-magnetized state. These are called ``soft magnetic materials".  But there may be a little bit of residual magnetization because a few domain walls can get "stuck" This is why, for example, paper clips can become weak magnets after being placed in a strong magnetic field. "Hard magnetic materials", by contrast, have  domains that all get stuck, so they retain magnetization once magnetized, unless they are heated or struck. These are called permanent magnets.

Tuesday 4/2



- circuits
- resistance: given a voltage drop, how much current flows?
For many materials, the current, I, is proportional to the voltage drop, V, which I'll write as I ~ V. The relation V = IR defines the resistance R.

What factors determine the current, given the voltage? That is, what determines the resistance? The current is proportional to (no. of conduction electrons)(avg. electron velocity). The electrons are accelerated by the electric field until they collide with something, so their (avg. velocity) ~ (acceleration)(collision time). Also (acceleration) ~ (electric force) ~ (electric field) = (voltage drop)/(length). Putting this together, we've got

I ~
(no. of conduction electrons)(collision time)/(length), so

R ~ (length)/
[(no. of conduction electrons)(collision time)]

That is, for a given wire, say, the resistance is proportional to the length. For wires of the same material, the number of conduction electrons is proportional to the cross-sectional area, so the resistance is inversely proportional to the area. For a conductor, the number of collisions decreases as the temperature decreases, since the collisions are caused partily by vibrations of the metal lattice. For a semi-conductor, the number of conduction electrons decreases as the temperature decreases, because some electrons get "locked in" and are not free to move. All these relations were demonstrated with demos K5-32 and K5-36 listed above.

The temperature dependence of resistance allows temperature to be measured electrically. This is how many temperature sensors work.

- power and resistance: Combining P = VI and V = IR, we can express the power without V as P = I2 R, or without I as P = V2/R. So more resistance means more power at fixed current, but less power at fixed voltage! This power refers to the thermal energy dissipated in a resistor.

MAGNETISM - discovered first in lodestone.

Magnetic monopoles do not occur. We can picture a simple magnet as a dipole, that is a separated pair of opposite magnetic "charges" called N (north) and S (south), and think of the magnetic force as acting on these poles in a way that mimics the electric force: F_mag = p B, where p is the pole strength and B is the magnetic field vector. However, this is just a fiction. There are no magnetic poles, and actually all magnetism comes from moving electric charges, or currents...

Thursday 3/28



- piezoelectricity: certain materials develop a potential drop across them when squeezed or stretched. Conversely, if a potential difference is applied to them they are squeezed or stretched. This is super useful, since it converts mechanical to electrical effects and vice versa.

- corona discharge

- how a photocopy machine works

- electric current; SI unit C/s = A "ampere" or "amp"

- power delivered by a current across a voltage drop: P = VI

Tuesday 3/26



- "attraction of neutrals" : two neutral collections of charge can attract each other, if the charge is separated, i.e. polarized. This can be a permanent polarization, like that of a water molecule, or a fluctuating polarization, like that in, say two atoms that are attracted to each other.

- Gecko feet
: work by attraction of neutrals:

- American Scientist article about Gecko feet
- movie of loading and unloading gecko tape

- lightning

Video about lightning (watch from 3:30 to 5:20)
National Weather Service Info on Lightning
More technical info on lighning from National Weather Service

- voltage: SI unit: J/C = V "volt"; electric potential energy per unit charge at a given location.

- electric field: SI unit: N/C = V/m;
electric force per unit charge at a given location.

- relation between electric field and voltage drop: force x distance = work, so electric field x distance = voltage drop, so (electric field) = (voltage drop)/(distance). This is called the gradient of the voltage. really it is a vector, whose direction is that of the steepest drop of voltage. So E = gradient V.

- electric breakdown of dry air occurs at an electric field, or voltage gradient, of ~ 30,000 V/cm, which is ~ 3 V/micron. This makes sense, since the distance an air molecule travels before colliding with another is around a micron, and the energy required to break up a molecule and release an electron is around 3 V.

spring break

Thursday 3/14 - exam

Tuesday 3/12 - review
Thursday 3/7

- Showed various images and animations from the following web pages. Discussed the operation of the Stirling engine, and of internal combustion engines. I didn't show the animation of the Wankel engine in the wikipedia internal combustion page, but I recommend it. It's also known as a "rotary" engine. Mazda used to use them in passenger cars. I put the animation on the home page of the course website...
(external combustion engine)

- Back to electricity. We started by looking at static electricity, produced by contact between certain surfaces. For instance fur gives up electrons to rubber, and silk takes electrons from glass. Once transferred, those charges don't move around much. But if we have a conductor of charge, in which some of the electrons can flow freely, the behavior is quite different. I demonstrated this with the demo
J1-12 INDUCTION - ELECTROSCOPE. When a charged object is brought near the electroscope, the needle deflects, since the electroscope is a conductor. For instance, if the negatively charged rubber is brought nearby, the conduction electrons in the electroscope "run the other way", i.e. they are repelled. On the other hand, they repel each other as well, so to only bunch up a certain amount until the force from the rubber and their self-force balance. The needle deflects because that way the electrons in the conductor can spread out from each other more. When the rubber rod is removed, the electroscope goes back to its original position. If we let charges transfer from the rubber to the electroscope, then there is a net negative charge on the electroscope, and the needle remains deflected even when the rubber rod is removed. Then I can discharge the electroscope by touching it, because my body can absorb the extra electrons.

- A balloon rubbed with fur (or a person's hair) will stick to the wooden door. Why? The balloon is negatively charged, but the door is neutral, so why should they be attracted? The reason is that although charge cannot flow in the door, the electrons can shift around sightly relative to the more stationary positively charged atomic nuclei. So the charge on the balloon pushes the electrons in the door away a bit, leaving the positive charge a little closer to the balloon. Now there is an imbalance, because the electric force is stronger when the charges are closer. So the balloon is more strongly attracted to the positive charge than it is repelled by the negative charge in the door. Hence it sticks! (I don't know if it is the wood or the finish on the surface that is more responsible for this, but I'm guessing it's the latter...) This phenomenon of charge separation is called polarization.

