Module 1 energy 2023

Energy resources using traditional materials 1.1.1 Energy resources using traditional materials 1.1.2 Problems with these resources 1.1.3 Alternative energy sources 1.5.1 Energy from th

MINISTRY OF EDUCATION AND TRAINING

NONG LAM UNIVERSITY

FACULTY OF FOOD SCIENCE AND TECHNOLOGY

Course: Physics 1 Module 1: Energy

Instructor: Dr Nguyen Thanh Son

Academic year: 2022-2023

Contents

Module 1: Energy

1.1 Energy resources using traditional materials

1.1.1 Energy resources using traditional materials

1.1.2 Problems with these resources

1.1.3 Alternative energy sources

1.5.1 Energy from the sun

1.5.2 Applications of solar technology

1.6 Other energy sources

1.6.1 Wind energy

1.6.2 Hydroelectric energy

1.6.3 Biomass energy

1.6.4 Fuel cells

Physics 1 Module 1: Energy 3

1.1 Energy resources using traditional materials

Energy is one of the most fundamental parts of our universe It is a scalar physical quantity In physics

textbooks, energy is often defined as the ability to do work or to generate heat

While one form of energy may be transformed to another, the total energy remains the same This

principle, the conservation of energy, was first postulated in the early 19th century, and applies to any

isolated system In other words, energy is subject to the law of conservation of energy According to this

law, energy can neither be created (produced) nor destroyed by itself and it can only be

transformed

We use energy to do work Energy lights our cities Energy powers our vehicles, trains, planes and

rockets Energy warms our homes, cooks our food, plays our music, and gives us pictures on television

Energy powers machinery in factories and tractors on farms

Energy from the sun gives us light during the day It dries our clothes when they're hanging outside on a

clothe line It helps plants grow Energy stored in plants is consumed by animals, giving them energy;

and predator animals eat their prey, which gives the predator animal energy

Everything we do is connected to energy in one form or another

There are many sources of energy Energy is present in the universe in various forms, including

mechanical, electromagnetic, chemical, and nuclear, etc Furthermore, one form of energy can be

converted into another For example, when an electric motor is connected to a battery, the chemical

energy in the battery is converted into electrical energy in the motor, which in turn is converted into

mechanical energy as the motor turns some device

The transformation of energy from one form to another is an essential part of the study of physics,

engineering, chemistry, biology, geology, and astronomy When energy is changed from one form to

another, the total amount present does not change Conservation of energy means that although the form

of energy may change, if an object (or system) loses energy, that same amount of energy appears

in another object or in the object’s surroundings

1.1.1 Energy resources using traditional materials

These traditional materials (or resources) include: coal, oil and natural gas (collectively called fossil

fuels) All three were formed many hundreds of millions of years ago before the time of the dinosaurs -

hence the name fossil fuels

• Coal

Coal is a hard, black colored, rock-like substance It is made up of carbon, hydrogen, oxygen,

nitrogen, and varying amounts of sulphur There are three main types of coal - anthracite, bituminous

and lignite Anthracite coal is the hardest and has more carbon, which gives it a higher energy content Lignite is the softest and is low in carbon but high in hydrogen and oxygen content Bituminous is in

between Today, the precursor to coal - peat - is still found in many countries and is also used as an

energy source

Coal is mined out of the ground using various methods Some coal mines are dug by sinking

vertical or horizontal shafts deep under ground, and coal miners travel by elevators or trains deep under

Figure 1 Process of oil formation

ground to dig the coal Other coal is mined in strip mines where huge steam shovels strip away the top layers above the coal The layers are then restored after the coal is taken away

The coal is then shipped by trains and boats and even in pipelines In pipelines, the coal is ground

up and mixed with water to make what is called a slurry This is then pumped many miles through pipelines At the other end, the coal is used to fuel power plants and other factories

Coal is used to generate electricity Power plants burn coal to make steam The steam turns turbines which generate electricity

