Chapter 4: Matter and Heat Part 2

1
Chapter 4 Matter and Heat Part 2

• Alyssa Jean-Mary

2
The Kinetic Theory of Matter

• The kinetic theory of matter involves a simple
  model that accounts for many physical and
  chemical properties of matter.
• This model says that all matter is composed of
  tiny particles.
• For a gas, these particles are referred to as
  molecules, which are substances that consist of
  two or more atoms.
• For liquids and solids, the particles can be one
  of three types molecules, atoms, or ions.

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The Kinetic Theory of Gases

• The sizes, speeds, and shapes of the molecules of
  many kinds of matter are known today
• For example, a molecule of Nitrogen, which is the
  chief constituent of air, is about 1.8 x 10-10m
  across. It has a mass of about 4.7 x 10-26kg. At
  0C, its average speed is about 500m/s, which is
  about the speed of a rifle bullet. Every second a
  molecule of Nitrogen collides with more than a
  billion other molecules. Most of the other
  constituents of air have a similar size and speed
  to that of Nitrogen. For every cubic centimeter
  of air, there are 2.7 x 1019 other molecules
  present. To get an idea of how many molecules
  this is if all of the molecules that are present
  in a cubic centimeter of air were divided equally
  amount 6.3 billion people, each person would have
  over 4 billion molecules of air.

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The Three Basic Assumptions of the Kinetic Theory
of Gases

• There are three basic assumptions that apply to
  the Kinetic Theory of gases
• 1. Gas molecules are small compared to the
  average distance between them.
• 2. Gas molecules collide with each other without
  losing kinetic energy.
• 3. Gas molecules exert almost no force on one
  another, except when they collide with each
  other.
• These assumptions have been verified by
  experimentation
• These assumptions show us that a gas is mainly
  empty space in which isolated particles are all
  moving around in different directions. Therefore,
  we can compare a gas to a swarm of angry bees
  that is in a closed room. Each molecule collides
  with other molecules about billions of times a
  second. Theses collisions change the speed and
  direction of the molecule, but when they arent
  colliding, they are unaffected by their
  neighbors. There is no order to the motion of
  these objects. They have no uniform speed or
  direction. All that can be said about the
  molecules is that they have an average speed and
  that, at any given instant, there are as many
  molecules moving in one direction as there are
  molecules moving in the opposite direction.
• If a molecule comes to a rest momentarily, it
  will not stay that way long i.e. another
  molecule will soon collide with it to send it
  back into motion.
• Also, if a molecule reaches a speed than the
  average speed of the molecules, it will not stay
  that way long either i.e. other collisions will
  slow its speed.

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Properties of Gases from the Kinetic Theory of
Gases

• Gases can expand and even leak through a small
  opening because of their rapid movement and the
  fact that they dont have a strong attraction for
  each other
• Gases can be easily compressed because on
  average, there molecules are far apart from each
  other
• One gas will mix with another gas because, since
  the molecules are far apart from each other,
  there is plenty of space in between them for
  other molecules
• The mass of a certain volume of a gas is much
  less than the mass of the same volume of a liquid
  or a solid because a gas is mainly empty space

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The Origin of Boyles Law

• A gas exerts a pressure on the walls of its
  container because the billions and billions
  molecules of the gas consistently hit the
  container. When we measure these billions and
  billions of tiny, separate hits of the molecules,
  what we see is that a continuous force is
  affecting the walls of the container.
• The Kinetic Theory of Gases accounts for Boyles
  Law, which states that p1V1 p2V2 when the gas
  is at constant temperature
• Think of the molecules of a gas in a cylinder as
  some moving vertically (i.e. in between the
  piston and the bottom of the cylinder) and as
  some moving horizontally (i.e. in between the
  walls of the cylinder) the molecules are moving
  equally in either direction. Now, if the piston
  is raised, which doubles the volume of the gas,
  the molecules that are moving vertically are
  going to have to travel further, which means that
  they will not hit the piston or the bottom of the
  container as much as they used to they will
  actually hit the container half as much. The
  molecules moving horizontally will also have to
  change their bombardment of the walls of the
  container because now they have more of the walls
  to interact with. Since these molecules will need
  to hit an area that is twice as big as before,
  the number of hits on the walls of the container
  will decrease just as those for the molecules
  with vertical motion did. This shows that the
  pressure in all parts of the cylinder (vertical
  and horizontal) is cut in half when the volume is
  doubled, which is what Boyles Law predicts. This
  can be expanded to a real gas that has molecules
  that are moving in random motion.