- We can build up much more charge with the "van de Graaf generator", as demonstrated with
J2-03 VAN DE GRAAFF GENERATOR WITH GROUND SPHERE. When the charge builds up enough, it can cause an electric breakdown of the air between the two metal spheres and a spark jumps across, discharging the charged sphere. What happens in electrical breakdown of the air and what determines when it occurs? To address this, I asked first of all why is air not a conductor normally? It may seem as if the reason is that it's not dense enough, but it's really the opposite. Any stray charged particle in the air will be accelerated by the charge on the sphere, but it will collide with an air molecule in a distance of order a micron- that's one millionth of a meter, one thousandth of a millimeter. The collision will slow the charge down, and not much will happen, unless the charge has acquired enough kinetic energy by the time of the collision to knock out another electron from the air molecule. If it does, then an "avalanche", runaway process happens, where each collision liberates more free charge, and the air becomes a good conductor. There is a certain minimum accelerating force needed to produce such an avalanche. That's why the discharges in the demonstration happened somewhat periodically, after the charge built up enough to produce such an avalanche.
Tuesday 3/5 


- Example of a home heat pump: Suppose the temperature inside the house is 295K (22˚C), the air temperature outdoors is 270K (-3˚C), and the temperature underground is 283K (10˚C). If 1000J of heat is to be put into the house, how much of that can come from the outside, and how much work must be done?

The entropy increase of the house is 1000J/295K, which must be greater than or equal to the entropy decrease of the outside.
If air is the source of outside heat, then 1000J/295K ≥ Q_air/270K, so Q_air ≤ (270/295)1000J = 915J, so the pump must do at least 85J of work. 
If gnd is the source of outside heat, then 1000J/295K ≥ Q_gnd/283K, so Q_gnd ≤ (283/295)1000J = 959J, so the pump must do at least 41J of work. 
So, if the heat pumps were ideally efficient, the pump would need to do about half as much work in the case of the ground heat source. Either way however, it's remarkable that more than 90% of the heat comes from the outside!

To emphasize and demonstrate that compression really does take work and injects heat into a system, I used the I5-22 FIRE SYRINGE demo. The work of pushing on the piston turns into thermal energy. If done quickly enough in the demo (I overdid it!), there is no time for the heat to escape the syringe and the temperature actually rises enough to ignite the piece of cotton placed in the bottom of the syringe.

- A heat engine is a heat pump run backwards. A heat pump does work to cause heat to flow from cold to hot. A heat engine extracts work from the natural flow of heat from hot to cold. Since total entropy cannot decrease, not all of the heat can be converted into work. Enough heat must be dumped at the lower temperature so that entropy does not decrease. This places an upper limit on the amount of work that can be extracted from the heat flow. The greater the ratio of the high temperature to the low temperature, the larger the fraction of the heat that can be extracted as work. 

- As an example, say a steamboat engine operates with 500K steam and dumps heat into the air at 300K. Starting with 1000J of steam heat, how much work can be done? Well the entropy decrease of the steam will be Q/T = 1000J/500K = 2 J/K. So the entropy of the air must go up by at least 2 J/K. That is, Q_air/300K ≥ 2 J/K, so the heat that enters the air must satisfy Q_air ≥ 600 J. Conservation of energy tells us that the difference between the steam heat and the air heat is the work W the engine does. Thus W = Q_steam - Q_air, and W ≤ 400J. The engine can extract at most 400J, or 40% of the thermal energy as work. The engine can be more efficient in colder weather. If the air temperature were zero, it could extract 100% of the thermal energy as work.

- This gives me an idea: since the space station is surrounded by near vacuum at near zero temperature, instead of radiating its waste heat into space, maybe it could get nearly 100% useful work out of that heat. It would need some kind of ideal heat engine, perhaps something coating the outside of the space station that would use the heat to charge batteries. Maybe there is a flaw in this idea... Anyway, they replenish the energy using sunlight captured by photovoltaic cells.
Electricity -

So far
this course has been about energy in general. Energy is transferred by work done by forces. We've discussed a few types of forces: gravity, macroscopic forces like tension in a rope, pushing on a piston, and friction, and also the microscopic forces involved when molecules collide with the walls of a container and produce pressure, or when molecules are attracted to each other as in a liquid or a solid. From this list, the only "basic" force is gravity. The rest are situations that can be decribed on a more fundamental level in terms of the interactions between atoms. The structure of atoms is governed by electricity. An atom is a nucleus and a bunch of electrons that are attracted to the nucleus and repelled by each other by the electric force. As we'll see, electricity in motion produces magnetism, and together electricity and magnetism produce electromagnetic radiation. The electromagnetic force is responsible for almost everything you see and experience, except for gravitational phenomena. One very notable exception is the sun! The sun is hot because of nuclear reactions taking place in its core. Although the energy that reaches and interacts with us is electromagnetic, the source of this energy can only be understood when also the so-called strong and weak interactions are taken into account. We'll come to those at the end of the semester. For the next several weeks, we'll be looking into the nature of electricity and magnetism and how it is used to make things work.

In the 18th century it was established that there are two varieties of electric charge. Like types attract each other and opposite types repel. Benjamin Franklin called on of the positive and one negative. In the late 18th century Coulomb established that the force law between electric charges has the same form as Newton's law of gravity, proportional to the product of the charges and inversely proportional to the square of their distance. However unlike gravity which is always attractive, the force is attractive if the product of the charges is negative (i.e. if they are opposite), and repulsive if the product of the charges is positive (i.e. if they are the same). This force law is called Coulomb's law.

Beginning in the late 18th and early 19th centuries, scientists started experimenting with electric currents. They thought of such currents as a fluid, but it was discovered at the end of the 19th century (and had been speculated earlier) that actually currents are composed of many elementary, discrete electric charges, all with the same mass. These are called electrons. The opposite charge is carried by protons. It turns out that other particles in nature also have electric charge, but they are not part of ordinary matter. The unit of electric charge is not the elementary charge on an electron, e, but rather one coulomb, 1C. The charge on an electron is 1.6 10^-19 C. Conversely, one coulomb contains around 10^19 elementary charges. The amount of charge on a sock that comes out of the dryer might be around 10^-7 C, so around 10^12 electrons. It turns out that electrons are what Franklin had already dubbed "negative" charges. Most currents are carried by electrons, since they are nearly 2000 times less massive than protons and there are many of them in atoms other than hydrogen, so it turns out they are more often liberated to flow freely and carry "electric current".  See the textbook for more about the force law and electrons.