`

A variety of industries use coal's heat and by-products Separated ingredients of coal (such as methanol and ethylene) are used in making plastics, tar, synthetic fibers, fertilizers, and medicines The concrete and paper industries also burn large amounts of coal

Coal is baked in hot furnaces to make coke, which is used to smelt iron ore into iron needed for making steel It is the very high temperatures created from the use of coke that gives steel the strength and flexibility for products such as

bridges, buildings, and automobiles

• Oil or petroleum

Oil is another fossil fuel It was

also formed more than 300 million years

ago Some scientists say that tiny diatoms

are the source of oil Diatoms (a kind of

algae) are sea creatures having the size of

a pin head They do one thing just like

plants: converting sunlight directly

into stored energy

In the Figure 1, as the diatoms died

they fell to the sea floor (1) Here they

were buried under sediments and other

rocks (2) The rocks squeezed the diatoms,

and the energy in their bodies could not escape Under great pressure and heat, oil and natural gas were eventually generated As the earth changed and moved and folded, pockets where oil and natural gas can be found were formed (3)

Oil has been used for more than 5,000-6,000 years The ancient Egyptians used liquid oil as a medicine for wounds, and oil has been used in lamps to provide light In North America, Native

Americans used oil as medicine and to make canoes water-proof The demand for oil continued to increase as a fuel for lamps Petroleum oil began to replace whale oil in lamps because the price for whale oil was very high

As mentioned above, oil and natural gas are found under ground between folds of rock and in areas of rock that are porous and contain the oils within the rock itself To find oil and natural gas, companies drill through the earth to the deposits deep below the surface The oil and natural gas are then pumped from below the ground by oil rigs They then usually travel through pipelines or by ship The petroleum or crude oil must be changed or refined into other products before it can be used

Physics 1 Module 1: Energy 5

Oil is stored in large tanks until it is sent to various places to be used At oil refineries, crude oil

is split into various types of products by heating the thick black oil Oil is made into many different products - fertilizers for farms, the clothes you wear, the toothbrush you use, the plastic bottle that holds your milk, the plastic pen that you write with There are thousands of other products that come from oil Almost all plastic comes originally from oil The oil products include gasoline, diesel fuel, aviation or jet fuel, home heating oil, oil for ships and oil to burn in power plants to make electricity

• Natural gas

Natural gas is lighter than air Natural gas is mostly made up of a gas called methane Methane

is a simple chemical compound that is made up of carbon and hydrogen atoms Its chemical formula is CH4 - one atom of carbon along with four atoms of hydrogen This gas is highly flammable

Natural gas is usually found near petroleum underground It is pumped from below ground and travels

in pipelines to storage areas

Natural gas usually has no odor, and we cannot see it Before it is sent to the pipelines and storage tanks, it is mixed with a chemical that gives a strong odor The odor smells almost like rotten eggs The odor makes it easy to smell if there is a leak

Natural gas is a major source of electricity generation through the use of gas turbines and steam turbines Natural gas is also used for heating and cooking Natural gas is an essential raw material for many common products, such as paints, fertilizers, plastics, antifreezes, dyes, photographic films, medicines, and explosives as well Another use is powering natural gas vehicles in many countries such

as Argentina, Brazil, Pakistan, Italy, Iran, and the United States

1.1.2 Problems with these resources

• Someday they will run out

Fossil fuels are generally such fuels as coal, natural petroleum (oil) and coal These materials were derived from the fossilized remains of plants and animals Much of the world has relied upon these fuels for decades and more As the years go on, the sources of these fuels have become less and less The problem with fossil fuels is that they will someday run out It takes time for these energy sources to develop within the crust of the earth At the current rate of consumption, there is no way that these fuels can develop naturally and not be used up Currently there are ways being developed to sustain these fuels

More efficient uses of these energies are being produced Cars with better gas mileage are being manufactured Hybrid cars which use electricity as well as gas are just one of many products which have been developed to sustain the use of fossil fuels Still these fuels are being depleted

