1. In what ways do the molecules or atoms of a gas differ from those in a liquid or a solid?
2. State the ideal gas law, define the terms used and explain what it means.
3. Why is it necessary to use Kelvin temperature in the equation of state for a gas?
4. What is absolute zero and how is it measured?
5. What is an "ideal" gas. How do real gases differ from the ideal gas?
6. Is an object at 100 degrees Celsius twice as hot (contain twice as much heat) as an object at 50 degrees Celsius? Explain.
1. What are the basic assumptions of the kinetic theory of gases?
2. Distinguish between translational, rotational and vibrational motion.
3. Define heat, temperature, kinetic energy, and pressure in terms of kinetic theory.
4. In terms of kinetic theory and conservation of energy, what happens to the latent heat involved in melting ice?
5. How does kinetic theory explain the cooling of water by evaporation?
6. What is Brownian motion and what does it have to do with atoms?
The pool table is one of the best models for visualizing the kinetic theory of gases, with one important imperfection, which is is friction, which causes the balls on the table to slow down.
1.3.1. conservation of energy, gas laws, atomic theory, statistics
2.1.1. Force per unit area
2.1.2. P = F/A
18.104.22.168. newtons per square meter or pounds per square inch
2.1.3. not to be confused with force: pressure is not just another word for force any more than velocity is another word for distance
2.1.4. pressure on an object should never be confused with the total force acting on it
2.1.5. our concern is with the pressure exerted by gases, but it will help to compare it with pressure in liquids
2.1.6. pressure in a liquid
The level to which a liquid rises is the same regardless of the shape of its container. This is because the pressure depends on the depth, and because the pressure is equal in all directions.
22.214.171.124. equal in all directions
126.96.36.199. change of pressure at any point is accompanied by a corresponding change at every other point if it is not flowing (Pascal's principle)
188.8.131.52. increases downward
184.108.40.206.1. due to weight of liquid above a given area
220.127.116.11.2. zero at surface
2.1.7. also true for gases
18.104.22.168. in ordinary sized containers the difference in pressure between top and bottom is negligible if not immeasurable
22.214.171.124. if gas or liquid is packaged under external pressure in a sealed container, the external pressure will be found throughout the fluid and will be in addition to any pressure due to weight
126.96.36.199. where the quantity of gas is large, such as in the earth's atmosphere, gravitational forces cause a significant difference in density, and also in pressure, between the top and the bottom
188.8.131.52. air pressure diminishes with height in the atmosphere
3.1.1. known since 16th century that water would rise in a tube with one end submerged if air were drawn out
3.1.2. like sucking on a straw
3.1.3. Scholastic physics explained it in terms of Aristotle's concept of "nature's abhorrence of a vacuum"
184.108.40.206. water rises in an attempt to fill the vacuum as the tube is evacuated
220.127.116.11. the basis of groundwater pumps
3.1.4. workman told Galileo that a pump would work only if the pipe were less than 34 feet long
3.1.5. Galileo wondered why nature's abhorrence stopped at 34 feet
3.2.1. rise of water in pipe is due to air pushing on the surface rather than a "pulling" of the water from the top
3.2.2. before the pump "sucked" the air out of the pipe this push was balanced by the air in the pipe pushing down with equal force per unit area
3.2.3. removing the air removes this force so water rises in the tube until the downward force of its weight balances the downward force of the air pressure outside the tube
3.2.4. pressure of the air should be equal to the weight of a column of water 34 feet long and 1 square inch in area, about 14.7 pounds per square inch
3.2.5. pressure inside tube equals pressure outside tube
3.2.6. people were not convinced
3.3.1. mercury is 13.6 times as dense as water so height of mercury column should be 34 ft./13.6 = 2.5 feet, or 30 inches.
18.104.22.168. still used in weather (US only. actually 29.96 inches of mercury is a standard atmosphere, equals 14.7 pounds per square inch)
3.3.2. fill a closed tube with mercury and invert in a dish of mercury
22.214.171.124. a vacuum exists above the mercury
126.96.36.199. except a small amount of mercury vapor which exerts a small pressure, but that's another story
3.3.3. a student of Galileo, along with Pascal at Padua
3.3.4. thought that the weight of the air should decrease with altitude
3.3.5. under Pascal's direction, measured the change
188.8.131.52. left an identical barometer behind with an observer to record changes in air pressure at the foot of the mountain
184.108.40.206.1. why did he do that?