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Molecular Motion and Temperature

• A fourth assumption is added to the Kinetic
  Theory of gases
• 4. The absolute temperature of a gas is
  proportional to the average kinetic energy of the
  molecules of the gas
• This assumption was added to account for the
  behavior of a gas with a change in temperature
• Since this shows that temperature is related to
  the energy of the molecules, it also is related
  to the speed of the molecules. Thus, if the
  pressure inside a container increases, the
  temperature inside that container also increases.
  This is because when the pressure increases, the
  molecules must be hitting the walls of the
  container with more force, which means that they
  are moving faster.
• Earlier, we saw that if the temperature of a gas
  is at 0K (or -273C), the pressure of the gas is
  at zero. For this to occur, the bombardment of
  the molecules must stop completely. So, at 0K
  (i.e. absolute zero), the molecules of a gas
  would lose all of their kinetic energy. (This is
  a simplified idea since in reality, even at 0K,
  there will be a small amount of KE that will
  never be able to disappear.) The reason that
  there is no temperature below 0K is that there is
  simply no way to have less than no kinetic
  energy. Thus, if there is constant volume, an
  increase in the pressure of the gas will increase
  the temperature of the gas, and if there is
  constant pressure, an increase in the volume of
  the gas will increase the temperature of the gas.

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The Origin of Charless Law

• When a gas is compressed, since the temperature
  of the gas is the measure of the average kinetic
  energy of the molecules of the gas, the
  temperature in the cylinder should rise
• Put a gas in a cylinder with a piston on top.
  When the piston is moving down, thus increasing
  the pressure inside the cylinder, the molecules
  rebound from the piston with an increase in
  energy, which causes an increase in the
  temperature of the gas. This can be shown when
  using a bicycle tire pump after you have used
  the pump for awhile, you will notice that it gets
  warmer because of the compression of the gas
  inside as the pump is being used. Also, when the
  piston is moving up, which decreases the pressure
  inside the cylinder, the molecules will give up
  some of their kinetic energy to the piston, which
  will cause the temperature of the gas to
  decrease.
• Thus, as a gas expands, it cools. This can
  explain the formation of clouds from rising moist
  air.
• As moist air is moving upward, since the
  atmospheric pressure is decreasing, the water
  vapor in the moist air is cooling, until it
  condenses into the water droplets that constitute
  clouds.

9
Liquids and Solids Intermolecular Forces

• If you compare a gas to a swarm of angry bees,
  then a liquid is bees in their hive, crawling
  constantly over one another.
• The molecules in a liquid slide past one another
  easily, which is why liquids flow. Liquids flow
  less readily than gases do because of the
  intermolecular attractions that act only over
  short distances.
• The molecules in a solid are held together with a
  stronger force than those that hold together
  liquids. Actually, this force is so strong that
  the molecules of solids are not free to move
  about. The molecules of solids still move,
  however they vibrate back and forth rapidly
  between the particles that they are in between,
  as if they were on a spring. This spring
  represents the bond that is between two
  molecules. This bond is electrical in nature.
• The reason why a solid is elastic is because
  after the molecules have been pulled apart or
  pushed together by some force, the molecules
  return to their original positions, with the
  normal amount of space between the molecules
  instead of too much or too less. A force that is
  too great may deform the solid permanently. When
  this occurs, the molecules move to new normal
  positions and find new molecules to bond with. A
  solid can actually break apart if too much force
  is applied.

