A Note of Caution. . . .
Remember, this study guide is only an aid: a guide to studying your notes. I will try to mention all of the important themes, and will illustrate these with some of the details -- but I certainly will omit some details. Nevertheless, these details may turn up on the exam.
If You Read Nothing Else . . .
Temperature, Pressure, and the First Law of Thermodynamics
Entropy and the Second Law of Thermodynamics
. . . then take this one crucial piece of advice:
Note down all of the basic quantities we've learned about (work, power, etc.),
memorize their definitions, and
memorize their measurement units!
Trying to think about conceptual physics without first learning the basic definitions is like trying to analyze Shakespeare without first learning how to read. There's much more to Shakespeare than simply knowing what the words mean -- but if you don't know what the words mean, you can't even begin to address the more complex issues. So it is with physics: There's much more to it than memorizing definitions, but memorize you must.
As I have often pointed out in class, introductory physics students are often tempted to make vague use of precisely defined physical quantities, based on the imprecise use of these words in ordinary English. Resist temptation. Energy isn't power, current isn't charge, efficiency isn't mechanical advantage, and force isn't work.
Everyone, "science person" or not, is capable of learning this basic terminology: It's just a matter of spending time studying.
In order to tackle energy, we must first understand work, which involves both force exerted and distance over which the force is exerted. No motion, no work, however much force is exerted. If we push in the direction of motion, we do positive work; if we push against the motion, we do negative work.
The motion of an object depends not just on how much work we do on it, but on the sum of work done on it by all outside forces. If this total ("net") work is positive, the object speeds up; if negative, it slows down.
If I throw a baseball, I do a lot of positive work on it, with the result that it speeds up as I move my arm forward. The ball, in short, obtains a large amount of kinetic energy. This in turn enables the ball to do a lot of work on whatever it might hit. That's all energy is: the ability to do work.
The baseball can do work by virtue of its motion, so it has kinetic energy. I had the ability to do work on the baseball by virtue of my breakfast, so I used up some chemical energy. In fact, I did work on the ball even before throwing it, using chemical energy to lift it a meter or two above the ground. This shows up as gravitational potential energy, enabling the thrown ball to do even more work as gravity makes it arc downward and speed up. When the ball finally reaches a waiting glove and stops, its kinetic energy is used to do work on the molecules of the ball, of the glove, and of the surrounding air: the result is thermal and sound energy.
Life would be easy if you could get something for nothing, but you can't: energy is conserved. This is the most important idea in all of science, so learn it well. You can convert one form of energy to another (or to several others), but you can't destroy or create any energy. As you can see from the preceding two paragraphs, transforming 1 J of energy involves using up 1 J of one form of energy to do exactly 1 J of work on something, with the result that this something now has exactly 1 J of some other form of energy. You can't end up with 0.99 J or 1.003 J at the end of the transaction, any more than you can change a twenty for three tens.
The analogy with money actually isn't bad, in that both money and energy are abstract but very real entities. (Once upon a time money was more tangible, but then we went off the gold standard; see an economist for details.) Even though energy is intangible, we can imagine divvying it up among various categories (KE, elastic PE) and passing it around between objects. Speed, for example, is not like this. If my baseball is struck by a swinging bat, the collision causes the ball to speed up and the bat to slow down -- but the ball speeds up by much more than the bat slows down. Hence we can't say that "the bat gives some of its speed to the ball."
You worked with power, efficiency, and mechanical advantage in lab. I'll leave it to you to review those topics.
The particles in any substance randomly move about and interact with each other and with the walls of any container. In a vapor they zoom from place to place (translational motion) and may also vibrate and rotate; in a solid crystal, they oscillate about their fixed positions in the crystal pattern. Interactions between particles means that each one is constantly changing speed and direction. Temperature is a measure of the average kinetic energy per particle. (Strictly speaking, it's proportional to the mean translational KE, involving only the motion of the entire molecule from point A to point B, as opposed to rotation or vibration of the molecule about its own center.) Low temperature means that the typical particle has low KE, whereas high-temperature material has most of its particles moving with high KE.
