Newton compared the acceleration of the moon to the acceleration of objects on earth. Believing that gravitational forces were responsible for each, Newton was able to draw an important conclusion about the dependence of gravity upon distance. This comparison led him to conclude that the force of gravitational attraction between the Earth and other objects is inversely proportional to the distance separating the earth's center from the object's center. But distance is not the only variable affecting the magnitude of a gravitational force. Consider Newton's famous equation
Fnet = m • a
Newton knew that the force that caused the apple's acceleration (gravity) must be dependent upon the mass of the apple. And since the force acting to cause the apple's downward acceleration also causes the earth's upward acceleration (Newton's third law), that force must also depend upon the mass of the earth. So for Newton, the force of gravity acting between the earth and any other object is directly proportional to the mass of the earth, directly proportional to the mass of the object, and inversely proportional to the square of the distance that separates the centers of the earth and the object.
But Newton's law of universal gravitation extends gravity beyond earth. Newton's law of universal gravitation is about the universality of gravity. Newton's place in the Gravity Hall of Fame is not due to his discovery of gravity, but rather due to his discovery that gravitation is universal. ALL objects attract each other with a force of gravitational attraction. Gravity is universal. This force of gravitational attraction is directly dependent upon the masses of both objects and inversely proportional to the square of the distance that separates their centers. Newton's conclusion about the magnitude of gravitational forces is summarized symbolically as
Since the gravitational force is directly proportional to the mass of both interacting objects, more massive objects will attract each other with a greater gravitational force. So as the mass of either object increases, the force of gravitational attraction between them also increases. If the mass of one of the objects is doubled, then the force of gravity between them is doubled. If the mass of one of the objects is tripled, then the force of gravity between them is tripled. If the mass of both of the objects is doubled, then the force of gravity between them is quadrupled; and so on.
Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces. So as two objects are separated from each other, the force of gravitational attraction between them also decreases. If the separation distance between two objects is doubled (increased by a factor of 2), then the force of gravitational attraction is decreased by a factor of 4 (2 raised to the second power). If the separation distance between any two objects is tripled (increased by a factor of 3), then the force of gravitational attraction is decreased by a factor of 9 (3 raised to the second power).
The proportionalities expressed by Newton's universal law of gravitation are represented graphically by the following illustration. Observe how the force of gravity is directly proportional to the product of the two masses and inversely proportional to the square of the distance of separation.
Another means of representing the proportionalities is to express the relationships in the form of an equation using a constant of proportionality. This equation is shown below.
The constant of proportionality (G) in the above equation is known as the universal gravitation constant. The precise value of G was determined experimentally by Henry Cavendish in the century after Newton's death. (This experiment will be discussed later in Lesson 3.) The value of G is found to be
G = 6.673 x 10-11 N m2/kg2
The units on G may seem rather odd; nonetheless they are sensible. When the units on G are substituted into the equation above and multiplied by m1• m2units and divided by d2 units, the result will be Newtons - the unit of force.
Knowing the value of G allows us to calculate the force of gravitational attraction between any two objects of known mass and known separation distance. As a first example, consider the following problem.
Sample Problem #1
Determine the force of gravitational attraction between the earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is standing at sea level, a distance of 6.38 x 106 m from earth's center.
The solution of the problem involves substituting known values of G (6.673 x 10-11 N m2/kg2), m1 (5.98 x 1024 kg), m2 (70 kg) and d (6.38 x 106 m) into the universal gravitation equation and solving for Fgrav. The solution is as follows:
Sample Problem #2
Determine the force of gravitational attraction between the earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is in an airplane at 40000 feet above earth's surface. This would place the student a distance of 6.39 x 106 m from earth's center.