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Evaporation Changing a Liquid into a Gas

• A liquid is placed in an open container. The
  molecules of the liquid are moving in all
  directions in the dish, some moving faster than
  others. Some of the molecules are moving fast
  enough upward to escape into the air. They escape
  into the air even though they have an attraction
  to their neighbor molecules because the
  attraction is not enough to stop them from
  escaping. This loss of molecules to the air is
  referred to as evaporation. Since it is the
  faster molecules, and thus, the warmer molecules
  that escape into the air, the slower molecules
  are left behind in the liquid, which makes the
  liquid cool.
• If you compare the evaporation of water to
  alcohol, you see that alcohol evaporates more
  quickly than water, and thus, cools more quickly
  than water. This is because the attraction liquid
  alcohol molecules have for one another is less
  than the attraction liquid water molecules have
  for one another, and thus a greater number of
  alcohol molecules can escape.

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Boiling Changing a Liquid into a Gas

• When a liquid is heated, at a certain
  temperature, even molecules that are traveling at
  average speed (i.e. not only the molecules that
  are traveling at high speeds) can overcome the
  attraction between their neighbor molecules and
  escape into the air. At this temperature, there
  are bubbles of gas throughout the liquid, and
  thus, the liquid is boiling. Therefore, this
  temperature is referred to the boiling point of
  the liquid.
• The boiling point of water is 100C, which is
  higher than the boiling point of alcohol, which
  is 78C. This reinforces the idea that alcohol
  evaporates more quickly than water.
• Evaporation and boiling differ in the following
  two ways
• 1. Evaporation occurs only at the surface of the
  liquid, whereas boiling occurs throughout the
  entire liquid.
• 2. Evaporation occurs at all temperatures,
  whereas boiling only occurs at the boiling point
  or temperatures above the boiling point.

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Heat of Vaporization

• To change a liquid to a gas, whether by
  evaporation or boiling, energy is needed
• For evaporation, the energy is supplied from the
  heat content of the liquid itself, which is why
  the liquid that is left behind is cooler
• For boiling, the energy is supplied from heat
  from an outside source
• The heat of vaporization of a substance is the
  amount of energy that is needed to change each
  kilogram of liquid into gas at its boiling point
• For water at its boiling point, 100C, the heat
  of vaporization is 2260kJ
• The temperature of a liquid and its gas are not
  different. Because of this, the kinetic energy
  that the liquid has is the same amount of kinetic
  energy that its gas has. Thus, the extra energy
  that is supplied to the liquid to turn it into a
  gas does not go into the kinetic energy of the
  gas. Because the molecules in a liquid are closer
  together, the intermolecular forces in a liquid
  are stronger than those in a gas. In order to
  change a liquid into a gas, the molecules of the
  liquid have to be broken apart and moved so that
  they are in positions that are far apart from
  each other, and thus have smaller attractions for
  each other. This requires that the strong forces
  between molecules in a liquid need to be
  overcome. The molecules of the liquid that are
  moving apart to become gas molecules are gaining
  potential energy, just like a stone that is
  thrown upward against the earths gravity gains
  potential energy, except this is potential energy
  with respect to intermolecular forces. Thus, the
  extra energy that is supplied to the liquid to
  turn it into a gas becomes potential energy of
  the gas.
• When the reverse occurs, i.e. when a gas becomes
  a liquid, instead of the liquid molecules
  escaping from the liquid into the air, the gas
  molecules are falling toward one another because
  of their attraction to one another. When this
  occurs, the potential energy that the gas
  molecules are losing is taken up as heat by the
  surroundings.