(As an aside, note that since KE depends on both mass m and speed v, the nitrogen molecules in a room tend to move a bit faster than the more massive oxygen molecules in order to have the two gases at the same temperature. If you put hydrogen or helium gas in the room, those extremely light particles would tend to move so rapidly that they would quickly escape Earth's gravitational pull altogether: They would evaporate into space. This is why our atmosphere contains no H or He, even though those two elements make up over 99% of the stuff in the universe! Jupiter, a colder place with a stronger gravitational field, does contain mostly H and He.)
Temperature isn't the same as internal energy or heat flow. Firewalking was one example of this. Phase transitions such as melting are a second example, as they occur at constant temperature. As a third example, imagine traveling to the upper atmosphere -- the "thermosphere" -- where the temperature is extremely high, since the particles (mostly ions) move very energetically. Yet you'd freeze to death if you went up there unprotected! Why? Because there are very few particles up there (extremely low density). Even though each particle hitting your body would hit it hard, these collisions would be rare, and hence very little heat would be conducted from the gas to you. You'd radiate away your body's thermal energy, and that would be the end.
There's no such thing as negative KE, so the lowest possible average KE is zero: every single particle sitting still. Such a state represents absolute zero, and you can't get colder than that even in theory. (Something called the Third Law of Thermodynamics says that you can't ever reach absolute zero, although you can get as close as you like.) Absolute temperature uses the Kelvin scale, which is essentially the Celsius scale shifted so that 0 K represents absolute zero.
(Any time you're asked to use a temperature T in a formula, you can't go wrong using absolute temperature. Using Celsius temperatures in formulae is risky; it works for temperature differences or changes, but not for anything else.)
Because particles are randomly moving, they will collide with neighboring particles and thereby exert force on them. That is, any material, be it vapor or liquid or solid, pushes outwards on surrounding material. If you focus on 1 m2 (unit area) of the boundary between the material and its surroundings, and add up all the outward forces exerted over that area, you have the pressure, the force per unit area. Pressure increases when the typical collision gets harder (higher temperature) or when there are more particles colliding across across each square meter (higher density -- due to more moles of gas or else compressing the same amount of gas into a smaller volume).
The first law of thermodynamics says that we can increase an object's internal energy (a.k.a. thermal energy) by doing work on it, by letting heat flow into it, or both. What this means is that heat is a form of energy (more precisely, an increase or decrease in thermal energy due to a temperature difference), not an invisible material substance as was once thought.
Heat flow always involves a temperature difference, and temperature in turn tells us the mean translational KE (i.e., KE of random motion from place to place) of the particles in the substance. There are three heat-flow mechanisms -- conduction, convection, and radiation -- and you should know how each of these processes fundamentally operates. Conduction, for example, involves collisions between neighboring molecules. (You fill in the details.) You should also be able to give examples of each heat flow mechanism, or else of situations where we try to prevent that type of heat flow.
When we increase an object's thermal energy, by heating it or by doing work on it (or both), one possible result is that the added energy shows up as extra KE of the randomly moving molecules -- that is, as a temperature rise. The specific heat (which was defined in one of the assigned Web readings) tells us about this. But that's not the only possibility! For example, the added energy might make possible an endothermic chemical reaction, which could result in a temperature drop. And at certain temperatures, added energy goes into doing work to break intermolecular bonds; this is a phase transition, such as melting or sublimation. The latent heat of fusion (or sublimation or vaporization) tells us how much energy per kg is involved in this process. The temperature doesn't change during a phase transition; a familiar example is ice water, which remains at exactly 0°C from when the first drop of meltwater appears to when the last ice chip melts.
(By the way, despite the terms "specific heat" and "latent heat," one can equally well do work to raise temperature or to produce a phase transition: The first law of thermodynamics says so.)
