Physics 12: Midterm Study Guide

This study guide summarizes the things you'll need to know for the midterm exam. In some cases, the full level of detail is not covered here, so consult the relevant material for more. Nothing will be presented on the exam that has not been covered in lectures. So treat the lecture notes as the primary resource, referring to the book for supplemental information/description. The exam will cover material through Lecture 11, and chapters 1–3 and sections 4.1, 4.2 in the book. The front page 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 and refer to the quizzes (on TED) as additional study guides.

• Understand that energy is the capacity to do work.
• Work is a force times a distance: 8 Newtons applied across 0.5 meters represents 4 Joules of work, requiring 4 Joules of energy to accomplish.
• 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.
• 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.
• 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, some fraction of this total energy is available to a windmill.
• 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.
• Heat energy is the amount of energy it takes to heat something up. In essence, heat energy is randomly oriented motion (kinetic energy) on the atomic/molecular scale. Examples of heat energy are contained in the list of units above (specifically, the Btu, the calorie, and the kilocalorie). For any substance, the amount of heat energy associated with a change in temperature ΔT is ΔQ = c_pmΔT, where m is the object's mass, and c_p is the heat capacity of the object. For water, c_p = 4,184 J/kg/°C. For most other substances (wood, air, metal), c_p ≈ 1000 J/kg/°C.
• Chemical energy results from the rearrangement of atoms in molecules, and often results in local deposition of heat (e.g., combustion). Sometimes the energy can be converted to electrical forms (battery). Typical energy content is several kcal (Calories) per gram.
• Food energy is a form of chemical energy, and we derive 4 kcal/g, 4 kcal/g, and 9 kcal/g, respectively from carbohydrates, protein, and fat. We can convert this energy source into useful work at a maximum efficiency of around 25%.
• 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. For all intents and purposes, mass is conserved in our ordinary experience.
• Radiant energy is the energy associated with thermal radiation of light. All objects glow by thermal radiation. The flux of energy dissipation is given by: F = σT⁴ in Watts per square meter, where σ = 5.67×10^-8 W/m²/°K⁴. The temperature must be represented in Kelvin for this to work. The radiant power emitted from a surface of area, A, is just P = F×A = σAT⁴.
• Be able to perform simple calculations on all the above forms of energy, and intermingle concepts (power associated with some energy process over some amount of time, for instance, or exchange of potential energy for kinetic energy or heat energy).
• Energy is Conserved, meaning that energy cannot be created nor destroyed, but can flow between forms. More technically correct is the statement that mass-energy is conserved, to account for the fact that mass can be converted directly to energy and vice-versa. Because the mass-exchange is terribly small in our daily experience, we can usually think of mass and energy as being separately conserved. In our power plants, we don't create energy, we simply transform one form of energy into another.
• Perpetual motion is impossible because this implies no loss of average kinetic energy. For this to be true, we must not allow any of the kinetic energy to convert into friction/heat/turbulence. But this will never be the case: energy will always leak off, and because energy is conserved, this reduces the kinetic energy and ultimately brings the system to a stop.
• The end-stage of most energy processes is heat, or disordered motion. When a pendulum set into motion eventually stops, all of its original motion has gone into heating the room.
• 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, earth would get hotter, and radiate more (via σT⁴ law) until a balance was achieved.
• We (along with Canada) use about twice the per-capita energy of other industrial nations (about 60 bbl of oil equivalent per year). This is about five times the global average.
• 81% of our energy resources stem from fossil fuels (36% oil, 23% natural gas, 22% coal). The remaining 19% is split roughly evenly between nuclear and renewable sources.
• 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 in the U.S.
• Very roughly speaking, 1/3 of our energy consumption is for electricity, 1/3 is for transportation, and 1/3 is for industry. Another 10% gets wedged into this for residential consumption. Electricity production is diversified, but dominated by coal. Transportation is almost entirely oil, and industry is split between oil and natural gas.