Fossils fuels cannot last forever at the current rate of consumption Alternatives are being

developed to sustain the lifestyles that we have become accustomed to

• They have adverse impacts on the environment

Another problem with the use of fossil fuels is no matter how safely and efficiently these fuels are being used, they still have adverse impacts on the environment The combustion of these fuels contributes pollutants to the atmosphere and contributes to the greenhouse effect This effect increases global warming and the melting of the polar ice caps

♦ Environmental problems with coal, oil, and gas

• We consider the wide variety of environmental problems in burning fossil fuels - coal, oil, and gas They probably exceed those of any other human activities The ones that have received the most

publicity in recent years have been the "greenhouse effect," which is changing the earth's climate; acid rain, which is destroying forests and killing fish; and air pollution, which is killing tens of thousands of people every year, while making tens of millions ill and degrading our quality of life in other ways

• Coal, oil, and gas consist largely of carbon and hydrogen The process that we call "burning" actually

is chemical reactions with oxygen in the air For the most part, the carbon combines with oxygen to form carbon dioxide (CO2), and the hydrogen combines with oxygen to form water vapor (H2O) In these chemical reactions, a substantial amount of energy is released as heat Since heat is what is needed

to instigate these chemical reactions, we have a chain reaction: reactions cause heat, which causes reactions, which cause heat, and so on

• The carbon dioxide that is released is the cause of the greenhouse effect A large coal-burning plant typically burns 3 million tons of coal and produces 11 million tons of carbon dioxide every year The water vapor release presents no problems, since the amount of water vapor in the atmosphere is

determined by evaporation from the oceans - if more is produced by burning, that much less will be evaporated from the seas

The greenhouse effect and global warming

• Electromagnetic radiation is an exceedingly important physical phenomenon that takes various forms depending on its wavelength Every object in the universe constantly emits electromagnetic radiation, and absorbs (or reflects) that which impinges on it According to the laws of physics, the wavelength of the emitted radiation decreases inversely as the temperature increases Conversely, the rate at which an object emits radiation energy increases very rapidly with increasing temperature (doubling the absolute temperature increases the radiation 16-fold) Now let us consider a bare object out in space, such as our moon It receives and absorbs radiation from the sun, which increases its temperature, and this increased temperature causes it to emit more radiation Through this process it comes to an equilibrium

temperature, where the amount of radiation it emits is just equal to the amount it receives from the sun That determines the average temperature of the moon If this were the whole story, our earth would be

54 degrees cooler than it actually is, and nearly all land would be covered by ice

• The reason for the difference is that the earth's atmosphere contains molecules that absorb infrared radiation They do not absorb the visible radiation coming in from the sun, so the earth gets its full share

of the visible radiation But a fraction of the infrared radiation emitted by the earth is absorbed by those molecules which then reemit it, frequently back to the earth That is what provides the extra heating This is also the process that warms the plants in a greenhouse - the glass roof does not absorb the visible light coming in from the sun, but the infrared radiation emitted from the plants is absorbed by the glass and much of it is radiated back to the plants That is how the process got its name - greenhouse effect It

is also the cause of automobiles getting hot when parked in the sun light; the incoming visible radiation passes through the glass windows, while the infrared emitted from the car's interior is absorbed by the glass and much of it is emitted back into the interior

• Molecules in the atmosphere that absorb infrared radiation and thereby increase the earth's

temperature are called greenhouse gases Carbon dioxide is an efficient greenhouse gas Our problem is

that burning coal, oil, and gas produces carbon dioxide, which adds to the supply already in the

atmosphere, increasing the greenhouse effect and thereby increasing the temperature of the earth The average temperature of the earth has been about 1 degree warmer in the 20th century than in the 19th

Physics 1 Module 1: Energy 7

century, which is close to what is expected from this carbon dioxide increase As the rate of burning coal, oil, and gas escalates, so too does the rate of increase of carbon dioxide in the atmosphere