220.127.116.11. most people still not convinced
3.3.6. cause of the pressure was assumed by Toricelli to be due to the weight of the air
18.104.22.168. not true but still assumed by many, including encyclopedias and physics texts
22.214.171.124. can be shown by several methods
126.96.36.199. put barometer in closed container and heat or cool the air to obtain greater or lesser pressure, even though the weight will not change(can do it on a scale to see no change in weight)
3.3.7. analogy between the sea of water and the "sea of air" is not a good one
188.8.131.52. pressure in water increases rapidly with depth with no appreciable change in density
184.108.40.206. pressure of air decreases rapidly with altitude with a corresponding decrease in density
220.127.116.11. numerical magnitude of the pressure of the atmosphere exactly equals the weight of a column of air 1 square inch in cross section, but this is not the same as saying that the pressure of the air is caused by the weight of the air
3.4.1. proof of Galileo's hypothesis had to wait for Boyle to invent the vacuum pump
3.4.2. put Torricelli's barometer in airtight container and pumped air out of it
3.4.3. pressure inside container equals pressure outside
3.4.4. weight of air above the dish could not hold up because it is sealed
3.5.1. The video program demonstrates the force of air pressure with a small version of the Madgeburg Hemispheres. The story of the hemispheres depicted in the engraving is related in the video.
4.1. relationships between temperature, pressure, and volume of gases
4.2. discovered in steps, now expressed as ideal gas law
The fact that decreasing volume increases pressure can be shown qualitatively with a balloon. Try it with a balloon of your own.
|The pressure inside of the closed part of the tube is equal to the equivalent of two atmospheres of pressure (one atmosphere from the atmosphere itself and one from the 30-inch column of mercury.||The volume of air inside the closed end is twice as large as when the pressure is half as much, or one atmosphere.|
The video program shows how the volume and pressure are inversely proportional using a pressure gauge and a glass cylinder with a piston.
Boyle argued that the properties of gases were due to stationary, compressible particles.
8.1.1. static contiguous particles at rest
8.1.2. must be compressible, like pieces of wool
8.1.3. if not touching then must be variable in size or in motion
8.1.4. static explanation does not account for ability to expand to fill any container
8.1.5. must then postulate that particles are self repulsive, which is consistent with caloric theory
8.2.1. deduced Boyle's Law using Newtonian mechanics
8.2.2. anticipated kinetic theory of gases
8.2.3. views were too advanced for his time
8.2.4. about three generations too soon
8.2.5. idea died for lack of attention
8.2.6. two important contributions to scientific thought
18.104.22.168. recognized the equivalence of heat and mechanical energy through particle motion
22.214.171.124. conceived the possibility that a quantitative relationship (Boyle's law) could be induced from the chaotic picture of randomly moving particles
8.2.7. Heat and Mechanical Work
126.96.36.199. PV (pressure times volume) has same units as work when conversions are made
188.8.131.52. shows utility of standard units in understanding concepts
9.1.1. note that Joule was a student of Dalton
9.1.2. resurrected Bernoulli's work in a series of lectures and papers from 1847-1857
9.1.3. sharpened the concepts
9.1.4. fortified it with convincing arguments and calculations
9.1.5. gave physical meaning to the concept of absolute zero
9.2.1. by other 19th century physicists Helmholtz, Maxwell, Boltzmann, and Gibbs
9.5.1. have mass and occupy space
9.5.2. obey laws of motion
9.5.3. obey energy and momentum conservation
A postulate is an assumption to be tested. In this case it is a model. We assume certain things about the nature of gases, then determine whether or not the behavior of gases is consistent with. We use the Newtonian paradigm (forces, momentum, energy) as a starting point for understanding the gas laws and other properties.
9.6.1. Gases consist of molecules
184.108.40.206. gases are substances
220.127.116.11. substances consist of molecules
18.104.22.168. changes of state are physical changes involving no new substances
22.214.171.124. gases consist of the same kinds of molecules as their solid forms
126.96.36.199. steam is gaseous water molecules
9.6.2. Molecules are in constant random motion
188.8.131.52. gases diffuse through space to fill available volume
184.108.40.206. pressure is exerted on the walls of gas containers by the forces of molecular collisions
9.6.3. Molecules are far apart compared to their size
220.127.116.11. gases are greatly compressible
18.104.22.168. gases are much less dense than their liquid or solid counterparts
9.6.4. Molecules exert no forces except during collisions
22.214.171.124. gravitational forces are extremely small and can be ignored
126.96.36.199. what other kinds of forces are there?
