Physics 111. Lecture 42 (Walker: 18.9) Entropy & Disorder Final Review. May 15, 2009

Transcription

1 Physics 111 Lecture 42 (Walker: 18.9) Entropy & Disorder Final Review May 15, 2009 Review Session: Today, 3:10-4:00, TH230. Final exam, Monday May 18, 10:45-1:15. Lecture 42 1/32 The Physics 111 Final Exam On Monday, May 18, 10:45-1:15 we will have the Final Exam, covering Chapters 1-11 and of Walker. It will be similar in format to the midterms, with 60 pts of multiple choice questions and 140 pts of free-response questions. Closed book; calculators needed. Sections not covered: 8-5, 9-6 details, 9-8, 11-8, 11-9, 13-6, 14-3, 14-9, 15-9 surface tension, 17-3, All three equation sheets provided on the Final Suggestions: Work in symbols as long as possible; include units in answers. Lecture 42 2/32

2 Work Required by Refrigerator - Correction Minimum amount of work W needed to remove heat Q L set by entropy balance. A reversible refrigerator S H has an output entropy S H = Q H /T H equal to the input entropy S L = Q L /T L. Thus Q H = Q L (T H /T L ). Also, Q H = Q L +W. Solving gives W = Q L [(T H /T L )-1] The higher T H & the lower T L, the more work required S L Lecture 42 3/32 Entropy of Universe The total entropy of the universe is unchanged whenever a reversible process occurs. The total entropy of the universe increases whenever an irreversible process occurs. Conversion of mechanical energy to heat by friction, viscosity, air drag Heat flow across a temperature difference Since all real processes are irreversible, the entropy of the universe continually increases. If entropy decreases in a system due to heat being taken of it, an equal or greater increase in entropy occurs outside the system. Lecture 42 4/32

3 Order to Disorder Entropy is a measure of the disorder of a system. This gives us yet another statement of the second law: Natural processes tend to move toward a state of greater disorder. Example: If you put milk and sugar in your coffee and stir it, you wind up with coffee that is uniformly milky and sweet. No amount of stirring will get the milk and sugar to come back out of solution. Lecture 42 5/32 Order to Disorder Another example: when a tornado hits a building, there is major damage. You never see a tornado approach a pile of rubble and leave a building behind when it passes. Thermal equilibrium is a similar process the uniform final state has more disorder than the separate temperatures in the initial state. Lecture 42 6/32

4 Order, Disorder, and Entropy Entropy can be thought of as the increase in disorder in the universe. In this diagram, the end state is less ordered than the initial state the separation between low and high temperature areas has been lost. Lecture 42 7/32 Unavailability of Energy; Heat Death Another consequence of the Second Law: In any natural process, some energy becomes unavailable to do useful work. As the total entropy of the universe increases, the ability to do work decreases. The excess heat exhausted during an irreversible process cannot be recovered; doing that would require a decrease in entropy, which is not possible. If we look at the universe as a whole, it seems inevitable that, as more and more energy is converted to unavailable forms, the ability to do work anywhere will gradually vanish. This is called the heat death of the universe. Lecture 42 8/32

5 Evolution and Growth; Time s Arrow Growth of an individual, and evolution of a species, are both processes of increasing order. Do they violate the Second Law of Thermodynamics? No! These are not isolated systems. Energy comes into them in the form of food, sunlight, and air, and energy also leaves them. The Second Law of Thermodynamics defines the arrow of time processes will occur that are not reversible. Lecture 42 9/32 Thermal Pollution and Global Warming The generation of electricity using solar energy (a) does not involve a heat engine, but fossil-fuel plants (b) and nuclear plants (c) do. Lecture 42 10/32

6 Thermal Pollution and Global Warming The heat output of any heat engine, Q L, is referred to as thermal pollution, as it must be absorbed by the environment. Air pollution is also emitted by power plants, industries, and consumers. Some of this pollution results in a buildup of CO 2 in the atmosphere, contributing to global warming. This can be minimized through careful choices of fuels and processes. The thermal pollution, however, is a consequence of the Second Law, and is unavoidable; it can be reduced only by reducing Lecture 42 11/32 the amount of energy used and minimizing loss. Summary of Chapter 14 A next to an equation means it will not be tested on the final exam. A wave is a propagating disturbance. Transverse wave: disturbance is at right angles to propagation direction Longitudinal wave: disturbance is along propagation direction Wave speed: Speed of a wave on a string: v = F m / L Lecture 42 12/32

7 Summary of Chapter 14 If the end of a string is fixed, an incoming wave is inverted upon reflection. If the end is free to move transversely, the wave is not inverted upon reflection. A sound wave is a longitudinal wave of compressions and rarefactions in a material. High-pitched sounds have high frequencies; low-pitched sounds have low frequencies. Human hearing ranges from 20 Hz to 20,000 Hz. Lecture 42 13/32 Summary of Chapter 14 Intensity of sound: (Unit: W/m 2 ) Intensity a distance r from a point source of sound: When the intensity of a sound increases by a factor of 10, it sounds twice as loud to us. Intensity level, measured in decibels: Lecture 42 14/32

8 Summary of Chapter 14 Doppler effect: change in frequency due to relative motion of sound source and receiver General case (both source and receiver moving): Top signs used when source & observer approaching When two or more waves occupy the same location at the same time, their displacements add at each point. If they add to give a larger amplitude, interference is constructive. If they add to give a smaller amplitude, interference is destructive. Lecture 42 15/32 Summary of Chapter 14 An interference pattern consists of constructive and destructive interference areas. Two sources are in phase if their crests are emitted at the same time. Two sources are out of phase if the crest of one is emitted at the same time as the trough of the other. Interference of waves arriving at a point from two sources (in phase) depends on path length difference L: L an integral number of wavelengths -- constructive interference L an odd number of half-wavelengths -- destructive interference. Lecture 42 16/32

