Thermal Physics Kittel Pdf next post Tolley S Industrial Commercial Gas Installation Practice Volume 3 Fourth Edition Pdf. Back to top. solutions manual is available via the freeman web site (http://whfreeman. com/ thermalphysics). Berkeley and Santa Barbara. Charles Kittel. Herbert Kroemer. wm-greece.info Uploaded by. Veerareddy Vippala. Kittel Thermal Physcis. Uploaded by. Eric Standard. Thermal.
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wm-greece.info - Ebook download as PDF File .pdf), Text File .txt) or read book online. Thermal Physics. Charles Kittel. Herbert Kroemer. W. H. Freeman and Company. New York. QCK52 '.7 ISBN 1. S TATES OF A M. Kittel, Kroemer - Thermal Physics - Ebook download as PDF File .pdf) or read book online.
The average was Our exam is Thursday, January 13, at pm. Problem sessions resume next Sunday, November 7. Monday, October Homework 5 due in department office by 5pm. Tuesday, October Karol leads evening review, pm, 4th floor lounge. Wednesday, October In class midterm. Karol's office hours are on Thursday. Course Instructor: Ed Groth , Jadwin , x, groth physics.
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CambridgeUniversity Press. The kind of motion we call heal. Introduction to the renormalizat'ton group and to critical phenomena. Prigogine and I.
Oxford Univesity Press. Physical metallurgy. Semiconductor devices R.. Carslaw and J. Introduction to phase transitions and critical [ihenomena. An introduction to liquid helium. Metais and affoys P. Smith and H.
Plasma physics I. Transport phenomena. Oxford Uni- University Press. Order out of chaos: Introduction to solid state physics. Experimental techniques in low-temperature physics. When two systems. Eventually the entropy will reach a maximum for the given total energy.
It is not difficult to show Chapter 2 that the maximum. What is the most probableoutcome ofthe encounter? One system will gain energy at lhe expense of the other. A transfer of energy in one direction. The entropy lhtis defined will be a function of ihe energy U. The entropy measures the number of quantum states accessible to a system.
The fundamental assumption biases the outcome in favor of that allocation of the total energy that maximizes the number of accessible states: Given g accessible states. Introduction Our approachto thermal physics differs from the tradition followed in beginning physics courses.
The statistical element. A closed system might be in any of these quantum states and we assume with equal probability. The use of the logarithm is a mathematical convenience: Therefore we provide this introduction 10set oul what we are going to do in the chapters that follow.
We show the main lines of the logical structure: We havebrought two systems into thermal contactso that they may transfer energy. This statement is the kernel of the law of increase of entropy. In order of lhcir appearance. The loia! C by the definition A ofthe temperature. Now consider a very MiiipJe csampli?
When the small sysiem is in the slate of energy e. Higher order terms in the expansion may be dropped. To show its use. This equality property for Iwo systems in ihermai coniaa is just the property we expect of the icmperat lire. By the fundamental assumpiion. For two systems in diffusive and thermal contact. We extend C for the reservoir entropy: S By anaiogy with D.
The result 9 after normalization is readily expressed as A0. The Gibbsfactorof Chapter 5 is an extension of Ihe Bolizmann factor and ailows treat systems ilia! The most important extension of the theory is to systems that can transfer particles ns well as energy with ttie reservoir.
F The argument can be generalized immediately to find the average energy of a harmonic oscillator at temperature r. The simplestcx: The sign in G is chosen to ensure thai the direction of particle flow as equilibrium is approachedIs from high chemicai potential to low chemical potential. The system is contact in with a reservoir at temperature r and chemicalpotential. This particular result is known as the Fermi-Dirac distribution function and is used particularly in the theory of metals to describe the electron gas at low temperature and high concentration Chapter 7.
Most in of the reiftaiiuier of the tcxl concerns applications that are useful in their own right and that illumi- illuminate the meaning and utility of the principal thermodynamic functions. The classicaldistribution function used in the derivation of the ideal gas law- is just the limit of A0 when the occupancyPA. The properties of the ideal gas are developedfrom this result in Chapter 6.
It unites the two parts of our world. Thermal physics connects the world of every iky objects. Other powerful tools for the calculation of thcnnodyiumic functions arc developed the text.
States of a ModelSystei. It is ihu only physical theory of universal content which I am convinced mil never be overthrown.
