Physics 12: Final Exam Study Guide

This study guide summarizes the things you'll need to know for the final exam. Nothing will be presented on the exam that has not been covered in lectures, and this guide specifies which topics are going to be treated on the exam. Refer to the lecture notes and the book for more information on the topics bulleted here. The exam will primarily cover material from Lecture 11 onward, (see reading assignments for chapter 4 onwards). The major themes from the first part of the class are also fair game, and are included on this study guide. The front of the exam will contain equations of relevance (but they will not be labeled as to what they pertain to), as well as any necessary constants and conversion factors.

See also the Transmitter Questions (PDF) from the second half of the class.

The first part of this study guide is a repeat of the midterm study guide, emphasizing the themes that have followed us into the second half of the quarter.

• There are a number of units for energy, but our primary unit is the Joule. Broken down, one Joule is one Newton-meter, or further, one kg-m²/s². If you think about the formula for kinetic energy: ½mv², or the famous formula E=mc², you'll see that the units are just kilograms times velocity-squared.
• Other units of energy that we use:
  • kJ, MJ, GJ, etc. are 1000, one million, and one billion Joules, respectively
  • 1 Btu (British thermal unit) is 1055 J (about 1 kJ), and is the energy required to heat one pound of water one degree Fahrenheit
  • 1 calorie is 4.184 J, and is the energy required to raise 1 gram (1 milliliter, or one cubic centimeter) of water 1 °C
  • 1 kilocalorie (kcal; sometimes Calorie) is 4,184 J, and is the energy required to raise 1 kilogram (1 liter) of water 1 °C
  • 1 kilowatt-hour (1 kWh) is the amount of energy expended at a rate of one kilowatt for one hour. Since 1 Watt is one Joule per second, and one hour is 3600 seconds, 1 kWh = 3,600,000 J = 3.6 MJ
• Power is the rate at which energy is expended. Our standard unit is the Watt, which is equivalent to one Joule per second. Another familiar unit of power is the horsepower, about 746 W.
• Be sure to clear up any confusion you still have over watts, kilowatts, and kilowatt-hours. Watts and kilowatts are a power, or the rate of energy use. A (wimpy) blow dryer runs at about 1 kW. If you run this blow dryer for an hour, the amount of energy it uses is 1 kWh, equivalent to 3,600,000 Joules. In five hours, it would use 5 kWh. A 100 W light bulb running for 24 hours uses 2.4 kWh of energy.
• Kinetic energy is the energy of motion, and for a mass, m, traveling at velocity, v, is equal to ½mv². If the mass and velocity are in kg and m/s, then the result will be in Joules. This is relevant to wind energy.
• Gravitational potential energy is the energy given to objects lifted in the gravitational field. It takes force to lift an object, and acting through some vertical distance results in work (taking energy). This energy can be released at some later time (e.g., into kinetic energy), and this is why it's called potential energy. Gravitational potential energy is given by mgh, where m is the mass, g is the acceleration due to gravity (mg is the force required to lift the object, or its weight in Newtons), and h is the distance through which the object is lifted. On earth, g = 9.8 m/s², though for the purposes of this class, 10 m/s² suffices. This principle is relevant for hydroelectric dams.
• Mass-energy draws a fundamental connection between our concepts of mass and energy. All energy actually has mass (i.e., weighs something). In nuclear processes in the sun and in reactors, the total mass is actually not conserved (not constant), but decreases as some mass is converted to energy by the famous relation E = mc². Note that the units work out—just like for kinetic energy. Here, the mass is in kg, and c ≈ 300,000,000 m/s (3×10⁸ m/s). Because c² is such a large number, the types of energy we deal with in our ordinary lives (kJ to MJ) has a negligible associated mass. In both nuclear fission and nuclear fusion, the total mass of the final product(s) is less than the total mass of the initial product(s). The difference in mass is released as (heat) energy.
• A natural radiative balance exists such that the earth's temperature settles to a point where the energy input from the sun is balanced by radiative output. For example, if the earth's radiated power fell short of the input power (e.g., if intercepted/absorbed by greenhouse gases), earth would get hotter, and radiate more (via σT⁴ law) until a balance was achieved.