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Melting Changing a Solid into a Liquid

• Heat is needed to change a solid into a liquid at
  its melting point, just like heat is needed to
  change a liquid to a gas at its boiling point
• The heat of fusion of a substance is the amount
  of heat that is needed to change each kilogram of
  solid into liquid at its melting point
• For water at its melting point, the heat of
  fusion is 335kJ/kg
• Most other substances have a lower heat of fusion
  than water
• The same amount of heat that is needed to change
  one kilogram of a solid to a liquid has to be
  released in order to change one kilogram of a
  liquid into a solid
• The heat of fusion of a substance is always much
  smaller than the heat of vaporization of the
  substance
• The molecules of a solid are arranged in such a
  way that they have the maximum amount of force
  between themselves and their neighbors. To become
  a liquid, the molecules of a solid have to become
  more random, to be able to move about more. To do
  this, energy needs to be added so that the forces
  between the molecules of a solid are overcome.
  But, the amount of energy that is needed to do
  this is not as much as for a liquid to become a
  gas since a liquid still has a definite volume,
  even if it doesnt have a definite shape, unlike
  a gas, which has no definite shape or volume.
  Since the molecules of a gas are so far apart,
  they move more freely and thus, can expand. In a
  vacuum, the molecules of a gas could expand
  indefinitely.

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Water

• If we start with 1kg of ice at -50C, and we add
  heat, the ice will increase in temperature until
  0C (i.e. the melting point of water), which is
  when it will start to melt. The temperature will
  remain at 0C until all of the ice has melting.
  After all of the ice has melted, and thus, has
  become water, the temperature of the water will
  increase until 100C (i.e. the boiling point of
  water) is reached, which is when it will start
  boiling. The amount of energy that is required at
  this point (i.e. to turn the water into steam) is
  a lot more than the amount of energy that was
  required to melt the ice. The temperature will
  remain at 100C until all the water has become
  steam, and then, the temperature of the steam
  will rise since more heat is still being added.

15
Sublimation

• Sublimation occurs when a solid turns directly
  into a gas, without first turning into a liquid.
• Most substances will sublime as long as the right
  conditions of temperature and pressure are
  present.
• Usually pressures well under atmospheric pressure
  are needed in order for sublimation to occur.
• One example of an exception is solid carbon
  dioxide, which is also referred to as dry ice.
  Solid carbon dioxide sublimes (i.e. turns into a
  gas) at temperatures above -79C, even if it is
  at atmospheric pressure
• Instant coffee can be made using sublimation.
  Coffee is first brewed, and then it is frozen.
  Following that, it is put into a vacuum chamber.
  The ice that is in the frozen coffee sublimes to
  water vapor, which is pumped away. Freeze drying
  coffee like this doesnt affect the flavor of the
  coffee as much as when you dry it by heating. The
  process of freeze drying is also used to preserve
  many other materials, including blood plasma.

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Changes of State
17
Energy Transformations

• Remember that any form of energy can be converted
  into another form of energy. This applies to
  heat, since it is a form of energy. The
  conversion of heat to another form of energy does
  not occur efficiently.
• For example, mechanical energy is obtained by
  heat that is given off from burning coal and oil
  in various types of engines. A large amount of
  the heat that is given off does not get changed
  into mechanical energy it is wasted. In an
  electric power station, about two-thirds of the
  heat is wasted. This is a serious situation since
  these loses occur on the raw energy that is
  available to us.
• This inefficient conversion of heat in engines
  was discovered in the nineteenth century, at the
  start of the Industrial Revolution. The loss of
  heat is not due to poor design or construction of
  the engines it is just because heat cant be
  converted to another form of energy without these
  losses. The reasons for this inefficient
  conversion was studied by engineers to get as
  much mechanical energy as they could out of a
  given amount of fuel and by scientists to study
  the properties of heat. What was learned was for
  the idea that heat is actually the kinetic energy
  of random molecular motion.