The solution of the problem involves substituting known values of G (6.673 x 10-11 N m2/kg2), m1 (5.98 x 1024 kg), m2 (70 kg) and d (6.39 x 106 m) into the universal gravitation equation and solving for Fgrav. The solution is as follows:
Two general conceptual comments can be made about the results of the two sample calculations above. First, observe that the force of gravity acting upon the student (a.k.a. the student's weight) is less on an airplane at 40 000 feet than at sea level. This illustrates the inverse relationship between separation distance and the force of gravity (or in this case, the weight of the student). The student weighs less at the higher altitude. However, a mere change of 40 000 feet further from the center of the Earth is virtually negligible. This altitude change altered the student's weight changed by 2 N that is much less than 1% of the original weight. A distance of 40 000 feet (from the earth's surface to a high altitude airplane) is not very far when compared to a distance of 6.38 x 106 m (equivalent to nearly 20 000 000 feet from the center of the earth to the surface of the earth). This alteration of distance is like a drop in a bucket when compared to the large radius of the Earth. As shown in the diagram below, distance of separation becomes much more influential when a significant variation is made.
The second conceptual comment to be made about the above sample calculations is that the use of Newton's universal gravitation equation to calculate the force of gravity (or weight) yields the same result as when calculating it using the equation presented in Unit 2:
Fgrav = m•g = (70 kg)•(9.8 m/s2) = 686 N
Both equations accomplish the same result because (as we will study later in Lesson 3) the value of g is equivalent to the ratio of (G•Mearth)/(Rearth)2.
In thermal generating plants, fuel is converted into thermal energy to heat water, making steam. The steam turns an engine (turbine), creating mechanical energy to run a generator. Magnets turn inside the generator, producing electric energy.
From fuel to electric energy
Coal, oil and gas are used to make thermal electricity. They all work basically the same way (with a few exceptions: for example, in an oil- or gas-fired plant, fuel is piped to the boiler).
Coal supply — After haulers drop off the coal, a set of crushers and conveyors prepare and deliver the coal to the power plant. When the plant needs coal, coal “hoppers” crush coal to a few inches in size and conveyor belts bring the coal inside.
Coal pulverizer — The belts dump coal into a huge bin (pulverizer), which reduces the coal to a fine powder. Hot air from nearby fans blows the powdered coal into huge furnaces (boilers).
Boiler — The boiler walls are lined with many kilometres of pipe filled with water. As soon as the coal enters the boiler, it instantly catches fire and burns with high intensity (the temperatures inside the furnace may climb to 1,300° C). This heat quickly boils the water inside the pipes, changing it into steam.
Precipitators and stack — As the coal burns, it produces emissions (carbon dioxide, sulphur dioxide and nitrogen oxides) and ash.The gases, together with the lighter ash (fly ash), are vented from the boiler up the stack. Huge air filters called electrostatic precipitators remove nearly all the fly ash before it is released into the atmosphere. The heavier ash (bottom ash) collects in the bottom of the boilers and is removed.
Turbine and generator — Meanwhile, steam moves at high speed to the turbines, massive drums with hundreds of blades turned at an angle, like the blades of a fan.As jets of high-pressure steam emerge from the pipes, they propel the blades, causing the turbine to spin rapidly. A metal shaft connects the turbine to a generator. As the turbine turns, it causes an electro-magnet to turn inside coils of wire in the generator. The spinning magnet puts electrons in motion inside the wires, creating electricity.
Condensers and cooling water system — Next, the steam exits the turbines and passes over cool tubes in the condenser. The condensers capture the used steam and transform it back to water. The cooled water is then pumped back to the boiler to repeat the heating process. At the same time, water is piped from a reservoir or river to keep the condensers constantly cool. This cooling water, now warm from the heat exchange in the condensers, is released from the plant.
Water purification — To reduce corrosion, plants purify water for use in the boiler tubes. Wastewater is also treated and pumped out to holding ponds.
Ash systems — Ash is removed from the plant and hauled to disposal sites or ash lagoons. Ash is also sold for use in manufacturing cement.
transformer and transmission lines — transformers increase the voltage of the electricity generated. transmission lines then carry the electricity at high voltages from the plant to substations in cities and towns.