• Two side effects will accentuate this temperature rise One is that the increased temperature causes more water to evaporate from the oceans, which adds to the number of water molecules in the

atmosphere; water vapor is also a greenhouse gas The other side effect is that there would be less ice and snow

Acid rain

• In addition to combining carbon and hydrogen from the fuel with oxygen from the air to produce carbon dioxide and water vapor, burning fossil fuels involves other processes Coal and oil contain small amounts of sulfur, typically 0.5% to 3% by weight In the combustion process, sulfur combines with oxygen in the air to produce sulfur dioxide (SO2), which is the most important contributor to acid rain Air consists of a mixture of oxygen (20%) and nitrogen (79%), and at very high temperatures, molecules of these can combine to produce nitrogen oxides (NO), another important cause of acid rain Sulfur dioxide and nitrogen oxides undergo chemical reactions in the atmosphere to become sulfuric acid and nitric acid, respectively, dissolved in water droplets that may eventually fall to the ground as rain This rain is therefore acidic

• After the rain falls, water percolates through the ground, dissolving materials out of the soil This alters the soil’s pH and introduces other materials into the water If the soil is alkaline, the water's acidity will be neutralized, but if it is acid, the acidity of the water may increase This water is used by plants and trees for their sustenance, and eventually flows into rivers and lakes There have been various reports indicating that streams and lakes have been getting more acidic in recent years

Air pollution and health effects

• The greenhouse effect and acid rain have received more media attention and hence more public concern than general air pollution This is difficult to understand, because the greenhouse effect causes only economic disruption, and acid rain kills only fish and trees, whereas air pollution kills people and causes human suffering through illness

• We have already described the processes that produce sulfur dioxide and nitrogen oxides, which are important components of air pollution as well as the cause of acid rain But many other processes are also involved in burning fossil fuels When carbon combines with oxygen, sometimes carbon monoxide (CO), a dangerous gas, is produced instead of carbon dioxide Thousands of other compounds of

carbon, hydrogen, and oxygen, classified as hydrocarbons or volatile organic compounds, are also produced in the burning of fossil fuels During combustion, some of the carbon remains unburned, and some other materials in coal and oil are not combustible; these come off as very small solid particles, called particulates, which are typically less than one ten thousandth of an inch in diameter, and float around in the air for many days Smoke is a common term used for particulates large enough to be visible Some of the organic compounds formed in the combustion process attach to these particulates, including some that are known to cause cancer Coal contains trace amounts of nearly every element, including toxic metals such as beryllium, arsenic, cadmium, selenium, and lead, and these are released

in various forms as the coal burns

• All of the above pollutants are formed and released directly in the combustion process Some time after their release, nitrogen oxides may combine with hydrocarbons in the presence of sunlight to form ozone, one of the most harmful pollutants

• Let us summarize some of the known health effects of these pollutants:

Figure 2 Left: Normal earth Right: What the earth would be if we

are not using alternative energy sources

Sulfur dioxide is associated with many types of respiratory diseases, including coughs and colds, asthma, bronchitis, and emphysema Studies have found increased death rates from high sulfur dioxide levels among people with heart and lung diseases

Nitrogen oxides can irritate the lungs, cause bronchitis and pneumonia, and lower resistance to respiratory infections such as influenza; at higher levels it can cause pulmonary edema

Carbon monoxide bonds chemically to hemoglobin, the substance in the blood that carries oxygen to the cells, and thus reduces the amount of oxygen available to the body tissues Carbon

monoxide also weakens heart contractions, which further reduces oxygen supplies and can be fatal to people with heart disease Even at low concentrations, it can affect mental functioning, visual acuity, and alertness