• The U.S. annual energy budget is roughly 100 QBtu per year. 100 QBtu is 10¹⁷ Btu, or about 10²⁰ Joules. Divided by 3.1557×10⁷ seconds (per year) yields about 3×10¹² Watts. Divided by about 300,000,000 people (3×10⁸) is about 10,000 W per person.
• Solar energy is transmitted to us across empty space in the form of radiant energy, with a spectrum peaking in the visible wavelengths. Above the atmosphere, the total energy delivered is 1370 Joules per second (Watts) into a square meter. With no clouds, this translates to about 850 W/m² at the ground, or may be as high as 1000 W/m² if the sky is very clear. Half of this is at infrared wavelengths.
• Be able to look at a figure like Figure 4.2 in the book and deduce secondary information like percentage cloud cover, direct sunlight fraction on a clear day, etc., like we did in class in lecture 11.
• The average global insolation on the earth is about 170 W/m². Here in San Diego, we do slightly better at about 200 W/m². This is a day/night and seasonal/weather average. In broad sunlight, the number may be closer to 850 W/m², or as high as 1000 W/m².
• If solar power is to replace our fossil fuel dependence, we need to cover about 1/75^th of our land with 10%-efficient solar arrays: about 4,500 square feet (20 by 20 meters) per person.
• The insolation numbers only tell you what's hitting the surface. We can't convert this with 100% efficiency, so that a 10%-efficient solar panel can only at best (in full sun) deliver about 100 W/m².
• Be able to figure out how much power would be available for a given collector area, given some efficiency. Know the difference between average power available (day/night/seasonal) and peak available.
• Solar photovoltaics involve photons of light liberating electrons in a semiconductor that then participate in a current (flow of charge). A special arrangement of materials creates a p-n junction that sweeps liberated electrons in one direction across the device. Silicon photovoltaics (single-junction) can achieve no more than about 30% efficiency due to fundamental physics limitations, but in practice achieve about half this, except in special (very expensive) productions.
• The price of an installed photovoltaic system is about $5 per Watt currently (perhaps a bit less), so that a 2,500 W system (typical residential demand) would run about $12,500. Rebates and incentives can pull the total price to the consumer to well below $5 per peak Watt.
• Flat-plate solar collectors are used to heat water, and typically achieve 50% efficiency. These are widespread in some places, like Cyprus and Israel.
• Solar thermal generation involves concentrating sunlight for the purpose of heating water into steam, which then drives a conventional turbine/generator power plant. Current installations achieve an overall efficiency in the neighborhood of 15–20%.
• Renewable energy means energy from sources that won't be reduced by using them: like sunlight, wind, hydroelectric, biomass (if used in equilibrium with growth rate). All of these are driven by the sun.
• Hydroelectric Power is a freebee of nature that we use for about 8% of our electricity (or about 3% of our total energy use). It is simply gravitational potential energy of water. The power available is given by mgh/t, so if you know the dam height, h in meters, g≈10 m/s², and the flow rate (m/t) in kilograms per second, you have the available power. Water is 1000 kg/m³, in case you know only the flow rate in m³/s. A typical hydroelectric plant can extract as much as 90% of the available potential energy.
• Hydroelectric power is 50% tapped out already, and it is unlikely we will pursue the remaining 50% vigorously. Dams also have finite lifetimes of 50 to 200 years due to silt build-up in some areas of the country.
• Wind energy is really just kinetic energy of moving air. All you need to know is the mass and velocity of the air, then use the formula for kinetic energy. This is the most energy you can pull out of the air, and corresponds to stopping the air completely. In practice, no more than 59% of this total energy is theoretically available to a windmill.
• Wind power is the rate of accumulation of wind energy. Slide 18 of Lecture 14 motivates the formula for wind power: ½ρv³, where ρ is the density of air, about 1.3 kg/m³. So in Watts, the amount of wind power available per square meter of windmill area is about 0.65v³, where v is in meters per second. The book uses the formula: 0.61v³, which is roughly the same thing (accounts for more typical air densities at typical temperatures and altitudes).
• Wind power, whose formula appears above, is a derivative of the sun (because the sun makes air currents), and could, if fully exploited, provide a large fraction of the electrical power for our country. The formula for wind power does not account for the fact that we can't ask a windmill to extract all of the available power, otherwise the air would have to stop (giving up all of its energy), and the windmill wouldn't turn. The theoretical maximum available power to a windmill is 59% of the value the formula gives. Moreover, engineering designs do not in practice achieve full efficiency, and windmills in the end only can get about 40% of the available power. Wind power is completely clean, though a big drawback is its intermittency.