Since the First Law of Thermodynamics says that we can change internal energy with work or with heat flow, we can devise a heat engine, a device whose "working fluid" -- such as the air inside a cylinder with a sliding piston lid -- expands when heated, thus doing work on the surroundings. We add heat to the fluid, raising its thermal energy; the fluid then gives up thermal energy by doing useful work. If only it were that simple! Unfortunately, if we want to keep this useful process going repeatedly (cyclically), we have to compress the working fluid after each expansion. This means letting some heat leave the fluid, thus lowering the pressure and making the fluid easier to compress. (Otherwise the compression would require us to do as much work as we'd obtained during the expansion, rendering the overall process pointless.) Bottom line: Some of the thermal energy we added (and paid for!) is used to heat a coolant fluid rather than to do useful work. Our engine is inefficient.
This unavoidable inefficiency of any engine cycle is one guise of the Second Law of Thermodynamics. In the 1820s a French engineer by the name of Carnot figured out what the most efficient possible engine cycle would be, and that even that engine wouldn't be 100% efficient. (Carnot was using the old idea that heat is a material fluid, but his analysis is correct anyway!) Cleverness and technological advances have nothing to do with it: You must waste some energy.
You should be able to describe the four steps in the Carnot engine cycle, and you should be able to do simple computations using the formula for Carnot efficiency. Remember, the Carnot engine is maximally efficient because all heat flow occurs isothermally. This, unfortunately, means that the engine's power is infinitesimal (why?), so you wouldn't actually want a Carnot engine in your car.
What goes on in most real car and truck engines can be approximated by the Otto cycle or else the Diesel cycle. Each of these idealized cycles includes a step in which thermal energy is added to the cylinder via combustion, a step in which heat flows from the cylinder to the coolant, and either two or four "strokes" in which work is done on or by the gas in the cylinder. You should know a fair amount about how the Otto and Diesel cycles work and how the two engines (and fuels) differ from each other.
If you run a heat engine in reverse, you have a refrigerator (or air conditioner). Instead of having heat flow from a hot reservoir to a cold reservoir in order to convert some of this energy to work done by the working fluid, you make heat flow from a cold reservoir to a hot reservoir by doing work on the working fluid (refrigerant). You should know the basics of how the process works, and you should understand why a good refrigerant (like Freon or ammonia) should be volatile.
For any practical heat device we can define a "figure of merit" that quantifies how well the device converts energy in the way we desire -- in other words, "useful energy transfer divided by costly energy input." The bigger this ratio, the happier we are. For a heat engine this figure of merit is simply the efficiency: the work performed (useful!) divided by the thermal energy added (via gasoline combustion, costly!).
The useful part of a refrigerator cycle is the step where heat is extracted from the cold reservoir. The costly, unfortunate part of the cycle is the work done on the refrigerant, since you have to pay the power company in order to run the compressor motor that does the work. Hence the appropriate figure of merit for a refrigerator is the "coefficient of performance" (COP), the ratio of heat extracted from the cold reservoir to the work done by the compressor motor. The bigger the COP, the better -- but it can never be infinite (zero work required). That's another guise of the Second Law of Thermodynamics: Heat will never flow from low temperature to high unless we also supply some other energy, such as the electrical energy needed to get the compressor motor to perform work.
If you turn an air conditioner around come winter, so that you extract heat from the cold outdoors and exhaust even more heat to the warm indoors, you have a heat pump. This increasingly popular device can be cheaper to run than a furnace, especially if it's not too cold outside, or else if you run the outside coils deep into the ground (a "ground-source" heat pump). The same logic as above tells you that for a heat pump the sensible figure of merit -- also called the COP, unfortunately -- is the ratio of heat expelled to the warm reservoir to work done by the compressor motor.
Would you be surprised if you kicked a pile of glass shards and they happened to jump together and weld themselves into a lovely, intact crystal goblet? Would you scratch your head if a tank of light pink water gradually changed before your eyes into a tank of clear water containing a single drop of concentrated red dye? Would you find it odd if a wooden block lying stationary on the floor suddenly cooled off by turning thermal energy into kinetic energy, zooming across the room in the process? Would you be amazed if you dropped an ice cube into a cup of hot coffee and the coffee got hotter while the ice cube got colder?