Particulates, when inhaled, can scratch or otherwise damage the respiratory system, causing acute and/or chronic respiratory illnesses Depending on their chemical composition, they can contribute

to other adverse health effects For example, benzo-a-pyrene, well recognized as a cancer-causing agent from its effects in cigarette smoking, sticks to surfaces of particulates and enters the body when they are inhaled

Hydrocarbons cause smog and are important in the formation of ozone

Ozone irritates the eyes and the mucous membranes of the respiratory tract It affects lung function, reduces ability to exercise, causes chest pains, coughing, and pulmonary congestion, and damages the immune system

Volatile organic compounds include many substances that are known or suspected to cause cancer Prominent among these is a group called polycyclic aromatic, which includes benzo-a-pyrene mentioned above

Toxic metals have a variety of harmful effects Cadmium, arsenic, nickel, chromium, and

beryllium can cause cancer, and each of these has additional harmful effects of its own Lead causes neurological disorders such as seizures, mental retardation, and behavioral disorders, and it also

contributes to high blood pressure and heart disease Selenium and tellurium affect the respiratory system, causing death at higher concentrations

• It is well recognized that toxic substances acting in combination can have much more serious effects than each acting separately, but little is known in detail about this matter Information on the quantities

of air pollutants required to cause various effects is also very limited There can however be little doubt that air pollution is a killer

1.1.3 Alternative energy sources

• Alternative energy is an

umbrella term that refers to

any source of usable energy

intended to supplement or

replace fuel sources without

the undesired consequences

of the replaced fuels

• The sources of alternative

energy are nuclear, solar,

wind, geothermal and other

energies; each of them having

its own advantages and

disadvantages Alternative

energy sources hold the key towards the future; without them, our planet will eventually head into a blackout, or back to the Middle Ages, as shown in Figure 2

Physics 1 Module 1: Energy 9

Figure 3 Schematic of a basic thermionic converter

• Oil fuels the modern world No other substance can have the enormous impact which the use of oil has had on so many people, so rapidly, in so many ways, and in so many places around the world

• Alternative energy sources must be compared with oil in all these various attributes when their

substitution for oil is considered None appears to completely equal oil

• But oil, like other fossil fuels, is a finite resource There will always be oil in the earth, but eventually the cost to recover what remains will be beyond the value of the oil Also, a time will be reached when the amount of energy needed to recover the oil equals or exceeds the energy in the recovered oil At that point oil production becomes a net energy loss

• Oil being the most important of our fuels today, the term "alternative energy" is commonly taken to mean all other energy sources and is used here in that context Realizing that oil is finite in practical terms, there is increasing attention given to what alternative energy sources are available to replace oil The table below mentions many alternative energy sources that have been developed so far

Alternative energy sources

Hydro-power electricity Solar energy Wind energy Wood/other biomass

Nuclear fission Nuclear fusion Geothermal energy Ocean thermal energy

1.2 Thermionic engine

Also known as thermionic generator or thermionic converter, thermionic engine is a device in

which heat energy is directly converted into electrical energy; it has two electrodes, one of which is

raised to a sufficiently high temperature to become a thermionic electron emitter, while the other, serving as an electron collector, is operated at a significantly lower temperature It utilizes the same principles as the thermionic vacuum

tube, an electronic device in which

electrons are driven from a cathode to

an anode by the application of a high

potential bias

1.2.1 Principle of thermionic

emission

♦ Principles of thermionic emission

• A thermionic converter can be

viewed as an electronic diode that

converts heat into electrical energy

via thermionic emission It can also be

regarded in terms of thermodynamics

as a heat engine that utilizes an

electron-rich gas as its working fluid

• A thermionic converter is a diode of which one electrode is heated to a sufficient high temperature (~1700 K) so that electrons are thermionically emitted The electrons are collected on a cooled counter electrode (~900 K), converting heat into electricity

