Sci 122 Telecourse Program 26 Kinetic Theory

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Kinetic Theory

Program 26

Lesson 4.4

Text References

Spielberg & Anderson 127-130; 138-140; 149-151; 152-154

Booth & Bloom 189-218


A . States of Matter & Gas Laws

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.

B. Kinetic Theory of Gases

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?

Coming Up

1. Introduction

2. Pressure, Volume & Temperature

3. Air Pressure

4. Gas Laws

5. Boyle's Law (1662)

6. Law of Charles and Gay-Lussac

7. Ideal Gas Law

8. Explanations for the Gas Laws

9. Kinetic Theory of Gases

10. Brownian Motion

11. Summary & Conclusion


1. Define Pressure, Volume and Temperature.

2. Distinguish between pressure in liquids and gases.

3. Trace the history of the concept of air pressure.

4. State the gas laws of Boyle and Charles.

5. State the Ideal Gas Law and discuss its meaning.

6. State the assumptions of the kinetic theory of gases.

7. Discuss the thermal behavior of matter in the context of kinetic theory

8. Distinguish between heat and temperature using kinetic theory

9. Distinguish between the atomic order of the three states of matter.

10. Describe Brownian motion and use kinetic theory to explain it.

1. Introduction

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.

1.1. Atoms and molecules join the Newtonian paradigm

1.2. Heat and Temperature linked to motion of Molecules

1.3. Newtonian mechanics connects with chemistry

1.3.1. conservation of energy, gas laws, atomic theory, statistics

1.4. Sets stage for understanding entropy and nonreversible reactions

1.5. Provides background for understanding electromagnetic theory of light

1.6. Newton's laws applied to matter at the atomic level

2. Pressure, Volume, Temperature

2.1. Pressure

2.1.1. Force per unit area

2.1.2. P = F/A 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. equal in all directions change of pressure at any point is accompanied by a corresponding change at every other point if it is not flowing (Pascal's principle) increases downward due to weight of liquid above a given area zero at surface

2.1.7. also true for gases in ordinary sized containers the difference in pressure between top and bottom is negligible if not immeasurable 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 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 air pressure diminishes with height in the atmosphere

2.2. Volume is measure of occupied space in units of meters cubed or liters

2.3. Temperature is in absolute or Kelvin degrees

3. Air Pressure

3.1. The Suction Pump

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" water rises in an attempt to fill the vacuum as the tube is evacuated 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. Galileo's hypothesis

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. Toricelli's barometer

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. 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 a vacuum exists above the mercury 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 left an identical barometer behind with an observer to record changes in air pressure at the foot of the mountain why did he do that? 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 not true but still assumed by many, including encyclopedias and physics texts can be shown by several methods 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 pressure in water increases rapidly with depth with no appreciable change in density pressure of air decreases rapidly with altitude with a corresponding decrease in density 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. Boyle's vacuum pump

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. Magdeburg Hemispheres

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. Gas Laws

4.1. relationships between temperature, pressure, and volume of gases

4.2. discovered in steps, now expressed as ideal gas law

5. Boyle's Law

5.1. demo: squeeze a balloon until it pops

The fact that decreasing volume increases pressure can be shown qualitatively with a balloon. Try it with a balloon of your own.

5.2. Published in 1662

5.3. PV = constant

5.4. P and V are inversely proportional when temperature is constant

5.5. Boyle did not have accurate thermometer to measure temperature change

5.6. Boyle's J tube

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.

5.7. demo: Boyle's Law apparatus

The video program shows how the volume and pressure are inversely proportional using a pressure gauge and a glass cylinder with a piston.

6. Law of Charles and Gay-Lussac

6.1. V/T = constant

6.2. V and T are directly proportional when pressure is constant

7. Ideal Gas Law

7.1. PV = kT

7.2. combination of Boyle's, Charles & Gay-Lussac

7.3. volume is proportional to temperature and inversely proportional to pressure

7.4. work done is proportional to change in temperature if no heat is exchanged

7.5. yet another statement of conservation of energy

7.6. STP and equivalent volumes

8. Explanations for the Gas Laws

8.1. Boyle (1662): Static vs. Kinetic

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. Daniel Bernoulli (1738)

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 recognized the equivalence of heat and mechanical energy through particle motion 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 PV (pressure times volume) has same units as work when conversions are made shows utility of standard units in understanding concepts

9. Kinetic Theory of Gases

9.1. Postulated by Joule to explain gas laws

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. Refined and extended to other phenomena