Any one of these processes could be arranged to occur without any energy being created or destroyed, so they don't violate the First Law of Thermodynamics. Yet none of them ever happens! This means that we need another law of nature that describes this obvious fact of life, and the law in question is the Second Law of Thermodynamics. (Trivia point: There's also a Zeroth Law of Thermodynamics....) Some things happen in one direction only, like red dye diffusing into clear water but never re-concentrating into a drop, or friction turning the KE of a sliding block entirely into thermal energy but never thermal energy entirely into KE.
Actually, these things could happen, but are absurdly unlikely to happen. You could imagine that the zillions of dye molecules spread throughout a tank of water, randomly colliding and moving about, would all just happen to show up in the same place at the same time: a concentrated drop of dye. But you wouldn't hold your breath waiting for this to happen! There are a huge number of different ways to arrange the molecules so that they're more or less evenly spread out; each such microscopic arrangement is called a particular "microstate" of the dye-plus-water in the tank. However, bigger-than-a-breadbox (macroscopic) creatures like us can't possibly observe the detailed locations and motions of all those molecules: we only notice the overall situation of the tank, such as "dye evenly spread out." Such an observable state is called a "macrostate." A different macrostate of the tank would be "concentrated dye drop," but there are far fewer ways to arrange the molecules if you insist on having them all close together like that: far fewer microstates corresponding to that macrostate. Thus the "concentrated dye drop" macrostate is much less likely to occur than the "dye evenly spread out" macrostate. Given the huge number of molecules involved, "much less likely" mathematically works out to mean "ridiculously, astronomically unlikely."
The entropy of a system is a quantitative measure of how likely its present macrostate is, that is, how many different ways one could arrange the molecules and get that macrostate. When you place a drop of dye into clear water, the system has low entropy; as the dye diffuses throughout the water, entropy increases. The opposite process never occurs. This is yet another statement of the Second Law of Thermodynamics: The entropy of a closed system (one that doesn't interact with its surroundings) never decreases.
Notice that the high-entropy system is more disordered than the low-entropy one. We can extend this "entropy = disorder" idea by thinking about ordered vs. disordered motion. In a heat engine, a cylinder filled with high temperature gas with lots of thermal energy represents disordered motion: random, rapid molecular motions. A moving piston lid represents ordered motion: all the molecules in the piston moving at the same speed in the same direction. So if we turned the thermal energy entirely into piston energy (i.e., entirely into work) during the engine's power stroke, we'd be decreasing entropy by making things more orderly. Impossible! says the Second Law. No, we must also increase the random motions of the molecules in some coolant fluid by letting heat flow into it. This increased disorder in the coolant more than compensates for the orderly piston motion, so the total entropy increases. Similarly, the inside of a refrigerator has its entropy decreased, yet overall entropy increases (why?).
As the refrigerator example shows, it's entirely possible for something to become less disordered, so long as it's not a closed system. The working fluid in an engine cylinder decreases its entropy when heat flows out of it into the coolant fluid; the Second Law is still valid because the coolant fluid's entropy increases even more than the working fluid's entropy decreases. Here's another example: When water freezes, the water molecules change from a disordered arrangement (liquid) to an orderly pattern (ice crystal). But the water's latent heat of fusion is released to the surrounding air as this phase transition goes on. This increases the random KE of the air molecules, resulting in an increase in disorder that outweighs the increased order of the water molecules!
Same goes for the formation of rock crystals. Same goes for the evolution of complex biological organisms, despite the silly claims of so-called "creation scientists" that this can't happen because it would violate the Second Law. A little knowledge is a dangerous thing....
Since this is our most recent topic, I'll say very little about it here. You needn't memorize everything that can be said about biofuels, but should be able to discuss some of the pros and cons (or techniques, such as genetic modification) encountered in our readings. Note that our classroom discussion didn't fully cover the readings, so you're encouraged to bring in considerations that we didn't discuss.