• A major problem in developing practical thermionic power converters has been the limit imposed on the maximum current density because of the space-charge effect As electrons are emitted between the electrodes, their negative charges repel one another and disrupt the current Two solutions to this problem have been pursued One involves reducing the spacing between the electrodes to the order of micrometers, while the other entails the introduction of positive ions into the cloud of negatively charged electrons in front of the emitter The latter method has proved to be the most feasible from many standpoints, especially manufacturing It has resulted in the development of both cesium and auxiliary discharge thermionic power converters

• Emission of electrons is fundamental to thermionic power conversion The energy required to remove

an electron from the surface of an emitter is known as the electronic work function (ϕ) Its value is

characteristic of the emitter material and is typically one to five electron volts (eV) Some electrons within the emitter have an energy greater than the work function and can escape The proportion

depends on the temperature The current density J 0, in amperes per square meter, or the rate at which electron is emitted from the surface of the emitter, is given by the Richardson–Dushman equation

2 0

where T is the absolute temperature, in kelvins, of the emitter, e is the electronic charge in coulombs, and k is Boltzmann’s gas constant, in joules per kelvin The parameter R in the above equation is also characteristic of the emitter material

• Note that the rate of emission increases rapidly with emitter temperature T and decreases

exponentially with the work function ϕ It is therefore desirable to choose an emitter material that has a small work function and that operates reliably at high temperatures

• Electrons that escape the emitter surface have gained energy equal to the work function, plus some excess kinetic energy Upon striking the collector, a part of the energy is available to force current to flow through the external load, such as a bulb or a resistor, thereby giving the desired conversion from thermal to electrical energy Part of this energy is converted into heat that must be removed to maintain the collector at a suitably low temperature The collector material should have a small work function

1.2.2 Thermionic engine (thermionic converter)

• Thermionic converters are designed for use in domestic heating systems They are also used in regulation of current in electric circuits

• In a thermionic converter, the electrons received at the anode flow back to the cathode through an external resistance However, because the cathode is hotter than the anode and the work function of the anode is lower than that of the cathode, the rate of electron emission at the cathode is greater than that required at the anode to complete the circuit The surplus electron flow may then be drawn off from the anode as additional electrical energy, effectively converting the heat energy from the cathode into electrical energy at the anode Such devices currently show efficiencies of up to 20% for the energy conversion

Physics 1 Module 1: Energy 11

• There are some advantages for using thermionic converters:

Heat sources such as solar energy, which is a renewable resource, may be used Heat energy which would otherwise be a wasted side-effect of an industrial process may be partially and usefully recycled using such devices

Devices may be manufactured using micro-electronic fabrication techniques, for very small converters, where conventional converters are impractical

When compared to conventional devices, such devices are likely to be smaller, weigh less, and cause little or no pollution

• Typically, the space between cathode and anode in such devices must be very small, and there are difficulties in constructing such devices Vacuum diodes may require spacing of less than 0.001 inch The spacing can be increased by the use of low pressure diodes with the space filled with a suitable plasma, such as cesium gas This advantage, however, brings with it further disadvantages, due to the complexity of analyzing the behavior of gases in such an environment and the heat exchange reactions within the plasma during the operation of the device, which tend to render it less efficient In order to encourage the release of electrons from cathode, surfaces of very low work functions must be

constructed Such surfaces have in the past been characterized by the use of very small points, or tips, which have the effect of increasing the potential gradient by concentrating it at the tips, to render electron emission easier

1.3 Electric energy

1.3.1 Electricity is a secondary energy source

• Electricity is a form of energy which can produce light, heat, magnetism, and chemical changes, and which can be generated by friction, induction, or chemical changes Electricity is a basic part of nature, and it is one of our most widely used forms of energy Electricity is usually produced using fossils, hydraulic power or nuclear reactions, etc Electricity is a controllable and convenient form of energy used in the applications of heat, light and power

• Electricity is a secondary energy source which means that we get it from the conversion of other sources of energy, such as coal, natural gas, oil, nuclear power and other natural sources, which are called primary sources In most cases a primary source of energy is used to drive a turbine; the turbine

in turn drives a generator, and the electric power from the generator passes through a transformer to power lines