Thursday 2/28

- Went over three homework problems:

S9.2: Reviewed the relation between wave speed, wavelength, frequency, and period, and pointed out how keeping track of the units help you catch errors in computations. For this example, the wavelength turns out to be around 3.4 mm. I made the connection between this wavelength and the size of the insects that bats locate with their sonar. It would not be possible to use the sound to locate an object much smaller than the wavelength of the sound. 

S9.4: Demonstrated this with a real guitar string. Showed how one can select the harmonic by lightly touching the string at a node location when plucking the string. If the string is later touched at the node, it keeps sounding because the node is not moving, but if touched anywhere else it's instantly damped.

S9.5: Demonstrated this with an aluminum tube, and explained how the closed end becomes an antinode of the pressure wave. This means that in the fundamental mode 1/4 of a wavelength fits inside the tube, i.e. the wavelength is 4 times the length of the tube. When both ends are open, they are both nodes, and 1/2 a wavelength fits in the tube. So the wavelength is twice as long with one end closed, and hence the frequency is half as high, so the pitch is one octave lower. The overtones of the tube with one closed end have an odd number of quarter-wavelengths in the tube. [I didn't say the following in class: The wavelengths of the fundamental and the overtones are thus 4L, 4L/3, 4L/5, 4L/7, ... Correspondingly, the frequencies are f_0, 3f_0, 5f_0, 7f_0, ...where f_0 is the frequency of the open/closed fundamental, which is 1/2 the frequency of the open/open fundamental. (For a pipe open at both ends the frequencies of the modes are f_0, 2f_0, 3f_0, 4f_0, etc., where now f_0 is the open/open fundamental.)]

- Entropy: See Tuesday 2/26 class notes for the background to the concept of entropy. Entropy is a measure of disorder. When heat Q enters a system at temperature T, the increase of entropy of the system is Q/T. This can be thought of as the amount of "thermal energy units" at that temperature, since T is (proportional to) the average thermal energy of a molecule at temperature T. If T is smaller, there is more entropy increase, since there is less disorder to begin with, i.e. because the thermal energy per molecule is smaller to begin with. So when heat Q flows from high to low temperature, the entropy increase of the cold system is greater than the entropy decrease of the warm system, hence the total entropy increases, in accordance with the 2nd law of thermodynamics, which states that the total entropy of the world never decreases. Were heat to flow in the opposite direction, the total entropy would decrease, which does not happen...

- So how then can a refrigerator work? Does it violate the 2nd law of thermodynamics? Certainly not! But in order not to violate that law, it must be that more heat is dumped into the room than was extracted from the fridge! The extra heat originates from the work done by the compressor in the fridge. Energy is conserved, so the work done by the compressor, plus the heat extracted from the fridge, is equal to the heat dumped into the room. (The law of conservation of energy is known in this context as the 1st law of thermodynamics.) The minimum possible amount of work the fridge could do would be if the total entropy remained constant during the process. This is called an "ideal" fridge.

- As an example, suppose the fridge temperature is 270K and the room temperature is 300K, and 900 J of heat is extracted from the fridge. Then the entropy of the fridge goes down by 900J/270K. The 2nd law of thermodynamics says that the entropy of the room must go up by at least this much. So if Q_room is the heat dumped in the room, it must be that Q_room/300K ≥ 900J/270K, hence Q_room ≥ 900J (300/270) = 1000J. So at least 100J more heat must enter the room than left the fridge. The origin of this extra heat is the work done by the compressor, so the compressor must do at least 100J of work. If the fridge is "ideal", it does exactly 100J of work.

- Good diagrams of how a heat pump is set up to heat a house in winter and cool it in summer

Tuesday 2/26

- Boiling: I explained the nature of boiling, and how the temperature of boiling depends on the ambient pressure. This is explained in the textbook as well. I used this phase diagram of water, taken from the wikipedia article on ice, to illustrate how the boiling temperature depends on pressure:
phase diagram of water
I also explained that water boils faster with the lid on the pot, since that keeps steam enclosed so it can re-condense, suppressing the heat loss from evaporation. Also, just before water boils, it starts to "roar". The is the sound of bubbles that cool as they rise, and drop below the boiling temperature, at which point the pressure in the surrounding water collapses the bubbles. The sound of many small bubbles collapsing is the roar.

- And on to chapter 8...

- Heat naturally flows from high to low temperature. That's because energy "diffuses", that is it gets spread out, in an irreversible way. If you watch a hot cup of coffee backwards in time, it absorbs thermal energy from the air and the table and spontaneously heats up. That would never happen... so

How can we make heat flow from cold to hot, to cool a refrigerator?

- Old fashioned way: put a block of ice in the fridge. This was called an icebox. The latent heat of melting is absorbed, the air next to the ice cools and becomes denser and falls, warmer air moves in to take its place and that is cooled, so there is a convection circulation in the box. As the ice melts you have to get rid of the water, and eventually you have to replace the ice.

- With available power and manufacturing technology, it became possible to produce affordable refrigerators that use evaporation of a fluid to cool. I explained the principles behind this. It is all described in the book, and in previous year's notes from my class. To state just the essentials:

Operation of a refrigerator using a working fluid and a pump:
Evaporator: extract heat by evaporating working fluid in coils inside fridge.
Compressor: compress vapor. This takes work, and heats the vapor.
Condenser: run vapor through cooling coils outside fridge, give off heat, liquify the vapor,
Expand: pass liquid through thermal expansion valve to drop pressure in preparation for evaporation.

