ATMOSPHERIC THERMODYNAMICS

by Bohren, Craig F.; Albrecht, Bruce A.

• ISBN13: 9780195099041
• ISBN10: 0195099044
• Format: Hardcover
• Copyright: 1998-02-19
• Publisher: Oxford University Press

Summary

This comprehensive text is based on the authors' course notes, refined and updated over 15 years of teaching. The core of the text focuses on water and its transformations. Four chapters lay the foundation, from energy conservation to the ideal gas law, specific heat capacities, adiabaticprocesses, and entropy. An extensive chapter treats phase transitions of water, and a lengthy discussion of the van der Waals equation sets the stage for phase diagrams. Free energy is applied to determining the effect of dissolved substances, total pressure, and size on vapor pressure. The chapteron moist air and clouds discusses wet-bulb and virtual temperatures, isentropic ascent of saturated air, thermodynamic diagrams, stability, and cloud formation. The final chapter covers energy, momentum, and mass transfer, topics not usually considered part of thermodynamics. Measurements areincluded and experiments and observations are suggested, all with the aim of breathing life into equations. The authors are careful to recognize and unafraid to criticize the treatments of thermodynamics that have been unchanged for more than a hundred years. Atmospheric Thermodynamics contains over 200 exercises, mostly applications of basic principles to concrete problems. Often inspired by inquisitive students and colleagues, the exercises cover everything from automobiles and airplanes to baseball, wind turbines, and ground hogs. The authors weavehistory into the text by drawing on original writings rather than using textbook anecdotes, and molecular interpretations are given wherever possible. Assumptions and approximations are carefully laid out, derivations are detailed, and equations are interpreted physically and applied. No previousknowledge of thermodynamics or kinetic theory is assumed, although students are expected to be well-grounded in calculus, differential equations, vector analysis, and classical mechanics.