9.6.5. Collisions are perfectly elastic
188.8.131.52. kinetic energy is completely conserved
184.108.40.206. compare to room full of bouncing balls
220.127.116.11. container of gases does not lose energy
18.104.22.168. molecules do not collect in the bottom of the container
22.214.171.124. this makes sense if the others make sense
Using this as a visual model we can try to "justify" that the kinetic theory of gases is easily extended to other states of matter. Imagine that the molecules are slightly sticky.
10.1.1. Kinetic Theory is easily extended to other states of matter
10.1.2.1. no fixed shape or volume, exert pressure on containers
10.1.2.2. molecules far apart compared to their size
10.1.2.2.1. gases are compressible
10.1.2.2.2. least restricted motion
10.1.2.2.2.1. billiard balls on table
10.1.2.2.2.2. a room full of super balls
10.1.2.2.3. mostly empty space so easily compressed
10.1.2.3. motion is constant, random, rapid
10.1.2.3.1. exert pressure
10.1.2.3.2. many collisions, small average distance traveled between collisions
10.1.2.3.3. no net movement
10.1.3.1. fixed volume, but no fixed shape
10.1.3.2. most complicated state
10.1.3.2.1. intermediate between gas and solid
10.1.3.2.2. most substances have only limited region of liquid stability
10.1.3.2.2.1. ie. water, carbon dioxide
10.1.3.3. molecules are closer together than gas but free to move in limited way
10.1.3.3.1. weak forces between molecules due to physical bonds
10.1.3.3.2. clusters of solid structure mixed with gaseous state
10.1.3.3.3. sliding motion
10.1.3.3.4. model: jar full of magnetic spheres
10.1.4.1. fixed shape and fixed volume
10.1.4.2. molecules are free to move, but only around fixed positions
10.1.4.2.1. held together by relatively strong forces, either chemical or physical bonds
10.1.4.3. model: lattice of balls connected by springs
10.2.1. Work, kinetic energy, and temperature are seen to be different forms of the same thing
10.2.2. Gas pressure is due to momentum changes during collisions
10.2.3. Molecules exert force on walls of container
10.2.3.1. like throwing a ball at the wall of a room
10.2.3.2. total force exerted on wall is sum of force exerted by all molecules
10.2.3.3. sum of forces of all collisions per unit area of wall is gas pressure
10.2.3.4. can calculate the relationship between energy and temperature
10.2.3.5. can calculate the relationship between momentum and pressure
10.3.1. IDEAL gases vs. REAL gases
10.3.1.1. All gases exert pressure due to molecular collisions
10.3.1.2. Real gases deviate from gas laws at low temperatures and high pressures
10.3.1.3. when gases are close to liquefaction point
10.3.2. Ideal Gases
10.3.2.1. exert forces during collision only
10.3.2.1.1. on walls of container
10.3.2.1.2. on other molecules
10.3.2.2. pressure is result of sum of collisions of all molecules
10.3.2.3. exchange energy and momentum during collisions
10.3.2.4. collisions are perfectly elastic
10.3.2.5. energy is conserved in collisions
10.3.2.6. air does not settle to bottom of room
10.4.1. small attractive forces between molecules are sometimes significant
10.4.2. cause gas to condense to liquid at a certain temperature
10.4.3. slightly inelastic collisions
10.4.4. different gases liquefy under different conditions of T and P
10.4.4.1. liquid nitrogen boils at -196° C (77 K) at 1 atmosphere pressure
10.4.4.2. liquid water boils at 100° C (373 K) at 1 atmosphere pressure
Here is a graphical representation of the mixing of two gases.
In the top we see a hot gas and a cold gas separated by an impermeble barrier. The graph on the right shows the distribution of kinetic energy of the gas molecules. Note thatthe average energy of the two gases is halfway between the average of the two gases.
When the barrier is opened and the gases mix , the molecules collide as the kinetic energy becomes equally distributed. During the entire process the average kinetic energy of the molecules remains constant.
The final temperature of the mixture has the same average kinetic energy as long as no heat is lost from the system. As postulated in the kinetic theory, the collisions of molecules are 100% elastic such that no energy is lost during collisions.