It takes energy input to run the fridge, because you have to compress the vapor in order to re-liquify it. This compression heats up the vapor, and to get rid of that heat the outside "fridge coils" are used. The fridge coils are the long tube and metal crossbars on the back of the fridge in this picture:
 fridge coils
The coils help to transfer the heat to the air in the room. In other fridges the coils might be underneath, with a fan blowing air past them to increase the heat transfer. The black thing at the bottom of the fridge is the compressor. More heat goes into the room than leaves the fridge, because heat comes from the work done by the compressor. (If you run the fridge with the door open, you'll just heat the room, while cooling air next to the inside coils.)

- Air conditioner window unit: Same idea, but cool the room and dump the heat outside.

- You could heat your room in the winter with an air conditioner: flip it around and put the outside coils inside. Then in effect you're absorbing heat from the outside and dumping the heat inside. This is called a "heat pump" (a fridge is also a heat pump), and is usually arranged with an outside heat absorber unit on the ground next to the house. The most efficient setup is to put that outside heat absorber under ground, since a few feet under the temperature is in the 50's all year round. The heat pump actually moves thermal energy from outside to inside where it's warmer. It takes work to do that (with the pump), but the closer the two temperatures the less work it takes.

- A natural question is what's the most efficient way to cool a fridge? That is, what's the least work you could possibly do to remove a given amount of heat from the fridge? We'll answer that next class, but first we can do some deep thinking. The origins of this analysis lie with the interesting French physicist Sadi Carnot. Carnot published one paper, called "Reflections on the motive power of heat", at age 28, in 1824. He died of cholera at age 36. He was concerned with extracting work from heat flow in steam engines and the like, but his conceptual insights are also relevant for heat pumps, which are essentially heat engines run backwards. Carnot was handicapped by the fact that the concept of conservation of energy was not yet understood, and he used a now discredited notion of heat as a fluid called "caloric". Despite these limitations, the essence of his reasoning was correct, and it led others (Clausius and Kelvin) later to a sharper and more complete formulation of the theory. The Wikipedia article linked above to his name gives a good account of this.
First of all, heat flow from high to low temperature is irreversible, because it amounts to a spreading of random motions. Any inefficiency in the fridge operation will generate wasted heat that will spread, hence the operation of the fridge will not be reversible, meaning it could not be run backwards to put heat back into the fridge and extract work by the backwards running pump. Therefore, the most efficient fridges must be reversible.

Next we can argue that any two reversible fridges must dump to the room the same amount of heat given the same work of the pump, assuming of course that the two fridges have the same temperature inside them, and both are sitting in the same room, with one room temperature. The argument goes like this: Suppose fridge #1 dumped less heat than fridge #2. Then we could run fridge #1 backward, using the work we get out of its pump to run the pump of fridge #2. Fridge #2 would then dump more heat than was put into the backwards running fridge #1. The overall result, considering the two fridges together, would then be that heat flows out of the fridges and into the room. But that heat is flowing from a colder to a hotter temperature. It's flowing the wrong way! That can't happen. It's against the 2nd law of thermodynamics. Heat does not flow from cold to hot without some work being put in. But here no work is put in, since the work to run fridge #2 comes from the work extracted from fridge #1. The only way to avoid this contradiction with the 2nd law of thermodynamics is if any two reversible fridges are exactly equally efficient, and dump the same heat given the same work.

- This is as far as I got Tuesday. Thursday I'll continue like this: Energy conservation, which is known in this setting as the 1st law of thermodynamics, tells us that the heat extracted from the fridge Q_in plus the work done W must be equal to the total heat dumped to the room Q_out. In an equation: Q_out = Q_in + W. Since we assumed W is the same for the two fridges, and we argued that Q_out must be the same if they are reversible, then also Q_in must be the same. Therefore Q_out/Q_in must be the same. Finally, this ratio is actually independent of the amount of work W done. For instance, if we double the work, then we'll just double the heat Q_in extracted from the fridge and double the heat Q_out dumped to the room, so their ratio Q_out/Q_in will be the same. This ratio depends only on the two temperatures, T_in and T_out. It turns out to just be equal to the ratio of the temperatures: Q_out/Q_in = T_out/T_in. In fact, it was a deep insight of British physicist William Thompson, later to be called Lord Kelvin, that an absolute notion of "thermodynamic temperature" could be defined by this heat ratio, that is, defining the right hand side of this equation by the left hand side. This defines the temperature up to one overall multiple that can be set arbitrarily. It turns out that this notion of temperature is the same as the one we've been using in class so far, namely the average kinetic energy of a gas molecule.

- A fruitful way to re-express this conclusion is to rearrange it as Q_out/T_out = Q_in/T_in. This ratio is defined as the change of entropy, and what the equation says is that the entropy dumped into the room must be equal to the entropy taken out of the fridge. Another way to state the 2nd law of thermodyamics is that the total entropy of the world never decreases, it can at best stay the same. If it increases, the reverse would be a decrease, so a process is reversible only if entropy stays the same. Our equation here says exactly that the entropy stays the same. We can use this fundamental equation to determine the work required by a maximally efficient heat pump,  or the work extracted by a maximally efficient heat engine, in terms of the given temperatures...

Thursday 2/21



Slides shown by Prof. Greene

Simulations shown to help visualize traveling waves and standing waves:

You may also want to look at Dr. Jacobson's notes on this material between the dates 10/1-10/13 in the 2010 notes:

A string vibrating freely contains simultaneously many harmonic modes, all added together. This is called superposition of vibrations. Here is an applet (not shown by Prof. Greene) that demonstrates this: choose "display modes", set the "number of loads" all the way to the right, and pluck the string in different places to see the different combinations of modes that are present.

Tuesday 2/19

Prof. Greene taught the class Tuesday 2/19 and Thursday 2/21. Here are the demos he used Tuesday.



Thursday 2/14


- A nice applet illustrating the ideal gas law. This law applies when interactions between the molecules, and the space they occupy, are negligible. That's what the "ideal" refers to in the name of the law.

- Different materials feel to the touch to have different temperatures in the classroom, even though they have had plenty of time to come to thermal equilibrium. This is because they absorb thermal energy from your hand at different rates. This raises two questions: why do objects absorb energy from you, and why do different objects do so at different rates?