Types of thermal plants
Many of Canada’s large thermal plants use a simple-cycle process to generate electricity. Fuel is burned to heat water to create steam, and much of the heat is vented as hot air or steam. While these conventional thermal plants use less fuel than plants in the past to generate the same amount of power, they still lose energy in the form of exhaust heat or steam.
Some thermal plants have been converted from simple cycle to combined-cycle generation, a form of more advanced thermal technology. These plants capture waste heat from exhaust gases to produce more electricity and to use fuel more efficiently. Gas-fired combined cycle plants have a heat conversion efficiency of about 60 per cent, compared to 35 per cent for conventional simple-cycle plants.
Cogeneration is another important innovative thermal technology, which is increasing in use. Cogeneration plants produce electricity and usable heat or steam from a single fuel source such as natural gas. A cogeneration plant captures heat that would be otherwise wasted to provide heat or steam to a building or facility.
Inorganic Chemistry is the study of the structures, properties, and behaviours incl. reactions, of elements, mixtures e.g. in solutions, and chemical compounds that do not contain carbon-hydrogen bonds (such compounds are defined as "organic" for the purposes of chemical classification so study of those compounds is considered organic chemistry).
In some subject-areas of study and research the distinction between organic and inorganic chemistry is unclear and is said to overlap. For example, organometallic chemistry (the study of chemical compounds whose molecules include bond(s) between carbon and a metal) includes aspects of both inorganic chemistry and organic chemistry. However, most (and often all) of the chemistry normally studied at school level may be clearly defined as either Organic orInorganic Chemistry.
It is useful to be aware that most biological chemicals, i.e. those generated by plant or animal life, are organic because they include carbon-hydrogen bonds. However that is a very general observation and there are too many common exceptions to use it as a "rule". Some inorganic chemicals e.g. carbon dioxide (CO2) are also found and created by living things.
It is useful to understand what is inorganic chemistry in order to know which books or sections to use when researching chemistry questions, e.g. looking-up information in textbooks and via other sources and media.
As much of introductory (school-level) inorganic chemistry is concerned with the chemical elements, a convenient way to identify key topics within introductory inorganic chemistry is using the periodic table: The periodic table is structured in such a way as to group together elements whose structures follow certain patterns and so have particular properties in common.
Inorganic Chemistry Topics identifiable from the Periodic Table include, the chemistry of the following elements, from left-to-right across the Periodic Table:
Groups I and II (of the Periodic Table), which are also known as the s-block elements.
The elements of Group I are known as Alkali Metals, and include: Lithium (Li), Sodium (Na), Potassium (K), Rubidium (Rb), Caesium (Cs), and the rare radioactive element Francium (Fr).
The elements of Group II are known as Alkaline Earth Metals, and include: Beryllium (Be), Magnesium (Mg), Calcium (Ca), Strontium (Sr), Barium (Ba), and the rare radioactive element Radium (Ra).
Transition Metals, which are also known as the d-block elements.
Group III This includes the non-metallic element Boron (B), Aluminium (Al), together with Gallium (Ga), Indium (In) and Thallium (Tl).
Group IV This includes the relatively common elements: Carbon (C), Silicon (Si), Germanium (Ge), Tin (Sn) and Lead (Pb). Note that the element carbon is one of the most important elements in organic chemistry but also forms some compounds classified within inorganic chemistry, e.g. carbon monoxide (CO) and carbon dioxide (CO2).
Group V This includes: Nitrogen (N), Phosphorous (P), Arsenic (As), Antimony (Sb) and Bismuth (Bi).
Group VI This includes: Oxygen (O), Sulphur (S), Selenium (Se), Tellurium (Te) and the radioactive element Polonium (Po).
Group VII, which are known as the halogens. This includes Fluorine (F), Chlorine (Cl), Bromine (Br), Iodine (I) and the radioactive element Astatine (At).