• Fossil fuels are a short-lived feature of our human existence, and at current rates of use, will be depleted in about 50 years (oil and natural gas: coal may last more than 100 years).
• Fossil fuels are generally hydrocarbons, delivering approximately 50 kJ/gram (if perfectly combusted: gasoline in practice delivers more like 9 kcal = 38 kJ per gram). The combustion with oxygen produces about 3 grams of CO₂ for every gram of fuel.
• Most of the oil in the world sits below countries with whom we have a knack for conflict. If, for political reasons (e.g., wars), we found ourselves cut off from international sources, we would be left with less than 20 years of conventional U.S. supply—even with rampant exploration/drilling. Fracking may change this story somewhat, but not in such a way that we need not worry.
• By most estimates, we've already used about half of the total petroleum resource in the world. Still, the U.S. government is not discouraging use of gasoline, with taxes six times lower than in most other industrial nations.
• Natural gas supplies are limited to local resources, because transport is awkward other than through pipelines. We've already used more than half of the available resource, with perhaps less than 50 years left. Again, fracking may change this story, but it is too early to make conclusive projections or statements.
• Coal is a carbon-based fossil fuel that we have in abundance (relative to the others). At present rates, we could survive on our proven reserves of coal for as long as 250 years (less than 100 years is more realistic if this became our sole source). But global warming and other environmental concerns about coal extraction/use may drive us to ignore this resource.
• Shale oil and tar sands may provide temporary relief from the petroleum crunch, but of these two, tar sands may be the only one that is economically viable and capable of being harvested at a fast enough rate.
• Heat engines are devices that extract useful work (turn a turbine/generator, turn a crankshaft, etc.) from the flow of heat. Thermodynamic Law prohibits this process from being more efficient than the ratio: (T_h - T_c)/T_h. For this relation to work, the temperatures must be in Kelvin.
• The thermodynamic limit mentioned above stems from the fact that total entropy (of the whole system) cannot ever decrease. You do not need to be able to follow the logic that produced the result above, but just know something about what entropy means and that it can never decrease, except locally.
• 99.9% of electrical plants turn generators, 97% via turbines, and 89% via steam (don't focus on the numbers themselves, but the sense that the numbers convey). So almost all of our electricity (coal, gas, nuclear) derives from steam (and are therefore heat engines). The sequence goes: an energy source creates heat; the heat boils water into steam; the steam turns a turbine; the turbine turns a generator; the generator puts out electricity; repeat until tired.
• Generators involve rotating coils of wire within a magnetic field to produce an alternating current.
• Our power plants are typically only 33% efficient, though a few have been built to 40% efficiency. The thermodynamic limit is closer to 65%, but practical engineering limitations prevent us from achieving this.
• Cogeneration can use the waste heat from a turbine/generator for space heating, increasing the total effective efficiency of the system to about 70%.
• Heat pumps and refrigerators are just heat engines run backwards, and may achieve efficiencies much greater than unity, working better the smaller the temperature difference between hot and cold. In effect, the mechanical work is used to move heat content from one environment to another, adding only a little bit to it. Efficiency factors above ten are not uncommon. This seems like magic, and means, for instance, that you can heat a room with ten times less energy by using a heat pump than by turning that energy directly to heat in the first place (via an electric heater or gas flame).
• The efficiency of a heat pump is T_x/(T_h − T_c), where T_x is T_h for warming applications, and T_c for cooling applications. It looks just like the heat engine efficiency turned upside down. Thus small ΔT translates to higher heat pump efficiency, as noted in the previous point.
• Be familiar with how to count up energy use at home: if you run a 1500 W space heater for 30 minutes, you use 0.75 kWh of energy, for example.
• 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 an average of about 850 W/m² at the ground. Half of this is at infrared wavelengths.
• 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 is closer to 850 W/m², or may be as high as 1000 W/m² if the sky is very clear.
• 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.
• 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 85 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.

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