- Your body is at a higher temperature than the room, so on average your molecules have more energy than molecules of objects in the room. Because of this imbalance, energy flows from you to the object. The flow rate depends on how quickly the thermal energy spreads out in the object. Copper and other metals contain freely moving electrons which readily spread thermal kinetic energy. Other materials, like wood, don't have mobile electrons. Moreover the structure of wood doesn't convey microscopic vibrations well either.

- Thermal energy in transition from one system or one state to another is called heat. In ordinary language, heat also can refer to thermal energy itself, as in the heat in a cup of hot coffee. But in strict physics speak, it's only heat if it's traveling from the cup to the surroundings, or vice versa, or creating steam that evaporates from the surface, etc.

- The spreading of thermal energy in a substance is called heat conduction. Two other types of heat transfer are convection and radiation. Convection is the motion of heated liquid or gas from one place to another, while radiation is electromagnetic wave energy (e.g. visible light, infrared, etc.) I demonstrated this with the hot plate: the light shining through the heated air above the plate showed on the screen that the air was rising. This happens because the air above the plate  has a higher temperature, but the same pressure as the room air. According to the gas law it therefore has lower particle density, so there is a buoyant force on the heated air and it rises. The heating element becomes red, showing that it is also emitting radiation. You can feel the radiation from the side. where no convection and not much conduction is operating.

- Discussed these types of heat in the operation of an oven. In particular, why the bottom of the cookies on the lower rack burns first, and the advantage of a convection oven.

- Discussed how a thermos bottle suppresses all three types of heat transfer.

- On a an extremely hot summer day when the air temperature is 38 C, a glass of ice water resting on a table outside stays at 0 C as long as the ice hasn't all melted. WHY? The colder ice water is absorbing energy from the hotter air, but that energy is not raising the temperature of the ice where is it going? It is being used to detach H2O molecules from the ice, into the surrounding water, i.e. to melt the ice. It costs energy to melt the ice. That energy ends up as chemical potential energy. The energy required to melt 1 kg of ice at 0 C is 330,000 J. This is called the latent heat of melting. When the reverse process happens, and chemical potential energy is transformed to thermal energy, it is called the latent heat of fusion. Sometimes the "latent" part of the terminology is dropped. Since it takes quite a while for all the ice to melt, it must be that this latent heat of melting is a rather large amount of energy. Indeed it is. It takes only 4190 J to raise the temperature of 1 kg of water by 1 degree celsius (at 0 C). This is called the heat capacity of the water. Since 330,000 is about 80 times larger than 4190, the latent heat of fusion would suffice to raise the temperature of water by 80 C.

- A student asked how the heat capacity depends on the temperature of the water... Good question. I think not terribly much under ordinary conditions; I will look into that.

- Showed the phase diagram of water at the wikipedia page, and talked a bit about it.

- melting and freezing are called phase transitions between ice and water, a solid and a liquid. Other types of phase transitions are evaporation and condensation between liquid and gas, or sublimation and deposition between solid and gas.

- The latent heat of vaporization or condensation of water is enormous: 2,300,000 J/kg. This 550 times the heat capacity of water, i.e. 550 times the energy required to raise the temperature per kilogram by 1 C. A fantastic demonstration of this is the Cryophorus, with with we can freeze water by evaporation. [I didn't mention the following in class, bu it's interesting to calculate what fraction of water must be evaporated in order to freeze it starting at room temperature? Its temperature has to drop from, say 20 C to 0 C, a drop of 20 C. For every one degree a fraction 1/550 must be evaporated, so in all 20/550 =~ 4% of the water must evaporate.

- We didn't have time to discuss any more, but I'd like to have discussed applications of the heat of vaporization or condensation of water: cooling by sweating, evaporative air conditioners for houses in hot, dry climates, speed up of boiling water with the lid on, cooking with steam... We also didn't get to discuss relative humidity and boiling. Please have a look at the discussion of these in the textbook.

Tuesday 2/12


- Why doesn't the atmosphere fall down, dissipate all its kinetic energy, and settle on the floor?
The answer is that the floor molecules are jiggling too, and they would transfer energy to the air. If the room is in thermal equilibrium, on average the energy is uniformly spread out among all the parts that carry energy. The parts trade energy back and forth. Actually the earth is radiating energy into space by electromagnetic waves, but it is always rewarmed by the sun. I mentioned that there are other sources of heat: radioactive decay, settling of the planetary interior, and tidal heating. According to this Wikipedia article on Earth's energy budget,  99.97% comes from the solar radiation!

- Nature of thermal equilibrium: molecules have the same average energy, regardless of their type or mass. If it were not so, energy would flow from the ones with more to the ones with less.

- Temperature: we can define absolute temperature as proportional to average kinetic energy of a gas molecule.

- Explained Kelvin, Celsius, and Farenheit temperature scales, nature of absolute zero. Tried to measure temperature of liquid nitrogen but the thermometer got stuck.

- How do helium and hot air balloon's float? Their density is less than that of the outside air, so the buoyancy force is greater than their weight. But how can we understand why their density is less than that of air?

- Nitrogen molecules in air are 7 times more massive than helium atoms, but before we can conclude that the helium in the balloon is lighter than air we need to know how many helium atoms there are compared to the number of air molecules in a balloon? It turns out there are the same number. The helium and outside air have the same temperature, and almost at the same pressure: neglecting the tension pressure of the balloon (which is rather small compared to atmospheric pressure) the inside and outside pressures must be equal, otherwise the balloon surface would be accelerating in or out. Avogadro's principle says that the number of gas molecules is determined by the volume, temperature and pressure, independent of the type of molecule.

- Avogadro basically made a good guess (I think). Here's the original article Avogadro published in 1811. The fact that his principle is true is what allowed the science of chemistry to develop. Why? Well chemistry has to do with reactions between different molecules, and to understand that you have to be able to compare the numbers of different types of molecules before and after reactions take place. But how can you observe the number of molecules?? Avogadro's principle is the answer: by measuring macroscopic things: volume, pressure and temperature, you have indirect access to a microscopic thing: the number of molecules! Not the absolute number, but relative numbers. Eg., twice the volume at the same pressure and temperature contains twice the number of molecules.