• Biomass as a source of energy usually means burning plant matter for heat (either for direct heating or driving heat engines). The total biological (photosynthetic) power budget of the earth is 40 trillion watts (half of which is in oceans, half on land), compared to >13 trillion watts of our global energy consumption (>80% of which is from fossil fuels). Biomass could be used to provide a substantial fraction of our energy needs, though this would entail a massive harvesting effort worldwide.
• Biofuels refer to biologically-derived liquid fuels like ethanol from corn or sugar, or bio-diesels. In the U.S., corn dominates the biofuel scene. Be aware of the limitations of corn ethanol: not much better than break-even energy-wise, if at all; not nearly enough agricultural land to sustain our liquid fuel needs; displaces food crops and drives food prices up.
• Nuclei are composed of protons and neutrons (collectively called nucleons)—both about the same mass, though the neutron is neutral while the proton has positive charge. Nuclei are distinguished by Z, the number of protons (determining element type), N, the number of neutrons (determining which isotope of an element), and total mass number, A = Z + N. Nuclei are often designated with A as a left superscript, Z as a left subscript, and N as a right subscript.
• A neutron on its own (i.e., not tied up in a nucleus) will decay with a half-life around 10 minutes, leaving behind a proton, an electron, and a neutrino. This is called beta-decay. Even in neutron-heavy nuclei a neutron can decay. This is how the radioactive ¹⁴C (6 protons, 8 neutrons) decays into ¹⁴N (7 protons, 7 neutrons).
• Certain nuclei undergo natural radioactive decay in one of three ways: beta-decay, wherein a nucleon changes flavor (neutron becomes proton or proton becomes neutron), emitting either an electron (β^-) or a positron (β⁺), respectively; alpha-decay, in which a ⁴He nucleus (two protons, two neutrons) is ejected; and gamma-radiation, where a high energy photon (light) is ejected, but the constituents of the nucleus do not change.
• The three types of natural radioactivity listed above are all around us all the time. Most of our exposure comes from the air we breathe and food we eat.
• Nuclear fission relates to atomic nuclei splitting apart into two large chunks. This is distinct from, for instance, alpha emission, where a large nucleus spits off a (small) helium nucleus. Only three nuclei are known to undergo spontaneous fission in the presence of slow neutrons: ²³³U, ²³⁵U, and ²³⁹Pu. Only ²³⁵U occurs naturally as 0.7% of the total uranium supply. The most abundant (99.3%) isotope of uranium is ²³⁸U, but this is not fissile.
• The fission of uranium produces two sizable fragment nuclei, plus a few extra neutrons. These extra neutrons, initially fast (a lot of kinetic energy) are slowed by a moderator (like water or graphite) in a nuclear reactor, so that they may trigger additional fission events. This allows a chain reaction to take place.
• The heat produced by fission (kinetic energy of fragments, neutrons) is transferred to the coolant, producing steam to drive turbines: a typical heat-engine application with typical power-plant efficiencies in the range of 33–40%.
• Our uranium comes from supernovae—exploding stars—that spread heavy elements into space prior to the formation of the earth. Thus this is the only energy source we currently use that does not derive ultimately from our own sun (except for geothermal, which similarly derives from radioactivity of unstable nuclei). As a side note, all the iron in the earth (the majority of the earth's interior) came from supernovae, as well as most of the mass in your body (carbon, oxygen).
• Though the abundant ²³⁸U does not participate in fission directly, it can grab an ambient neutron to become ²³⁹U, which beta-decays twice into the fissile ²³⁹Pu. Typical reactors get about a third of their energy from the subsequent fission of this self-produced plutonium. Reactors designed for the express purpose of creating plutonium are called breeder reactors, and are popular for weapons-makers.
• Our ²³⁵U resource will last us 150 years at the present rate of use, but only 30 years if we got all of our electricity from nuclear plants. This would be extended to 4,000 years under a full-scale breeder program because this would make use of the otherwise unusable ²³⁸U that is 140 times as abundant as ²³⁵U.