Table of Contents

Preface	viii	(5)
Acknowledgments	xiii
1 INTRODUCTION: CONSERVATION OF ENERGY	1	(33)
1.1 Thermodynamics: A Science of Measurable Quantities	2	(4)
1.2 Conservation of Energy in Mechanics	4	(2)
1.3 Conservation of Energy: A System of Point Masses	6	(4)
1.4 A Few Examples of Energy Conservation	10	(1)
1.5 Kinetic Energy Exchanges in Molecular Collisions	10	(6)
1.6 Working and Heating	16	(5)
A Simple Example of Working	18	(3)
1.7 Some Necessary Thermodynamic Concepts and Jargon	21	(1)
1.8 Thermodynamic Internal Energy and the First Law	22	(7)
Some Irreverent Thoughts About Heat	24	(5)
Selected References and Suggestions for Further Reading	29	(1)
Problems	30	(4)
2 IDEAL GAS LAW: PRESSURE AND ABSOLUTE TEMPERATURE	34	(55)
2.1 Gas Pressure and Absolute Temperature: What Are They?	35	(19)
Ideal Gas Law	36	(4)
A Perspective on Units	40	(3)
Pressure Measurement: Barometer and Manometer	43	(2)
Temperature Scales and Thermometers	45	(2)
Atmospheric Temperature Measurements	47	(2)
A Linguistic Sin of Meteorologists: Repent!	49	(1)
The Nature of Statistical Laws	49	(2)
History of the Gas Law	51	(3)
2.2 Pressure Decrease with Height: Continuum Approach	54	(4)
Thickness: A Surrogate for Average Temperature	58	(1)
2.3 Pressure Decrease with Height: Molecular Approach	59	(1)
2.4 The Maxwell-Boltzmann Distribution of Molecular Speeds	60	(6)
Why Don't Air Molecules Escape to Space?	64	(2)
2.5 Intermolecular Separation, Mean Free Path, and Collision Rate	66	(5)
Mean Free Path	67	(2)
Intermolecular Collision Rate	69	(1)
Local Thermodynamic Equilibrium	70	(1)
2.6 Is the Pressure Gradient a Fundamental Force of Nature?	71	(1)
2.7 Surface Pressure and Weight of the Atmosphere	72	(2)
Flat Earthers Beware!	73	(1)
Why Aren't We Crushed by Airplanes Flying Overhead?	73	(1)
2.8 The Atmosphere Is a Mixture of Gases: Dalton's Law	74	(5)
Mean Molecular Weight	75	(4)
Selected References and Suggestions for Further Reading	79	(2)
Problems	81	(8)
3 SPECIFIC HEATS AND ENTHALPY: ADIABATIC PROCESSES	89	(46)
3.1 A Critical Discussion of the Mathematics of Thermodynamics	89	(10)
Those Accursed Differentials	93	(4)
Differentials and Infinitesimals	97	(1)
Are Differentials Necessary in Thermodynamics?	97	(2)
3.2 Specific Heats and Enthalpy	99	(7)
An Incompressibility Paradox: The Perils of Idealization	104	(1)
Enthalpy of the (Hydrostatic) Atmosphere	105	(1)
3.3 Adiabatic Processes: Poisson's Relations	106	(2)
3.4 Dry Adiabatic Lapse Rate	108	(3)
Do Pistons and Cylinders Inhabit the Atmosphere?	109	(2)
3.5 Stability and Buoyancy	111	(3)
Buoyancy	112	(2)
Dry Adiabatic Lapse Rate and Stability	114	(1)
3.6 Specific Heats of Gas Molecules	114	(9)
The Ratio of Working to Heating at Constant Pressure	120	(3)
3.7 Heat Capacities of Mixtures of Gases	123	(4)
Water Vapor Demystified	123	(1)
Isobaric, Adiabatic Mixing of Moist Parcels	124	(3)
Selected References and Suggestions for Further Reading	127	(1)
Problems	127	(8)
4 ENTROPY	135	(46)
4.1 Entropy of an Ideal Gas	136	(19)
Entropy Change In a Free Expansion	137	(1)
Entropy Changes Upon Heating and Cooling	138	(7)
The Second Law and Stability	145	(1)
Entropy of Mixtures; Entropy of Mixing and Gibbs's Paradox	146	(2)
Entropy Changes Upon Mixing of Two Gases With Different Temperatures and Pressures	148	(1)
An Entropic Derivation of Joule's Law	149	(1)
Entropy and Disorder: A Persistent Swindle	150	(2)
Integrating Factor and Entropy	152	(3)
4.2 Entropy Changes of Liquids and Solids	155	(2)
4.3 Potential Temperature: Meteorologists' Entropy	157	(4)
Parcel Oscillations	159	(2)
4.4 Atmospheric Applications of the Second Law	161	(16)
Entropy Maximization in the Atmosphere	164	(5)
Entropy Maximization in the Atmosphere: General Case	169	(2)
Thermodynamic Efficiency: The Carnot Cycle	171	(4)