- Actually, though we can understand why Avogadro's principle holds, and more, by thinking about the fact that pressure is due to collisions of molecules with the walls. See 2010 notes for details, but we derived the ideal gas law: pressure ~ (particle density)x(absolute temperature), and particle density = (number of particles)/(volume).

- Hot air balloon: now the molecules inside the ballon have the same mass as outside, but the air is at a higher temperature inside. Since the pressure is still equal to atmospheric pressure inside, the ideal gas law tells us that the particle density is less: there are fewer air molecules per unit volume inside the hot air than in the cold air.

- Cold helium balloon: A helium balloon cooled to liquid nitrogen temperature (77 K) has temperature about 1/4 as much as room temperature, ~300 K. The ideal gas law then tells us that since the pressure remains the same as the ambient pressure, the particle density in the balloon must be 4 times as high as it would be at room temperature. If no helium went out of the balloon when we cooled it from room temperature, this means the volume must be 4 times smaller. 

Thursday 2/7


- Hydraulic press demo and explanation.

- Mechanical advantage: bicycle gears. The circular arc distance the pedals travel is greater than the arc distance the rear sprocket travels, so the force on the rear sprocket is greater than the force applied on the pedals. The smaller the rear sprocket the greater the difference.

- Skydiver Felix Baumgartner breaks sound barrier
He jumped from his balloon at around 39,000 m  = 39 km = ~24 miles. His chute opened after 4 minutes and some, and he did get up to around 1.25 times the speed of sound (which at sea level is 340 m/s). We can infer that there was a lot of air resistance, because if he had fallen freely without air resistance it would have taken only 88 s, about 1.5 minutes, to fall the whole way, and he would have been going around 880 m/s at the bottom, which is around 2.6 times the speed of sound. [FYI, not covered in class: We can determine the falling time as follows: if t is the time, his speed at the bottom would be gt and, since the speed grows in proportion to the time, his average speed would be half this, gt/2. Multiplying this by the time traveled we get the distance d traveled: d = gt^2/2. Solving gives t = (2d/g)^1/2 = (78,000 m/10 m/s^2)^1/2 = (7800)^1/2 s =~88 s.]

- Microworld: so far we discussed mainly motion, energy and forces on objects we can see and feel. But many phenomena depend on the behavior of objects too small to see or feel, like molecules and atoms. The simplest example I could think of is friction: when an object slides across the table and stops, friction is responsible. The microscopic mechanism of friction is a complicated mess. The two surfaces adhere partially, they are rough, they bump and grind, etc. The next example we considered is the pressure in a balloon: what is pushing back? The ancient Greeks inferred the existence of atoms, and atomic theory was deeply and eloquently discussed by the Roman poet/philosopher/scientist Lucretius in his book On the nature of things. The nature of the atoms wasn't known, and at the beginning of the 19th century some scientists imagined that air pressure would be due to squishy atoms or molecules that filled all the space, pushing up against each other like marshmallows. Avogadro was a leader in understanding that in fact, molecules occupy a tiny fraction of the volume of the air or any gas, and that pressure is due to myriads of collisions of the molecules with the walls of the container. It seems to me that this was already clear to Lucretius.

- Discussed fluid pressure, atmospheric pressure, water pressure, increase of water pressure with depth, 10 meters of water is equivalent to one atmosphere, as is 760mm of mercury (Hg), which is 13.5 times as dense as water. See 2010 notes from 9/13,15,17 for more on all this... I might add some later.

-  Helium balloon floats...why? Because the net force of the air on it is upward and greater than its weight. Explained this with Archimedes' principle, and the fact that helium atoms are much light than air molecules.

- What is air? nitrogen N_2 (78%) and oxygen O_2 (21%) molecules, argon Ar atoms (1%), a smidgen of carbon dioxide CO_2 (0.03%), and tiny fractions of other things.
The molecules are on average about 20 times farther apart than their own size (their size is ~ 1.5 x 10^-10 m). Thus there is one molecule per volume 20x20x20=8000 times the volume of a molecule.  They must therefore travel on average 8000 times their own length before colliding with another molecule. This distance is around 10^-6 m, otherwise known as one micron, 1. This doesn't take long: at room temperature they are moving around 500 m/s (they must be moving faster than the speed of sound in air, because sound propagates by collisions of air molecules). So in 10^-9 s (one nanosecond) they travel half a micron, so it takes on average a couple of nanoseconds for a molecule to collide with another.

- I put an air balloon on a liquid nitrogen bath and cooled the air in it enough to liquefy! The liquid is 8000 times less dense than the gas (see above) so basically there is almost no liquid in the balloon, and it just looked totally empty. But as the air evaporated, it quickly puffed up again. Then I put a helium balloon on a bath of liquid nitrogen, and it got smaller, but didn't liquify. You need to go to much lower temperature to liquify helium, but it can be done!

Tuesday 2/5


- Relation between work and kinetic energy: I showed how the work on a baseball, for example, is equal to the change of kinetic energy of the ball. The point of this is to show you a bit of how the calculations in physics work, and to illustrate why kinetic energy is defined the way it is. This derivation is not in the book, so I'll show it here. Consider straight line motion of a body of mass m that starts at speed v, and as a result of a force F acquires a change of speed ∆v. Then the change of kinetic energy is 1/2 m (v + ∆v)^2 - 1/2 m v^2 = mv ∆v + 1/2 m (∆v)^2. Over a very short time interval, the change ∆v is much smaller than v, so we can drop the second term, so the change of kinetic energy is just mv ∆v. Now ∆v = a∆t, where a is the acceleration a and ∆t is the time interval, so the change of kinetic energy can be expressed as ma v∆t. Finally, Newton's 2nd law says that ma = F, and v∆t = ∆d, the distance traveled, so the change of kinetic energy is F ∆d, which is the work done by the force F over the displacement ∆d! [For a different derivation of this, which assumes a constant force and uses the average velocity, see the 2010 notes, Friday 9/10.]

- Work can also transfer potential energy, by changing the configuration of a system. I illustrated this with the examples lifting a brick and twisting a spring. When lifting a mass m a height h, the work done is the force required to oppose the weight, mg, times h, so work = mgh. This is the change in gravitational potential energy of the system.