• Nuclear waste storage is a big unsolved problem, with the most likely solution being a deep underground storage facility. But a suitable site has not yet been developed for commercial nuclear waste storage.
• Nuclear fusion involves building larger nuclei from smaller ones. Typically this involves building ⁴He out of protons or deuterium nuclei (deuterium is an isotope of hydrogen: one proton, one neutron). The resulting helium nucleus has less mass than the total mass of the building blocks, the rest going into energy via E = mc².
• Using nuclear fusion as an energy source involves no emissions, no radioactive waste (discounting radioactive containment vessel), is 5 times more potent than uranium fission per pound of fuel (if you start from deuterium rather than protons), and would last us hundreds of thousands of years given the deuterium available in the ocean. Unfortunately, it requires a roughly 50 million degree (Celsius) plasma, making it hard to achieve, technologically.
• We have succeeded in getting fusion to work, producing 6 MW at the Princeton Tokamak (for a 12 MW input!), and also in hydrogen bombs. We still seem to be 50 years away from economic success, if it is to happen at all.
• Fossil fuels are generally hydrocarbons. The combustion with oxygen necessarily produces about 3 grams of CO₂ for every gram of fuel.
• CO₂ emissions from the burning of fossil fuels have accumulated in our atmosphere so that today we have 43% more (400 ppm) than the pre-industrial average (which was rather steady at 280 ppm for at least the last 1000 years). If we spend the remaining petroleum and natural gas (very likely), we will end up with more than twice the pre-industrial amount. Ice core records show that CO₂ has never been more abundant than about 280 ppm for the last 400,000 years.
• CO₂, after water vapor, is the chief greenhouse gas. Based on a computation of how much fossil fuel mass we've run through (per year and cumulative), it is easy to show that the observed magnitude of CO₂ increase is consistent with its deriving from our fossil fuel activity. No big surprise there.
• Greenhouse gases are infrared absorbers. So when the earth tries to dump its heat into space via thermal radiation, the greenhouse gases intercept the radiation and return some of that energy to the ground. So earth has to get hotter to strike a radiation balance.
• The pre-industrial greenhouse effect amounted to 33°C, 7°C of which is attributable to the pre-industrial concentration of CO₂ in the atmosphere of 280 ppm per volume. Simply scaling by the increasing CO₂ concentration (today at 385 ppm) gives an idea of how warm the added CO₂ might make us, absent feedback mechanisms.
• Global warming is seen to be affecting many different terrestrial systems: temperatures are rising; sea level is rising; ice is melting; earth rotation is slowing (veeery slightly: don't reset your clocks); insect and plant seasons are longer, etc.
• Predictions from an international panel of scientists are for a temperature rise of 1.4 to 5.8 °C by 2100 and a sea-level rise from 0.1 to 0.9 meters (typical value is 0.4 meters). Many displaced people, crop failures, environmental refugees, etc. The story doesn't change much even if we stop emitting CO₂ today, and the damage doesn't stop for about 300 years, by which time the oceans may be several meters higher. Alarmingly, many of the (conservative) predictions are already proving to be milder than what actually unfolds.
• Positive feedback is when a system responds to a change by wanting to change more in the same direction. This leads to runaway. Example: warmer oceans absorb less CO₂ so global warming intensifies, etc.
• Negative feedback is a stable, self-correcting feedback. If the system gets a little out of whack, natural processes tend to bring it back in line. Many examples of negative feedback exist in nature: anything in equilibrium.
• Most major oil-producing countries have peaked in their production. Economic pressures are not sufficient to coax the oil out of the ground faster. The U.S. peaked its production in 1970, and no amount of wishful thinking will bring us back to this level. It's how oil works. No country will be exempt.
• In our lifetimes, world oil production will peak. If we are not ready for this in advance, we face the possibility of global energy shortages—especially in transportation. Since economic performance has been tightly tied to energy production historically, we may expect financial upheavals to result. This is one reason that it is very important to mobilize into a full-scale effort to replace fossil fules before we get caught in the noose.
• You have more control over our predicament than you think. Whether apparent or not, you make lifestyle choices (that may seem altogether normal) that fuel the cycle of consumption and energy use. Simply keeping these factors in mind when making decisions about where to live, what career to follow, what (or if) to buy, etc. can collectively have a substantial impact.

Back to Physics 12 Main Page