Group 0, which are known as the Noble Gases and, due to their inactivity, also as "inert gases". This includes Helium (He), Neon (Ne), Argon (Ar), Krypton (Kr), Xenon (Xe) and Radon (Rn).
Sulfuric acid is the product of the U.S. chemical industry produced in largest quantity in terms of mass. About 40 million tons are produced annually. There are two major processes used in the production of H2SO4, lead chamber process and contact process. The lead-chamber process is the older of the two processes, and its product is aqueous sulfuric acid containing 62% to 78% H2SO4. The contact process yields pure sulfuric acid. In both processes, sulfur dioxide, SO2, is oxidized to sulfur trioxide, SO3, and the SO3 is dissolved in water.
Sulfur dioxide is obtained by burning sulfur,
S(s) + O2(g) SO2(g)
by roasting pyrite (iron sulfide) or other metal sulfides prior to smelting,
4 FeS(s) + 7 O2(g) 2 Fe2O3(s) + 4 SO2(g)
or by burning hydrogen sulfide,
2 H2S(g) + 3 O2(g) 2 SO2(g) + 2 H2O(g)
The sulfur dioxide is oxidized to sulfur trioxide catalytically.
2 SO2(g) + O2(g)
Without the catalyst the oxidation of SO2 is quite slow. In the old lead-chamber process, the catalyst is nitrogen dioxide gas. In the contact process, the catalyst is vanadium(V) oxide, V2O5, mixed with an alkali metal sulfate. The mixture is supported on small silica beads, and at the high temperature inside the reactor, the mixture is a liquid. The product SO3 is dissolved in 98% sulfuric acid. The dissolved SO3 reacts with the 2% water, forming H2SO4.
SO3(g) + H2O(l)
Pure sulfuric acid is a colorless, odorless, oily liquid. It freezes at 10.5°C. It fumes when heated, because some of the H2SO4 decomposes to H2O and SO3. The H2O is retained in the liquid, while SO3 gas is released. Therefore, the concentration of H2SO4 decreases, reaching a concentration of 98.33%. This solution boils at 338°C and is the material sold as "concentrated sulfuric acid." Concentrated sulfuric acid, which is 18M, has a strong affinity for water and is sometimes used as a drying agent. It can be used to chemically remove water from many compounds. It dehydrates sucrose (table sugar), C12H22O11, leaving a spongy black mass of carbon and diluted sulfuric acid. Concentrated sulfuric acid reacts similarly with skin, paper, and other animal and plant matter. When it is mixed with water, a highly exothermic reaction occurs, and the energy released can be enough to heat the mixture to boiling. Therefore, concentrated sulfuric acid must be diluted by adding the acid slowly to cold water while the mixture is stirred to dissipate the heat.
Sulfuric acid has a wide range of uses and plays a part in the production of nearly all manufactured goods. About 65% of the H2SO4 produced annually is used in the production of agricultural fertilizers.
Fractions are expressed as one number over another number, like this:
The number on the top is called the numerator and the number on the bottom is called the denominator.
When you think of a fraction, think of a PIZZA!!
Suppose a pizza is cut evenly into the number of pieces in the DENOMINATOR. If the number of pieces YOU get is the NUMERATOR, the fraction of the pizza you get is:
Adding and taking away (subtracting) fractions can be pictured using slices of pizza. For example:
Multiplying fractions means cutting a portion into smaller portions. For example:
Unit 1 show you how to do this multiplication.
Dividing fractions means determining how many smaller pieces there are in a larger piece. For example:
This means there are 2 one-fourth pieces of pizza in a half pizza.
Unit 4 shows you how to do this division.
Unit 12 will introduce you to decimals.
Here's another way to look at fractions. Imagine that each of these lines is a board and you want to cut it into halves, thirds, fourths, sixths, and fifths. Here is what those board fractions look like:
one whole board!!
Notice that the 2 1/4th boards add up to a half board and that the 2 1/6 boards add up to a 1/3 board.
This means that 2/4=1/2 and 2/6=1/3. (We will investigate this more in unit 9.)