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Heat Engines

• Since all that is needed to obtain heat is to
  burn a fuel, heat is an easy and a cheap form of
  energy to obtain
• A heat engine is a device that turns heat into
  mechanical energy
• Some examples of heat engines are the gasoline
  and diesel engines of cars, the jet engines of
  aircraft, and the steam turbines of ships and
  power stations.
• All engines operate in the same basic way a gas
  is heated and then it expands against a piston or
  the blades of a turbine
• When a gas in a cylinder on top of which is a
  piston is heated, since the temperature of the
  gas is increasing, the pressure of the gas is
  increasing, which makes the piston move upward.
  This upward movement is what is used to make use
  of an engine. When the piston reaches the top of
  the cylinder, the conversion of heat into
  mechanical energy stops since the piston stops
  moving. If we want to continue to make use of an
  engine, we need to push the piston back down
  again. Then, we can start another cycle to expand
  the gas.
• If the piston is pushed back down to continue the
  cycle when the gas is still hot, the amount of
  work that needs to be done is the same as the
  amount of energy that was produced by the
  expansion of the gas. This means that if it is
  pushed back down when the gas is still hot, no
  net work will be done. Thus, for some work to be
  done, the gas first must be cooled so that there
  is less work required for the piston to be pushed
  back down. This is where the heat is lost in an
  engine. Thus, if you want an engine to continue
  to work, there is no way to prevent this heat
  loss. The heat that is lost usually ends up in
  the atmosphere around the engine, in the water of
  a nearby river, or in the ocean.

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The Complete Cycle of Heat Engines

• In the compete cycle of an engine, heat flows
  into and out of the engine. During this process,
  some of the heat is converted into mechanical
  energy.
• In order for an engine to operate, both a hot
  reservoir and a cold reservoir are needed. A gas
  flows naturally from the hot reservoir to the
  cold reservoir.
• In a gasoline or diesel engine, the hot reservoir
  is the burning gases of the power stroke, and the
  cold reservoir is the atmosphere.
• Even though a vast amount of heat is contained in
  the molecular motions of the atmosphere, the
  oceans, and the earth itself, it is only rarely
  used because a colder reservoir is needed for the
  heat to flow into.
• A refrigerator is the reserve of a heat engine.
  It uses mechanical energy to push heat from a
  cold reservoir to a warm reservoir. Energy is
  required for this movement because heat naturally
  flows from a warm reservoir to a cold one. Since
  there is a large amount of energy that is needed
  to drive a refrigerator, it is not a good cold
  reservoir for an engine to use.

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Thermodynamics

• Thermodynamics is the study of heat
  transformation
• There are two fundamental laws of thermodynamics
• 1. Energy cannot be created or destroyed, but it
  can be converted from one form to another.
• 2. It is impossible to take heat from a source
  and change all of it to mechanical energy or
  work some heat must be wasted.
• As you can see, the first law of thermodynamics
  is actually the law of conservation of energy. It
  basically is saying that we cannot obtain
  anything from nothing.
• The second law of thermodynamics referrers only
  to heat. It says that the conversion of heat into
  another form of energy is inefficient.
• Thermodynamics specifies the maximum efficiency
  of a heat engine only by ignoring the losses to
  friction and some other practical difficulties.
  The maximum efficiency depends only on the
  absolute temperatures of the hot reservoir and
  the cold reservoir by which the engine operates
• Maximum efficiency (work output/energy
  input)maximum
• OR
• Eff(max) 1 (Tcold/Thot)
• where Eff(max) is the maximum efficiency, Tcold
  is the temperature of the cold reservoir, and
  Thot is the temperature of the hot reservoir
• This equation shows that the greater the ratio
  between the two temperatures, the less heat is
  wasted, and therefore, the more efficient the
  engine is.

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A Steam Turbine

• A steam turbine is what is used in a power
  station. The steam comes from a boiler that is
  heated by either a coal furnace, a oil furnace, a
  gas furnace, or a nuclear reactor. The turbine
  shaft is connected to an electric generator. In a
  typical power station, the steam enters the
  turbine at about 570C (843K) and exits at about
  95C (368K) into a partial vacuum. The maximum
  efficiency of a turbine like this is equal to 1
  (368K/843K) or 0.56, so the maximum efficiency
  is 56 percent. The actual efficiency is less than
  40 percent due to friction and other sources of
  energy loss.