9.2.1. by other 19th century physicists Helmholtz, Maxwell, Boltzmann, and Gibbs

9.3. Links atomic theory and Newtonian paradigm

9.4. Still does not explain chemical bonding

9.5. Atoms and Molecules are Newtonian Particles

9.5.1. have mass and occupy space

9.5.2. obey laws of motion

9.5.3. obey energy and momentum conservation

9.6. Postulates of Kinetic Theory

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 gases are substances substances consist of molecules changes of state are physical changes involving no new substances gases consist of the same kinds of molecules as their solid forms steam is gaseous water molecules

9.6.2. Molecules are in constant random motion gases diffuse through space to fill available volume 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 gases are greatly compressible gases are much less dense than their liquid or solid counterparts

9.6.4. Molecules exert no forces except during collisions gravitational forces are extremely small and can be ignored what other kinds of forces are there?

9.6.5. Collisions are perfectly elastic kinetic energy is completely conserved compare to room full of bouncing balls container of gases does not lose energy molecules do not collect in the bottom of the container this makes sense if the others make sense

10. Kinetic Behavior

10.1. States of Matter

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. GAS no fixed shape or volume, exert pressure on containers molecules far apart compared to their size gases are compressible least restricted motion billiard balls on table a room full of super balls mostly empty space so easily compressed motion is constant, random, rapid exert pressure many collisions, small average distance traveled between collisions no net movement

10.1.3. LIQUID fixed volume, but no fixed shape most complicated state intermediate between gas and solid most substances have only limited region of liquid stability ie. water, carbon dioxide molecules are closer together than gas but free to move in limited way weak forces between molecules due to physical bonds clusters of solid structure mixed with gaseous state sliding motion model: jar full of magnetic spheres

10.1.4. SOLID fixed shape and fixed volume molecules are free to move, but only around fixed positions held together by relatively strong forces, either chemical or physical bonds model: lattice of balls connected by springs

10.2. Gas Pressure

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 like throwing a ball at the wall of a room total force exerted on wall is sum of force exerted by all molecules sum of forces of all collisions per unit area of wall is gas pressure can calculate the relationship between energy and temperature can calculate the relationship between momentum and pressure

10.3. Gas Laws and Real Gases

10.3.1. IDEAL gases vs. REAL gases All gases exert pressure due to molecular collisions Real gases deviate from gas laws at low temperatures and high pressures when gases are close to liquefaction point

10.3.2. Ideal Gases exert forces during collision only on walls of container on other molecules pressure is result of sum of collisions of all molecules exchange energy and momentum during collisions collisions are perfectly elastic energy is conserved in collisions air does not settle to bottom of room

10.4. Real Gases

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 liquid nitrogen boils at -196° C (77 K) at 1 atmosphere pressure liquid water boils at 100° C (373 K) at 1 atmosphere pressure

10.5. Heat and Temperature

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 heat is energy which can be transferred potential energy of physical bonds between molecules work must be done to break chemical or physical bonds to cause change of state 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 translation: movement of molecules from place to place rotation: around a center of mass vibration: about fixed locations in solid, liquid, or diatomic gas

10.5.4. Temperature is average kinetic energy of molecules Kinetic energy is not the same for all molecules in a sample some move fast, some slowly average kinetic energy and distribution of energy depend on temperature speed of molecules can be calculated from Newtonian mechanics Derivation of Newtonian Energy (after Bernoulli) Veolocity of air molecules at room temperature

10.6. Specific and Latent Heat

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. Gases and Absolute Temperature

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 0 K = -273.15° C = -454 °F The temperature where ideal gas would exert zero pressure The point where the ideal gas would have zero volume 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 200° C is not twice as hot as 100° C because 0° C is not lowest temperature 200° C is not twice as "far" from O Kelvins, although it is twice as far from O° Celsius. 200 K is twice as hot as 100 K because 0 K is the lowest temperature Kelvin temperature is always used in calculations involving gases

10.7.5. All real gases liquefy before reaching absolute zero The ideal gas is theoretical only It is one which obeys gas laws under all conditions of temperature and pressure any gas closely approximates the ideal gas under certain conditions at high temperature and low pressure relative to boiling point

10.8. Heating/cooling vs. Compression/expansion

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. Gaseous Diffusion

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. Cooling By Evaporation

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. Boiling Temperature vs. Pressure

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. Brownian Motion

11.1. Discovered by Robert Brown in 1840s

11.1.1. small particles move in random, zig-zag patterns ie smoke in still air, pollen grains in liquid 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. Explained by Einstein in 1905

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. experimentally verified the same year by Perrin

11.3.1. found to be in close agreement with kinetic theory

12. Summary & Conclusions

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.