• In the late-1800s, Nikola Tesla pioneered the generation, transmission, and use of alternating current (AC) electricity, which can be transmitted over much greater distances than direct current Tesla's inventions used electricity to bring indoor lighting to our homes and to power industrial machines

1.3.2 Electricity generation

• A generator is a device that converts mechanical energy into electrical energy The process is based

on the relationship between magnetism and electricity (electromagnetic induction) In 1831, Faraday discovered that when a magnet is moved inside a coil of wire, electrical current flows in the wire

Figure 4 Diagram of a turbine generator

of alternating current electricity

Figure 5 A graphic depictions of electrical power generation, transmission, and distribution

• A typical generator at a power plant uses an

electromagnet - a magnet produced by electricity - not a

traditional magnet The generator has a series of

insulated coils of wire that form a stationary cylinder

This cylinder surrounds a rotary electromagnetic shaft

When the shaft rotates, it induces a small electric current

in each section of the wire Each section of the wire

becomes a small, separate electric conductor The small

currents of individual sections are added together to form

one large current, as shown in Figure 4 This current

carries the electric power that is transmitted from the

power plant to the consumers

• Steam turbines, internal-combustion engines, gas

combustion turbines, water turbines, and wind turbines

are the most common methods to generate electricity

Most power plants are about 35 percent efficient That

means that for every 100 units of energy that go into a

plant, only 35 units are converted into usable electrical

energy

• The electricity produced by a generator travels along

cables to a transformer, which changes electricity from

low voltage to high voltage Electricity can travel over

long distances more efficiently using high voltage

• Transmission lines are used to carry the electricity to a substation Substations have transformers that change the high voltage electricity into lower voltage electricity From the substation, distribution lines carry the electricity to homes, offices, and factories, which require low voltage electricity Figure 5 depicts electrical power generation, transmission, and distribution

Physics 1 Module 1: Energy 13

1.4 Nuclear energy

1.4.1 Einstein’s mass – Energy relation

• In physics, mass-energy equivalence is the concept that any mass has an associated energy and vice versa In special relativity, this relationship is expressed using the mass-energy equivalence formula

where m is the mass of the object of interest, c is the speed of light in a vacuum, c = 3x108 m/s, and E is

the energy equivalent of the mass

• Because the speed of light squared is a very large number when expressed in appropriate units, a small amount of mass corresponds to a huge amount of energy Thus, the conversion of mass into energy could account for the enormous energy output of the stars, but it is necessary to find a physical

mechanism by which that can take place

Example: A stick of wood is burned, and it releases 1000 joules of heat energy How much mass was "converted into energy?" (Ans 1.1 x 10-14 kg)

• Two definitions of mass in special relativity may be validly used with this formula If the mass in the formula is the rest mass, the energy in the formula is called the rest energy If the mass is the relativistic mass, then the energy is the total energy

• Formula (2) does not depend on a specific system of units In the International System of Units (SI), the unit for energy is the joule, for mass the kilogram, and for speed the meter per second Note that

1 joule equals 1 kg·m2/s2 In the SI unit system, E (in joules) = m (in kilograms) multiplied by

(3x108 m/s)2

• The concept of mass-energy equivalence unites the concepts of conservation of mass and conservation

of energy, allowing rest mass to be converted to forms of active energy (such as kinetic energy, heat, or light) Conversely, active energy in the form of kinetic energy or radiation can be converted into

particles which have rest mass The total amount of mass/energy in a closed system (as seen by a single observer) remains constant because energy cannot be created or destroyed, and in all of its forms, trapped energy exhibits mass In relativity, mass and energy are two forms of the same thing, and neither one appears without the other

• The energy equivalent of one atomic mass unit (1 u):

1 uc2 = (1.66054 × 10-27 kg) × (2.99792 × 108 m/s)2 = 1.49242 × 10-10 kg (m/s)2 = 1.49242 × 10-10 J

