E1_Rev_F23

Energy and Environment

First Review Sheet

This document provides an outline of the material we have covered so far in the course. The first exam (and eventually the final) will cover these topics. However, the tests may ask for more detail than is provided here, and I might ask minor questions about material not presented here. Please review questions in the first three homeworks for the first exam.

For the exam, I will provide physical constants (such as the speed of light, or the diameter of the Earth). I will not provide equations, so you should be familiar with those I list below. However, there will only be about 2 problems on the exam that require actual calculation. The exam will consist of 10 multiple choice or short answer questions, and then 6 half page essay questions.

The Earth is 4.6 billion years old and 8000 miles in diameter. Atop this surface, there is a thin (20-60 mile) layer of atmosphere which consists mostly of nitrogen and oxygen. The presence of oxygen indicates that life exists here. Small quantities of water vapor and carbon dioxide in the air help warm our planet, and negative feedback tends to keep the temperature roughly constant. However, over geologic time the average global temperature has been both much warmer and much cooler than it is now.

Directly or indirectly, the Sun provides nearly all of our energy. There are also much smaller amounts of geothermal energy, tidal energy, and fuel for nuclear fission. A tiny fraction of the Sun’s energy is converted into fossil fuels – our species is now rapidly using up supplies accumulated over millions of years. Globally, fossil fuels account for about 80% of our energy usage; nuclear fuel accounts for another 5%. Once these “fuels” are used up, they will be gone, unlike energy “flows” (solar, hydropower) that will continue to be available. Energy usage varies by sector; the ~30% of Energy we use for transportation is provided almost exclusively by oil. Energy consumption rates are affected by our population growth, as there are over 8 billion people on the planet, and our numbers are growing at about 1% a year.

People can provide about 100 W of power over a sustained period of time. Given that the typical American uses over 10,000 W of power, we clearly use a lot more energy than our own bodies can produce. Electricity is much cheaper than manual labor, costing roughly $0.10 per kWh. Using a little more energy per capita than an agrarian society leads to large gains in life expectancy and productivity, but further energy usage may easily be squandered.

Science is a body of knowledge acquired using the scientific method. Scientists make observations, formulate theories, and then test their theories by making new predictions. This process is iterative; there is no final answer. To explore what will occur in complex systems, scientists rely on models which approximate the real world – these models often give reasonable predictions of the future (think of weather reporting). Peer-review is the process by which scientists evaluate work before accepting it for publication; this step is crucial for scientists to trust the work.

Energy and Power are closely related ideas, with Power defined as Energy per time. Some common units for Energy are Joules (J), calories (cal = 4.184 J), British Thermal Units (BTU = 1,054 J), and kilowatt-hours (kWh = 3.6 million J). Power is usually measured in Watts (Joules per second), or Btu/hour. There are many kinds of energy, but in this class we’ll focus on kinetic energy ( ½ m v²), gravitational potential energy ( m g h), electrical energy (Power = Voltage*Current), chemical energy, and nuclear energy.

Electricity is the flow of charge (current) through a closed loop (circuit). Power plants turn mechanical energy into electricity through Faraday’s Law of Induction. In practice this means that a turbine spins a coil of wire in a magnetic field. Storing large amounts of electrical energy is a serious technical challenge today.

Thermal energy, or molecular motion, is quantified by Temperature – scientists use the Kelvin temperature scale, where 0 K means no molecular motion. Heat is then the transfer of thermal energy from one object to another – from hot to cold, normally, though we can force it to go the other way by inputting work (e.g. refrigerators). There are three methods by which heat can flow: conduction, convection, and radiation. Convection (“Warm air rises”) is involved in weather patterns and is difficult to describe mathematically. Conduction is heat transferred directly through a material (Heat per time = k Area (Th – Tc)/d = Area (Th-Tc)/R). Radiation from any dense object (blackbody) follows two important laws: Wien’s Law that peak (in nm) = 2.9 million/T and Stefan’s Law: Power/Area = e  T^4. Wien’s law says that objects at everyday temperatures radiate infrared light, and Stefan’s Law says that power increases very rapidly with temperature: doubling the temperature of a star (from 3000 K to 6000 K, for instance) leads to 16 times more power radiated.

As heat flows into or out of an object, it will change in temperature. How much the temperature changes depends on the mass of the object, and on the specific heat of the material (Heat = m c dT). Water has an unusually large specific heat, 4184 J/kg. Phase changes (e.g. water to ice) also require a transfer of heat, specifically the latent heat of the material.

PLEASE NOTE: This paragraph will NOT appear on Exam 1, but WILL appear on the Final. One statement of the Second Law of Thermodynamics is that it is impossible to completely convert heat into work. The maximum (Carnot) efficiency of a heat engine is given by the temperatures of its hot and cold reservoirs: e = 1 – Tc/Th, where the temperatures are in Kelvin. Electricity and Kinetic Energy are “high quality” because they can be used for any type of work – thermal energy is “lower quality”: because not all of it can be converted into high quality forms.