9 Summary of Chapter 14 Standing waves on string; resonant frequencies: Standing waves in a half-closed column of air: Standing waves in a fully open column of air: Lecture 42 17/32 Summary of Chapter 16 Heat (Q) is the energy transferred between objects due to a temperature difference. Objects are in thermal contact if heat can flow between them. Objects that are in thermal contact without any flow of heat are in thermal equilibrium. Thermodynamics is the study of physical processes that involve heat. If objects A and B are both in thermal equilibrium with C, they are in thermal equilibrium with each other. Lecture 42 18/32

10 Summary of Chapter 16 Temperature determines whether two objects will be in thermal equilibrium. Celsius scale: water freezes at 0 C, boils at 100 C Fahrenheit: water freezes at 32 F, boils at 212 F (nothing about Fahrenheit on final) The lowest attainable temperature is absolute zero. T = 0 K Kelvin scale: absolute zero is 0 K; water freezes at K and boils at K Lecture 42 19/32 Summary of Chapter 16 Temperature scale conversions: Most substances expand when heated. Linear expansion: Volume expansion: Water contracts when heated from 0 C to 4 C. Lecture 42 20/32

11 Summary of Chapter 16 Heat is a form of energy; SI unit Joule (J) Heat capacity of an object: (Unit: J/K or J/ C) Specific heat is heat capacity per unit mass: (Unit J/kg-K or J/kg- C) Energy is conserved in heat flow. Lecture 42 21/32 Summary of Chapter 16 Conduction: heat exchange from hotter part of material to cooler part, with no bulk motion of material. Heat Q conducted through length L of material of cross-section area A and thermal conductivity k in time t if temperature difference is T: Convection: heat exchange due to the bulk motion of an unevenly heated fluid. Radiation: heat exchange due to electromagnetic radiation. Lecture 42 22/32

12 Summary of Chapter 16 Radiated power as a function of temperature: Stefan-Boltzmann constant: Net radiated power with surroundings at temperature T s : P net = eσa(t 4 -T s4 ) Lecture 42 23/32 Summary of Chapter 17 An ideal gas is one in which interactions between molecules are ignored. Equation of state for an ideal gas: Boltzmann s constant: Universal gas constant: Equation of state again: Number of molecules in a mole is Avogadro s number: Lecture 42 24/32

13 Summary of Chapter 17 Molecular mass: Boyle s law: Charles s law: Kinetic theory: gas consists of large number of pointlike molecules; pressure is a result of molecular collisions with container walls Lecture 42 25/32 Summary of Chapter 17 Molecules have a range of speeds, given by the Maxwell distribution Relation of kinetic energy to temperature: Relation of rms speed to temperature: Internal energy of monatomic gas: Lecture 42 26/32

14 Summary of Chapter 17 Most common phases of matter: solid, liquid, gas When phases are in equilibrium, the number of molecules in each is constant Evaporation occurs when molecules in liquid move fast enough to escape into gas phase Latent heat: amount of heat required to transform mass m from one phase to another Q = ml Latent heat of fusion L F : melting or freezing Lecture 42 27/32 Summary of Chapter 17 Latent heat of vaporization L V : vaporizing or condensing Latent heat of sublimation: sublimation or condensation directly between gas and solid phases When heat is exchanged within a system isolated from its surroundings, the energy of the system is conserved. Heat lost from one part of system is gained by another part. Lecture 42 28/32

15 Summary of Chapter 18 When two objects have the same temperature, they are in thermal equilibrium. The First Law of Thermodynamics is a statement of energy conservation that includes heat. U = Q in -W by The internal energy (U) of a system depends on its temperature, pressure, volume, and phase. A quasi-static process is one in which the system may be considered to be in equilibrium at all times. Lecture 42 29/32 Summary of Chapter 18 In a reversible process, it is possible to return the system and its surroundings to their initial states. Irreversible processes cannot be undone. Work done by system at constant pressure is The work done at constant volume is zero. Lecture 42 30/32

16 Summary of Chapter 18 An adiabatic process is one where no heat transfer occurs. The value of the specific heat of a gas depends on whether it is at constant pressure or at constant volume. Molar specific heat is defined by: For a monatomic gas at constant volume: For a monatomic gas at constant pressure: Lecture 42 31/32 Summary of Chapter 18 Entropy (S) is a measure of disorder. Units: J/K Change of entropy during a reversible heat exchange: Second Law of Thermodynamics: S universe 0 in Total entropy of the universe increases when an irreversible process occurs; total entropy is unchanged after an ideal reversible process. Heat flows spontaneously from a hot object to a cold one, but not the reverse. A given amount of heat cannot be changed entirely to work. Natural processes tend to increase entropy of universe. Lecture 42 32/32

17 Summary of Chapter 18 A heat engine converts heat into work. Efficiency of a heat engine: Lecture 42 33/32 Summary of Chapter 18 A reversible engine has the maximum possible efficiency, The maximum possible work: Refrigerators, air conditioners, and heat pumps use work to transfer heat from a cold region to a hot region. Heat exhausted to the hot region is always more than heat removed from cold region. Lecture 42 34/32

18 End of Lecture 42 Final exam: Monday, May 18, 10:45-1:15. Review Session: Today, 3:10-4:00, TH230. Homework 18b (last one!) due at 11:00 p.m. tonight. Lecture 42 35/32