- How much work to lift one liter of water 10 cm? One liter = 1000 cm^2, and each cm^3 has a mass of 1g, so one liter of water has a mass of 1kg. (Those metric units are pretty convenient, eh?). So the work is mgh = (1 kg)(10 m/s^2)(0.1 m) = 1 kg m^2/s^2 = 1 J = 1 joule. The nickname for the SI unit of work or energy is the joule (J), named after the scientist James Prescott Joule.

- Power is the rate of transfer of energy. The SI unit of power is one joule per second, also called one watt (1 W = 1 J/s).  A 100 watt bulb consumes 100 joules in 1 second. To run the bulb for one second takes as much energy as it takes to lift a liter of water 10 meters.

- Discussed the waterfall example in the homework.

- One AAA battery stores about 5000 J of energy, enough to lift 1 liter of water 500 meters. A human can fairly easily output 400 watts of power, at which rate it would take only 12.5 seconds to deliver the same energy as is stored in the battery. This is a striking thought. Is it possible to design a generator and battery that would let us recharge a battery like that in 12.5 seconds?! (Am I making some computational error here?)

- An LED such as used in my bike lamp might consume only about 0.1 watts of power, for example. At that rate, it could run for 50,000 seconds, or about 14 hours, on one AAA battery.

- Mechanical advantage: Transferring the same work with a smaller force acting over a longer distance. Examples: ramp, lever, block and tackle. The ramp I illustrated with pyramid building, and it's discussed in the textbook with a piano. The lever is a rigid bar that pivots on a fulcrum. It transfers work done at one end to work done at the other end. If the force F1 is applied at one end, which travels a distance d1, the work done is F1 d1. This must be equal to the work done by the force at the other end (since the lever doesn't add or subtract any work, it just transfers the work from one end to the other), so F1 d1 = F2 d2. The ratio of the forces is thus F1/F2 = d2/d1. The ratio d2/d1 is the same as the ratio of the lever lengths from the fulcrum, r2/r1. I used this principle to lift two students on a platform applying only a force with my pinky finger. Of course, I only lifted them a couple of inches, but with a ratchet mechanism like you find on some car jacks, I could repeat the lever motion and lift them to any height, applying only a small force, but over a long distance. Another example I showed is the block and tackle in this demonstration: B3-13 PULLEY VS NO PULLEY. This is rigged up so that the rope loops around two full times before attaching, so that the bucket is suspended from four sections of rope. Then for each meter the bucket goes up, you have to pull four meters of rope. The pulling force is thus one fourth of the total force holding up the bucket.

Thursday 1/31


- reviewed and explained again concepts from previous class.

- more on law of universal gravitation. This is covered a bit in Chapter 4, Section 4.2, "Orbiting the Earth", but I went into it in more depth.

- The story I've heard is that Newton first conjectured that when the gravitational forces due to all the parts of the spherical earth are added together (as vectors), the net result is the same as if all the mass of the earth were located at the center of the earth, and that it took him 20 years to develop tools of calculus to demonstrate this. The link above goes into the complicated history of discovery of this law and its implications in some depth.

- I demonstrated with a crumpled piece of paper and a bean bag that all things fall at the same rate at the surface of the earth, and explained why: an object with more mass has more inertia, but also the gravitational force on it is more, in the same proportion. So the effect of the mass cancels. In a formula,  the magnitude of the acceleration is

a = F/m = (GMm/d^2)/m = GM/d^2 = g,

where M is the mass of the earth and d is the distance from the center of the earth to the surface.

- [This cancellation of the mass seems very odd. Why should the same quantity that determines inertia determine the magnitude of the gravitational force? Einstein zeroed in on this coincidence and explained it in his general relativity theory, according to which gravity is regarded as a shift in the local inertial motions, rather than as a real force. This shift is described in the theory as being due to "curvature of spacetime."]

- The magnitude of the acceleration of gravity g at the earth's surface is about 10 m/s^2. This means that in free-fall, every second an object picks up 10 m/s of speed. After 2 seconds a dropped object would have a speed of 20 m/s, etc (neglecting air resistance). (A closer value is 9.8 m/s^2, within 2% of 10 m/s^2, so close enough for our purposes. Actually, g varies over the surface of the earth.)

-  This video of somersaulting astronauts shows that regardless of their mass, they all "fall" the same way, in fact the same way that the space station itself falls.

- Orbits of satellites around the earth (or of planets around the sun) can be understood as a consequence of continuously falling toward the earth. I showed a nice simulation illustrating this with Newton's picture of how it works. For a satellite right at the surface of the earth, it picks up 10 m/s downward velocity every second. The speed of the satellite is related to the acceleration of gravity and the radius of the earth.

- [For the mathematically inclined student: if the satellite is going horizontally with a speed v, in one second its direction of motion rotates by an angle of  (10 m/s)/v radians. At the same time its angular position rotates around the earth by an angle given by the distance it covers (v)(1s) divided by the radius r of the earth, (v)(1 s)/r. Setting these two angles equal to each other yields 10(m/s)/v = v(1 s)/r, so v = Sqrt[10r] ~ 8 km/s, since r = 6,370 km. That's pretty fast! The circumference of the earth is 2π r ~ 40,000 km, so at 8 km/s it takes around 5000 s to complete the orbit, i.e. about 5000/60 ~ 83 minutes.]

- Weight and gravity: The force of gravity on a mass m at the earth's surface is mg. This is called the weight of the mass. When you stand on a scale at rest, you are not accelerating, so this force is evidently balanced by the upward force of the scale on your feet. Now Newton's 3rd law comes into play: when the scale exerts a force on you, you exert an "equal and opposite" force on the scale. That is

Newton's third law:  force of A on B = negative of force of B on A

So, the force you exert on the scale is equal to the force gravity exerts on you, i.e. your weight. The scale measures this force and reports your weight.