10.5.1. Heat is the total energy of the molecules
10.5.1.1. heat is energy which can be transferred
10.5.1.2. potential energy of physical bonds between molecules
10.5.1.3. work must be done to break chemical or physical bonds to cause change of state
10.5.1.4. kinetic energy of molecular motion
10.5.2. Molecules can have various types of kinetic energy
10.5.3. Molecules can have various types of kinetic energy
10.5.3.1. translation: movement of molecules from place to place
10.5.3.2. rotation: around a center of mass
10.5.3.3. vibration: about fixed locations in solid, liquid, or diatomic gas
10.5.4.1. Kinetic energy is not the same for all molecules in a sample
10.5.4.1.1. some move fast, some slowly
10.5.4.2. average kinetic energy and distribution of energy depend on temperature
10.5.4.3. speed of molecules can be calculated from Newtonian mechanics
10.5.4.3.1. Derivation of Newtonian Energy (after Bernoulli)
10.5.4.3.2. Veolocity of air molecules at room temperature
10.6.1. both are forms of potential energy
10.6.2. depends on intermolecular forces which are electrical in nature
10.6.3. specific heat is stored in intermolecular forces
10.6.4. latent heat is energy required to break physical bonds between molecules
10.7.1. fractional change in pressure is proportional to fractional change in temperature
10.7.2. graphs of P vs. T for all gases converge towards a common point called absolute zero
10.7.3. Absolute zero is the basis of the Kelvin Temperature Scale
10.7.3.1. 0 K = -273.15° C = -454 °F
10.7.3.2. The temperature where ideal gas would exert zero pressure
10.7.3.3. The point where the ideal gas would have zero volume
10.7.3.4. All gases change their volume and pressure by 1/273 (0.37%) for each Celsius degree change in temperature
10.7.4. Kelvin scale is absolute scale
10.7.4.1. 200° C is not twice as hot as 100° C because 0° C is not lowest temperature
10.7.4.1.1. 200° C is not twice as "far" from O Kelvins, although it is twice as far from O° Celsius.
10.7.4.2. 200 K is twice as hot as 100 K because 0 K is the lowest temperature
10.7.4.3. Kelvin temperature is always used in calculations involving gases
10.7.5. All real gases liquefy before reaching absolute zero
10.7.5.1. The ideal gas is theoretical only
10.7.5.2. It is one which obeys gas laws under all conditions of temperature and pressure
10.7.5.3. any gas closely approximates the ideal gas under certain conditions
10.7.5.4. at high temperature and low pressure relative to boiling point
10.8.1. molecules either acquire or lose energy from collision with moving container wall
10.8.2. like a baseball gains energy when hit by a bat but loses energy when bunted
10.8.3. work is done on/by gas which increases/decreases its internal energy
10.9.1. kinetic energy of a molecule depends on its temperature
10.9.2. more massive molecules are moving slower at a given temperature
10.9.3. less massive molecules move faster and therefore diffuse more rapidly
10.9.4. basis for gaseous diffusion for enrichment of uranium for reactors
10.10.1. water molecules need to have certain speed to "escape" from liquid
10.10.2. at any temperature some molecules will have enough energy to escape
10.10.3. higher temperature means a higher percentage of molecules will escape
10.10.4. when the higher energy molecules escape they leave behind the slower or lower energy molecules
10.10.5. the average energy decreases with the loss of the high energy molecules
10.10.6. decrease in average energy is reflected as a lowering of temperature
10.11.1. vapor pressure
10.11.2. higher pressure means there are more molecules exerting more forces
10.11.3. more molecules in the air above a boiling pot will increase the chance that an escaping molecule will be knocked back into the pot
10.11.4. so higher pressure requires more energy to escape the liquid
10.11.5. higher pressure increases the boiling temperature
11.1. Discovered by Robert Brown in 1840s
11.1.1. small particles move in random, zig-zag patterns
126.96.36.199. ie smoke in still air, pollen grains in liquid
188.8.131.52. small motion even if fluid is still
11.1.2. smaller particle ==> faster motion
11.1.3. higher temperature ==> faster motion
11.1.4. no explanation at the time
11.2.1. used kinetic theory to predict average speed of particles as a function of particle size and temperature
11.2.2. removed last doubt about the existence of atoms and the correctness of kinetic theory
11.2.3. finalized link between chemistry and physics (atomic theory and kinetic theory)
11.3.1. found to be in close agreement with kinetic theory
In this lesson we have seen how the kinetic theory of matter, originally formulated to explain the gas laws, can be extended to other forms of matter. Many, if not all aspects of the physical behavior of matter can be explained or understood in the context of kinetic theory.
It is through kinetic theory that we obtain our best understanding of the distinction between heat and temperature and the nature of heat as a form of energy.
It also allows us to understand how conduction takes place as energy is transferred molecule to molecule by elastic collisions.