× (1 MeV/1.60218 × 10-13 J) = 931.49 MeV, so 1 uc 2 = 931.49 MeV

where ∆E designates a change in the energy of the system and ∆m designates a change in the mass of

the system

• This formula also gives the amount of mass lost from a body when energy is removed In a chemical

or nuclear reaction, when heat and light are removed, the mass is decreased So ∆E in the formula is the energy released or removed, corresponding to a mass lost, ∆m In those cases, the energy released and

removed is equal in quantity to the mass lost, times c2 Similarly, when energy of any kind is added to a resting body, the increase in the mass is equal to the energy added, divided by c2

• The rest mass of a system, however, is not the sum of the rest masses of its parts taken one-by-one, free from the system The difference between the rest mass of a system and the total rest mass of the

(free) component parts in the system is called the mass difference of the system, ∆m; the corresponding

energy is called the binding energy of the system It is the energy which has been emitted in the

formation of the system

• Nuclei are found to be made out of two constituents: protons and neutrons We label a nucleus by its

atomic number Z which is the number of protons it contains, and by its mass number A = Z + N where

N is the number of neutrons the nucleus contains The letter A (number of nucleons in the nucleus) denotes the sum of Z and N.

The symbol used to identify a nucleus is Z AX where X is the name of the chemical element For

example the carbon-14 nucleus, which contains 8 neutrons and 6 protons, is denoted by 146C Since the

element’s name specifies the number of electrons, and hence the atomic number Z, and since A = N + Z,

we can fully specify the nucleus by just the symbol for the chemical and the mass number

• Nuclear binding energy, denoted by BE, is the minimum energy that would be required to

disassemble the nucleus of an atom into its component parts.To calculate the binding energy we use the formula

BE = (∆m)c2 = [Zmp + Nmn − mnucleus]c2 (3’) where Z denotes the number of protons and N number of neutrons in the nucleus, respectively and

mnucleus the rest mass of the nucleus of interest We can take mpc2 = 938.2723 MeV and mnc2 = 939.5656 MeV

Example: A deuteron 2

1D, which is the nucleus of a deuterium atom, contains one proton and one neutron and has a rest mass of 2.013 553 u This total deuteron mass is not equal to the sum of the masses of the proton and neutron Calculate the mass difference and determine its energy equivalence, which is called the binding energy of the nucleus

Solution: Using atomic mass units (u), we have mp = mass of proton = 1.007 276 u,

mn = mass of neutron = 1.008 665 u, mp + mn = 2.015 941 u The mass difference is therefore

∆m = 2.015 941 u − 2.013 553 u = 0.002 388 u By definition 1 u = 1.66 x 10-27 kg, thus

∆m = 3.96 x 10-30 kg Using ∆E = (∆m)c2, we found the binding energy of the deuteron is

BE = (3.96 x 10-30 kg)(3.00 x 108 m/s)2 = 3.56 x 1013 J = 2.23 MeV

As a result, the minimum energy required to separate the proton from the neutron of the

deuterium nucleus (the binding energy) is 2.23 MeV

• Nature contains nuclei of many different sizes In hydrogen they contain just one proton, in heavy hydrogen ("deuterium") a proton and a neutron; in helium, two protons and two neutrons; and in carbon, nitrogen and oxygen - 6, 7 and 8 protons of each particle, respectively The weights of all these nuclei have been measured, and an interesting fact was noted: a helium nucleus weighed less than the total weight of its components The same held even more for carbon, nitrogen and oxygen - the carbon nucleus, for instance, was found to be slightly lighter than three helium nuclei By measuring the mass

of different atomic nuclei and subtracting from that number the total mass of the protons and neutrons

as they would weigh separately, one gets the exact binding energy available in an atomic nucleus This

is used to calculate the energy released in any nuclear reaction, as the difference in the total mass of the nuclei that enter and exit the reaction