Cibbs A theory is the more impressive the greater the simplicity of its premises. Therefore the deep impression that classical thermodynamics made upon me. Bul although. For brevity we usually omit the word stationary. Tlte number of quantum stales belonging to the sameenergy level is in parentheses. Chapter 1: States of a ModelSyster. Stales with identical energies arc said to belong to the same energy level. Let us look antic qiu. There are three new quantities in thermal physics that do not appear in ordinary mechanics: The simpler is hydrogen.
We shall frequently deal fti'th sums over all quantum states. The systems we discuss may be composedof a single particle or. We shall motivate their definitions in the first three chapters and deduce their consequences thereafter. Mechanicstells us the meaning of work.
The theory is developed to handle genera! The dependenceof the entropy on the energy of the system defines the tempera- temperature. The multiplicity or degeneracy of an energy level is the number of quantum states wiih very nearly the some energy.
The zero of energy in the figure is taken at the state of lowest energy. Thermal physics is the fruit of the union ofslatistica! From rhe entropy. When we can count the quantum states accessibleto a system. Fora system in a stationary quantum state.!. Our point of departure for the developmentofthermal physics is the concept of thestationary quantum statesofa system of particles.
Each quantum slate has a definite energy. Two states at the same energy must always be counted as two slates. Chapter 1. The energiesare given votis. The zero of energy in the figure is taken forcouvei ai die lowest energy slaie of each aiom. An atom of lithium has three electrons which move about the nucleus. Each electron interacts with the nucleus. To takeaccount of the two orientations we should double the values of the multiplicities shown for atomic hydrogen.
The energy ofa system isthe total energy ofal!
The energiesofthe levels of lithium shown in the figure are the collective energies of the entire system. Quantum states ofa one-pariicie system are called orbitals. Chapter I: A quantum state of the system is a state ofall particles. The energy leveis shown for boron. We shall find in Chapter 3. The sites are plus numbered. Indices such as s may be assigned lo the quantum states in any convenient arbitrary way. This assumptionleadsto predictions that always agree with experiment.
You might even tltink of the sites as numbered parking spaces in a car parking lot. Whatever llic milure of otlr objects. The energy is The multiplicities of the levelsare indicated tn the figure.
What general statistical properties are of concern will become clear as we go along. N We assume there are separate and distinct sites fixed in space. If the magnet points down. This requites no of magnelism: It is a good idea to siart program by studying the properties of simple our model for which systems the energies A' can be calculated e. If he magnet points up. Each moment may be oriented in two ways with a probability independent of the orientation ofa!!
TiseO's denotespaces occupied by a car. Each magnetic moment may be oriented in two up or down. Binary Model Syster 10 Number of the site Ffgure 1. If ihe arrangements arc selectedin a random process. Now consider N different sites. We may use ilio following simplettotation for a single state of the system of N sites: This particular state is equivalent to that shown in Figure.
Figure 1. It is not hard to convince yourself that every distinct state of the system is contained a symbolic in product of N factors: For a system of two elementary magnets. The product on the left-hand side of the equation is calleda generatingfunction: The sites themselves are assumed to be arrangedin a definite order. Each term is a product of N individual magnetic moment symbols. We may numbcr4hem in sequence ftom left to right.
F The sum is not a state but is a way of listingthe four possible states of the system. There are many more states than values of [he total moment. Three magnets up: T1T1T3 Two magnets up: The value of M varies from Nm to -. The set of possible values is given by.
S There arc N ways to form a slate with one magnet down: We will calculate in the next section how many states have a given value of M. We may reverse iV magnets to obtain llie ultimate state for which al! I and? We with W. Enumeration of Stales and the Multiplicity Function We use the word spin as a shorthand for elementary magnet. The facior of 2 in I! The spin excess of the 4 states in Figure 1. The difference W.
When we turn one magnet from Ihe up [he down to orientation. Slates of a Mode! System and the other slates with one magnet down are formedfrom S by reversing any single magnet. It is convenient lo assume that N is an need a mathematical expressionfor the even number. V s magnets down. This class of - states lias spin excess JV. For a coin. The reason for our deltnttion emerges when a magnetic field is applied to the spin system: Until we introduce a magneticfield. Enumeration of Stales and the Multiplicity Function We may write the exponents of x and y in a slightly different.
Tlic toul numtwt of stales is TTic values of the 9's arc taken fro the binomial coefficients. Each siteis occupiedby either an atom of chemical species A or an atom of chemical species B. A could be copper and B zinc. In analogy to C. Chapter t: Slatesofa Model System Figtorc 1. Values of yf Npi are for N. I -8 I -4 j 0 2 4 6 -6 -2 Spin excess 2s Binary Alloy System To illustrate that the exact nature of the two states on each site is irrelevant to the result. In brass.