- Example: I have a french scale that reports weight in kilograms. If it tells me my mass is 65 kg, my weight is mg = (65 kg)(10 m/s^2) = 650 N. I weigh 650 Newtons. If I use this scale on the moon, where the acceleration of gravity is about 6 times smaller, it will tell me my mass is ~ 65kg/6 ~ 11 kg. This is WRONG! My mass doesn't change when I go to the moon (at least it didn't last time I went there). But my weight, i.e. the force of gravity on me, does change. So a scale that measures weight would still read the correct thing on the moon. A scale that measures pounds is indeed measuring weight, since a pound is a unit of force, not a unit of mass.

- So far we've focused on energy and force. There is a relation between them, captured by the concept of work. Work is the way energy is transferred from one system to another by the action of a force:
work = force x displacement in the direction of the force.

It's only the displacement in the direction of the force that matters. For example, when I twirl a ball around in a circle on the end of a rope, the speed of the ball and therefore its energy does not change. The direction of the velocity changes, so the ball is accelerating, and this requires a force. The force is exerted by the rope, which pulls toward the center of the circle. But the displacement of the ball is along the circle, perpendicular to the force. So this force does no work on the ball, and therefore transfers no energy to it. By contrast if the force is applied in the same direction as the displacement, energy is transferred. Here's a beautiful example, Sandy Koufax pitching a baseball. And another, without the good music but with a better view of the motion. (Koufax pitched from 1955-1966 for the Brooklyn and LA Dodgers.) In this example, the ball picks up kinetic energy. It's also possible for work to transfer potential energy, that is, energy of configuration, as we'll discuss next time.

Tuesday 1/29


What sections of the book we will cover:
Chap. 1: Sections 1.1 and 1.3, all; Section 1.2 only the first part, "Weight and gravity".
Chap. 2: only section 2.2
Chap. 3: none
Chap. 4: none
Chap. 5: all
Chap. 6: none

to be continued...

Today we discussed several basic concepts:

energy: needed to make new things happen, conserved

: resistance to change of velocity (see below for definition of velocity)

: more mass has more inertia; defined specifically by Newton's 2nd law below

: change of position, described by a distance and a direction

: rate of change of position; displacement per unit time; described by a speed and a direction

: rate of change of velocity; has magnitude and direction

: "a push or a pull"; makes an object change its velocity, i.e. makes it accelerate

: A vector is a quantity with both magnitude and direction; so displacement, velocity, and force are all vectors; NOTATION: In the book and on this webpage, vectors are denoted with boldface. In class on the chalkboard, vectors are denoted with an arrow on top of the letter.

addition of vectors: To add two vectors, you can represent them as arrows, and add them like you would add displacements, along one vector first, followed by the other. The order makes no difference.

Newton's laws of motion:
I. motion of an object is uniform (no acceleration) if no force acts on the object.
II. acceleration = force/mass, a = F/m
III. (will come back this)

units: - measurement units: we'll use the SI (Systeme Internationale) units;
For some history and current definitions of these units see:



(m/s)/s = m/s2
N = kg m/s2

1 meter was defined from 1791-1889 as 1/10,000,000 times the distance from equator to pole of the earth. If the earth were perfectly spherical (instead of having a bulge at the equator due to its spinning motion) one degree of latitude would be 10,000 km/90 degrees, or approximately 111 km = 67 miles. Now it is defined in terms of the distance light travels in a certain amount of time. For more history see
1 second is defined in terms of the duration of a certain kind of oscillation in a Cesium atom.

1 kilogram = 1000 grams, 1 gram = 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. Soon it will be defined in atomic terms.

- Fundamental forces of nature: gravitational, electromagnetic, weak, nuclear
; We should also include the "Higgs field interaction", which is really not part of this list of four. I commented that one day we may understand these forces as unified into one kind of interaction, perhaps in the context of string theory. I also mentioned that perhaps the fact that we seem to see these four forces is an accidental feature of our neighborhood of the universe, and that far away, beyond what we could ever see, perhaps there are other parts of the universe with different forces...

- universal gravitation: Newton figured out that the falling of an apple, the motion of the moon, the tides, and the motion of the planets, could all be explained by the same universal mechanism: any two bodies attract each other with a force directed along the line joining them, with a magnitude equal to (mass 1)(mass 2)/(distance squared) times a constant called Newton's constant G. The apple is pulled by each part of the earth in the direction towards that part. It falls "down", toward the center of the earth, because that is the direction of the TOTAL force. The total force is the vector sum of all the individual forces. The sideways components cancel because the earth is spherically symmetric.

Thursday 1/24


- course logistics & policies
- note: the reading for this week is Chapter 1.
- This course will address how things in the natural world work at the basic physical level, for example:

energy, temperature, heat, entropy, freezing, boiling, electricity, lightning, magnetism, atoms, color, sunlight, rainbows

as well as how human-made things work, for example:
refrigerator, crystal watch, stringed instrument, battery, motor, generator, fluorescent light, LED, computer display
3d glasses, radio, cell phones, lasers, CD/DVD/Blu-ray, fiber optics, X-ray imaging, radiation cancer therapy, nuclear power and bombs



- energy: most important concept in physics; needed to make things change; never created or destroyed: conserved
         - fundamental types of energy:
                 - kinetic (energy of motion: 1/2 x (mass) x (velocity)^2)
                 - potential (energy of configuration)

         - forms of energy:
                 - chemical (microscopic kinetic and potential energy stored in structure of atoms and molecules)
               - nuclear
(microscopic kinetic and potential energy stored in structure of nuclei)
                 - thermal, "heat": (random, microscopic kinetic and potential energy)
                 - gravitational
                 - electromagnetic

- entropy: a measure of disorder
         - second law of thermodynamics: total entropy of the world cannot decrease (but always increases)
         - despite the 2nd law of thermo, life continues on earth because the sun provides ordered energy (also some
            heat from gravity and radioactivity inside earth). Solar energy comes from nuclear fusion. Gravity essential
            to squeezing nuclei close enough to undergo fusion. Earthbound attempts to generate fusion include:
            NIF: National Ignition Facility, and ITER: International Thermonuclear Experimental Reactor.
            [Nuclear fission reactors exploit the release of energy when certain large nuclei break up, whereas nuclear
             fusion involves release of energy when small nuclei fuse.]

- inertia: resistance to change in motion (speeding up, slowing down, or changing direction). More mass has more inertia.