Entropic Derivation of the Dry Adiabatic Lapse Rate	175	(2)
Selected References and Suggestions for Further Reading	177	(1)
Problems	178	(3)
5 WATER AND ITS TRANSFORMATIONS	181	(91)
5.1 Evaporation and Condensation of Water Vapor	182	(3)
5.2 Measures of Water Vapor in Air	185	(7)
Dew, Frost, Defrosters, Dehumidifiers, and Swamp Coolers	188	(4)
5.3 The Clausius-Clapeyron Equation	192	(12)
Other Enthalpy Differences	195	(1)
Entropy and Enthalpy Differences in Phase Changes	196	(1)
Temperature Dependence of Enthalpy of Vaporization	197	(1)
Temperature Dependence of Saturation Vapor Pressure: A More Accurate Equation	197	(3)
Difference Between the Saturation Vapor Pressure Above Ice and Above Subcooled Water at the Same Temperature	200	(2)
Dew Points and Human Comfort	202	(1)
Lapse Rate of the Boiling Point	203	(1)
5.4 van der Waals Equation of State	204	(14)
Must a Liquid Boil in Order to Evaporate?	214	(1)
Can a Solid Boil Before it Melts?	215	(1)
Departures From Ideality According to the van der Waals Equation	215	(1)
The Maxwell Construction and Saturation Vapor Pressure	216	(2)
An Overview of the Many Successes of the van der Waals Equation	218	(1)
5.5 Phase Diagrams: Liquid-Vapor; Liquid-Solid-Vapor; Triple Point	218	(5)
5.6 Free Energy	223	(3)
5.7 Effect of Air Pressure on Saturation Vapor Pressure	226	(3)
5.8 Lowering of Vapor Pressure by Dissolution	229	(4)
5.9 Air in Water: Henry's Law	233	(5)
Change in Saturation Vapor Pressure with Total Pressure	237	(1)
5.10 Size Dependence of Vapor Pressure: Droplets and Bubbles	238	(14)
Droplet Vapor Pressure: The Kelvin Equation	239	(4)
Bubble Vapor Pressure	243	(4)
Mechanical Equilibrium of Bubbles and Droplets: The Laplace Equation	247	(3)
Boiling Demystified and More Heresy	250	(2)
5.11 Vapor Pressure of Solution Droplets	252	(4)
Selected References and Suggestions for Further Reading	256	(4)
Problems	260	(12)
6 MOIST AIR AND CLOUDS	272	(63)
6.1 Precipitable Water in the Atmosphere	272	(2)
6.2 Lapse Rate of the Dew Point: Level of Cloud Formation	274	(4)
6.3 Density of Moist Air: Virtual Temperature	278	(3)
6.4 Wet-Bulb Temperature	281	(6)
Is the Temperature of a Wet Bulb the Wet-Bulb Temperature?	285	(1)
Humidity Measurements	286	(1)
6.5 Lapse Rate for Isentropic Ascent of a Saturated Parcel	287	(12)
Equivalent Potential Temperature and Wet-Bulb Potential Temperature	292	(7)
6.6 Thermodynamic Diagrams	299	(12)
A Smattering of History	300	(1)
Skew T-log p Diagram	301	(6)
Tephigram	307	(1)
Other Diagrams	308	(3)
6.7 Stability and Cloud Formation	311	(11)
Entrainment	317	(5)
6.8 Mixing Clouds	322	(2)
6.9 Cloud Formation on Ascent and Descent	324	(3)
Selected References and Suggestions for Further Reading	327	(2)
Problems	329	(6)
7 ENERGY, MOMENTUM, AND MASS TRANSFER	335	(49)
7.1 Energy Transfer	335	(31)
Fourier Conduction Law	337	(1)
Thermal Resistance	338	(2)
An Application of Thermal Resistance to Consumer Fraud	340	(2)
Convective Transfer of Energy	342	(1)
Conductivity of a Gas: A Few Myths Exploded	343	(3)
The Effective Conductivity of Porous Materials	347	(1)
The Skin Diver's Fallacy	348	(2)
Newton's Law of Cooling: A Study in Error Propagation	350	(4)
The Freezing of Lakes	354	(2)
Radiative Energy Transfer	356	(1)
Radiation and Convection Combined: Dew and Frost Formation	357	(2)
To Insulate or Not to Insulate?	359	(1)
Radiation in Porous Media	360	(2)
Newton's Law of Cooling According to Newton	362	(1)
The Thermometer As a Low-pass Filter	363	(1)
Engineer Heal Thyself	365	(1)
7.2 Momentum Transfer: Viscosity	366	(6)
7.3 Mass Transfer: Diffusion	372	(7)
Diffusion Coefficient	374	(2)
Growth of Cloud Droplets	376	(3)
Selected References and Suggestions for Further Reading	379	(1)
Problems	380	(4)
Selected Physical Constants	384	(2)
Bibliography	386	(9)
Index	395