The number of heads in each throw was recorded. When you confront a very. Every distinct state of a binary alloy system on N sites is contained in the symbolic product of N factors: We look for an approximation that allows us to examine the form of g S. The symbolic expression is analogous to the result A2. We can show explicitly thai for a very large system. A9 in analogy to The Liverage composition of a binary D.
The stability follows as a consequenceof the exceedingly bharp peak in the multiplicity function and of the steep variation of that function away from the peak. The international standard usage is In for log base c. Sharpnessof ihe Multiplicity Function We know from common experience that systems held at constanttemperature usually have well-defined properties. An approximation is clearly needed. Sharpnessof the Multiplicity Function 2iV.
B2 by virtue of ihe characteristicproperlyofthe logarithm of a product: Nu B9 After rearrangement of B7. B2 appears as logg N. U loobl: BPJ logN. B7 Similarly! For sufficiently large N. This result is derived in Appendix A. We take the logarithm of both sidesof B6 to obtain logN! Several useful integrals are treated in Appendix A. This may be simplified because logOV. C6 Such a distribution of values of sis caiicda Gaussian distribution.
C3 On subsliiuiion in C! The exact value of y N. For example. The approximate vylue from C6 is 1. Thedistribution plottedin Figure t. It is this sharp peakand the continued sharp variation of the multiplicity function far from the peak that will lead to a prediction that properties of systems in thermal equilibrium the physical are well defined.
We now consider one such property.
When N is very large. That is. If all states are equally probable. D1 and is nol normalized lo unity. We shall con- sec later hat a continuous or quast-conttnuous spectrum will creafe no difficulty. This funcitotutl dependence is. Reversing a single moment lowers 2s by The energy difference bsiween adjacent levels is dcnotcJ by Ac. For If the energyof the system is specified. Constant spacing is a special feature of the particular tnodcl. For the model system of Ar elementary mngncts.
This means that the central peak of the distribution function becomes relatively more sharply defined as the size of the system increase..
V H6 This is the potential energy of the magnet m in the field B. Energy of the Binary Magnetic System The thermal properties of the model system become physically relevant when the elementary magnets arc placedin a magnetic ticid. In this example lite spcclnttn of values of ihe encrcy U is discrete. The original derivation is often felt to be not entirely simple. Chopset UM.
The number of states is infinite. We want to find the number of ways in which a given total excitation energy. D9 where the quantum number s is a positive integer or zero. Tor this Example: Multiplicity function for harmonic oscillators. The modern way to do the problem is given in Chapter 4 and is simple.
The beginning Sludent need nol worry about this derivation. Another exactly solvable problem is the harmonic oscillator. Now consider a system of N such oscillators. The levels m m a magnetic are labeled by where 2s is ihe spin excess their s values. The problem of tlic binary model system is the simplest problem for which an exact solution for the multiplicity function is known.
ES This result will be needed in solving a problem in the next chapter. We begin the analysis by going back to tlie multiplicity function for a single oscillator. The oscillator multiplicity function is not the same as the spin mufti- pitcitv function fount! For the problem of JV oscillators. E4 Thus for the system of oscillators. To sojve the problem of E3 below.
The energy of the modelspin syslem in a siaie of spin excess 2s is where in is the magnetic moment of one spin and B is the magnetic field. States of a Mode! Construction of. Quantum HarmonicOscillator 52 4. Two Spin Systems in Thermal Contact 3? Integrated Deviation 54 Note on problems: Additivity of the Entropy for Two Spin Systems 53 6.
Entropy and Temperature 52 2. Paramagnetism 52 3. Entropy and Temperatui One shouldno! One may recognize that this is practically equivalent to never.
Chapter 2. On the contrary. A quantum state is accessible if its properties arc compatiblewith the physical specification of the system: We then consider systems in thermal equilibrium. The second law of thermodynamics appear will as the taw of increase of entropy. We slart this chapter with that enables us to a definition of probability define the average physical property value of a of a system.
Statesthat are not accessible are said to have zero probability. Wtlh large systems we can never know either of theseexactly. Fof example. The chapters th.