Fossil fuels are formed by applying pressure and heat to organic matter. For ancient swamps, this results in peat and eventually coal, a fuel that it nearly all carbon. For ancient seabeds, this results in kerogen and eventually petroleum (liquid = crude oil, vapor = natural gas) which are saturated hydrocarbons (C_nH_2n+2). Crude oil is refined into a variety of products (including gasoline) – this process itself requires a great deal of energy. Burning fossil fuels combines their carbon with oxygen to produce carbon dioxide (and perhaps water) and release chemical energy. Of the fossil fuels natural gas produces the most energy per mass and coal produces the least

Power plants are “external combustion engines” that convert about a third of their input chemical energy into electrical energy. A large coal-fired power plant typically delivers about 1 GWe of power. Most vehicles rely on internal combustion engines; gasoline engines are most common for cars. Diesel engines burn hotter and so are most energy efficient (but more polluting). Hybrid cars get better mileage for city driving, mostly through regenerative breaking.

Each fossil fuel “resource” refers to the total quantity on Earth – the “reserves” are then the amount of that resource that we can recover in an economically viable way. How long before we run out of fuel entirely depends on the available reserves and the rate of resource consumption; as both of these vary with time such projection are rough estimates. However, it is likely that we won’t run out of coal for over a century. Oil and natural gas will last for decades (50 years?), or longer if we account for unconventional sources such as tar sands (from Canada, for instance) or shale deposits such as the Marcellus Shale. Oil and natural gas can be extracted through technologies such as fracking, dramatically increasing US petroleum production in recent years. However, long before we completely run out of these fuels we will pass Hubbert’s peak – the point where supply begins to decrease even as demand continues to rise. Hubbert’s peak for Oil may even occur in the next few years.

A carbon tax is a fee levied on a fuel based on the amount of carbon it emits. The tax could apply when the fuel is extracted, or where it is used (burned). British Columbia has a carbon tax that is revenue neutral, rebated through reductions in income tax. In Cap and Trade plans, the government gives out or sells allowances to emit carbon. Companies that emit less carbon than permitted can sell allowances; those that want to emit more can buy them. The European Union has such as system; New York is part of the Regional Greenhouse Gas Initiative for eleven northeastern states.

Pollution is harmful substances released into the environment as a consequence of obtaining, transporting or using energy. Particulate matter (e.g. soot) is the most dangerous of these, and in the modern U.S. it kills about 7,500 people per year. Sulfur dioxide causes acid rain, and is a problem particularly for the Northeast, which is downwind of Midwestern coal-fired power plants. Cap-and-trade policies implemented under the Clean Air Act have dramatically cut SO₂ emissions over the past 30 years. Unfortunately levels of NOx and tropospheric Ozone (which affects the most U.S. citizens) have only fallen very slowly. In most cases technology exists to reduce pollution (filters, electrostatic precipitators, scrubbers, catalytic converters, etc), but often their implementation is expensive and energy-intensive.

Coal also can cause environmental damage when it is extracted from the ground, particularly for strip mines or mountaintop removal. On the other hand coal is cheaper than the other fossil fuels, leading to the “Tragedy of the Commons”; unless an explicit price is set on clean air, clean water, etc., then market forces are incapable of protecting the environment we all depend on. The extraction of unconventional fossil fuel reserves (from tar sands or the fracking of shale) is particularly energy intensive and damaging to the environment.

Chapter 7 covers nuclear power, so we covered some basic nuclear physics. The chemical structure of an atom is determined by its electrons, but the nuclear structure of the atom is determined by the protons and neutrons in its nucleus. The number of protons is called the atomic number and determines the name of the element. The number of protons and neutrons together then determines the atomic weight; the number of neutrons determines the isotope. Nuclear forces are much stronger than chemical bonds (by a factor of about 10 million), leading to the “nuclear difference” – you need a lot less nuclear fuel than you do chemical fuel.

Iron-56 is the most tightly bound nucleus. For lighter nuclei, we can combine them (fusion) to get energy. For heavier nuclei, we can split them (fission) to get energy. All present-day nuclear power plants use nuclear fission to generate electricity; nuclear fusion is the source of the Sun’s energy. Heavy nuclei that split fairly easily (e.g. ²³⁸U) are called fissionable; those that split very easily (e.g. ²³⁵U, ²³⁹Pu) are called fissile. The critical mass of a fissile isotope is the minimum needed for a chain reaction. A multiplication factor of one leads to the sustained reaction used in power plants; inserting neutron-absorbing control rods allows this value to be varied. The basic form of the power plant (heating water to make steam to spin turbines) is the same as fossil-fuel power plants. There are different reactor types, depending on the type of moderator used to slow the neutrons, and depending on how the reactor is cooled. France in particular generates most of its electricity through nuclear power.

Waste from nuclear fission plants will need to be stored for 100,000 years to become safe. Radioactive decays occur through alpha, beta, or gamma emission, and are characterized by a half-life (the time it takes half the nuclei to change). Background radiation for US citizens is about 4 mSv/year, roughly half from medical procedures. Exposure to 100 mSv raises the risk of getting cancer by 1%. Accidents at power plants can lead to hundreds or thousands of deaths, but they are rare, so that overall they hurt far fewer people than pollution from coal-fired plants. However, lingering fear over radiation, and the tremendous upfront costs to build a reactor, make it unlikely that nuclear fission will increase its fraction of world energy supplied.

The fusion of hydrogen isotopes (such as deuterium) into helium holds the prospect of providing a nearly endless supply of clean energy, but many technological hurdles remain before such plants are economically feasible. Methods relying on magnetic confinement (such as ITER, under construction) of the plasma are more developed than those which rely on inertial confinement.