Unusual properties of a system may sometimes make it impossible for certain states to be accessible during the time the system is under observation. A closed system will have constant energy. You will recognize many exclusions of this type by commonsense. We treat all quantum states as accessible unless they are excluded by the specification of the system Figure2. Of course. This chapter is perhapsthe most abstract in the book. If we specify that ihe. IlovG vjfju We shall be concerned taier with systems that are not dosed.
For these N may systems P s wtH not be a constant as in A. Each system in the ensemble is a replica of the actual system in one of the quanium states accessible to the system. B The probabilities tead to ihe definition of the averagevalue defined by I of any physical properly. The average in D elementary exampleof is an what may be called an ensemble average.
Such a group of systems constructed alike ts catted an ensemble of syslems. Every quantum stale. HereP s] is the probability equation that the sysiem is in the state s. If there are g accessible stales. Here X might denote magnetic moment. For a dosed system. Construction of an ensemble. We conslruci in Figure 2.
Do not confuse! The energy of each in a magnetic field is -mB. Each system represents one of the muliiptes of. This is called hermnl contact Figure 2. The direction of energy flow js not simply a matter ofwhethef the energy of one system is greater than the energy of the other.! ThiS is. Tlic number ofsuch slatesis given by tlic multiplicity function Tile 10 systems shown m Figure 23 make up ttic cuwnibk.
The answerleadsto the concept of temperature. Most ProbableConfiguration Let two systems 5. The numbersof spins N u N2 maybe different. The energy of ihe combinedsystem is dirccily proportional to the total spin excess: Thespin excess of a state of ilie combinedsystem will be denoted by 2s.
We keep N. The most probabledivision of the t6tal energy is that for which the combined system has the maximum number of accessible states.
We first solve in detail the problem of thermal contact between two spin systems All spins have magnetic moment m. We shall enumerate the accessible slates of two model systems and then study what characterizes the systems when in thermal contact. A constant lotal energy can be sbared in many ways between two systems.
Tlie actual exchangeof energy might take place via some weak residual couplingbetween the spins near the interface between the two systems. N2 constant. In the sum we hold s.
F where the multiplicity functions gx. Any large physical system will have enough diverse modes of energy storage so that energy exchange with another system is always possible.
The configuration for which glg1 is a maximum is called the most probab! To see how F comesabout. Si accessible stales of ihe second system.
H2 Nj. Sl g2[Nl. The range of s. The result F is a sum of products of the form G. We sum over a!! We thus obi a in F. From the sharpness properly it follows that'fluctuations about the most probable configuration are small. Such a sharp maximum is a property of every realistic type of large system for which exact solutions are available. The most probable configuration alone will describe many of these properties.
A relatively of configurations small number will dominate the statistical properties of the combined system. Entropy am! In the example below we estimate ihe errorinvolved in such a replacement and find the error lo be negligible. Because of the sharp maximum. Such average values used in either of these two senses are called thermal equilibrium values. Ai the cxt where Nt. Most Prabahte ConfiSui Example: Tn-o sprn systems in thermal contact.
I do want to point out that.
Consider W. Recall U as a thermodynamic potential.
V for U. V for each thermodynamic state. Carnot cycle. Using energy conservation and how Q is defined. Wout net work can be done. This violates the law of increasing entropy. Carnot cycle for an ideal gas. Path Dependence of Heat and Work. So they are path-dependent. W becomes an exact 1-form. Q and W are not necessarily exact 1-forms. When liquid boils under atmospheric pressure.
Consider this change of volume: Problem 8. Heat pump. Absorption refrigerator. Recalling that there are 2 polarization states for a photon in 3-dim. Helmholtz free energy F is needed.
To get the entropy. Thermal pollution. Consider the heat engine as a Carnot cycle. Room air conditioner. Isentropic compressiong: Heat engine-refrigerator cascade. Assume refrigerator throws out QH heat into the environment. Consider a Carnot cycle. Light bulb in a refrigerator Carnot refrigerator draws W.
For any Carnot cycle. Tl lower reservoir temperature stays constant. Geothermal energy. For the refrigerator: Suppose Carnot cycle part of the refrigerator must input in heat from light bulb to cool down its inside. I is energy required in reaction to dissociate composite particle into its constituents and is taken to be positive.
Their concentrations must therefore be proportional to the probability of occurrence of these states. June 6. Heywood Tam Thermal ionization of hydrogen.
We also need to take into account the fact that the first excited electronic state of hydrogen is 4-fold degenerate i. Recall that G N. Biopolymer growth. FN is the free energy of one N mer molecule. Consider manifold M. For flat metric. Problem 1. E-mail address: Cambridge University Press.
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