What is Boltzmann: Definition and 210 Discussions

Ludwig Eduard Boltzmann (German pronunciation: [ˈluːtvɪg ˈbɔlt͡sman]; 20 February 1844 – 5 September 1906) was an Austrian physicist and philosopher. His greatest achievements were the development of statistical mechanics, and the statistical explanation of the second law of thermodynamics. In 1877 he provided the current definition of entropy,



S
=

k


B



ln
⁡
Ω



{\displaystyle S=k_{\rm {B}}\ln \Omega \!}
, interpreted as a measure of statistical disorder of a system. Max Planck named the constant kB the Boltzmann constant.Statistical mechanics is one of the pillars of modern physics. It describes how macroscopic observations (such as temperature and pressure) are related to microscopic parameters that fluctuate around an average. It connects thermodynamic quantities (such as heat capacity) to microscopic behavior, whereas, in classical thermodynamics, the only available option would be to measure and tabulate such quantities for various materials.

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  1. S

    Stefans Boltzmann Law: Find Star Luminosity

    how do i find the luminosity of a star
  2. G

    What Textbooks Cover the Boltzmann Transport Equation in Statistical Mechanics?

    Hello. Do you know any textbook about Statistical Mechanics that discusses Boltzmann Transport Equation? It is not discussed in the textbooks that I know. Thank you.
  3. C

    Boltzmann Constant in definition of entropy

    I don't remember why the Boltzmann constant is the perfect number that let's us convert the log of the multiplicity to a unit that works with other SI units. I understand that this constant was "given" units of J/K but why does it work exactly to convert a rather odd made-up number (log of the...
  4. S

    Boltzmann distribution and energy difference

    Homework Statement The first excited state of Ca is reached by absorption of 422.7-nm light. • Find the energy difference (kJ/mol) between ground and excited states. • The degeneracies are g*/g0 = 3 for Ca. Find N*/N0 at 2 500 K. • By what percentage will N*/N0 change with a 15-K rise in...
  5. S

    Boltzmann expression question

    Homework Statement Use the Boltzmann expression where v is the vibrational quantum number to complete the following table. Vibrational State Populations Molecule D2 (v=3115) F2 (v=917) I2 (v=214.5) Find Nv/No for 389 K and 1899 K Assume gv = go = 1 Homework Equations Nv/No=(gv/go)*...
  6. M

    Maxwell - Boltzmann Distribution Integral: Proving Its Normalization

    Show that the Maxwell - Boltzmann distribution integral: the integral of f(v) dv from zero to infinity is equal to one. I know what the formula is but I am unsure on how to approach this problem. Please help in any way. Thanks. Also, I know that the integral is the area under the curve of...
  7. B

    Boltzmann Distribution: Mean Energy & Mean Square Energy

    Homework Statement Compute the mean energy and mean square energy of a free particle using the Boltzmann distribution. Homework Equations The Attempt at a Solution I calculated the mean energy to be 3/2 kT by computing the mean square velocity directly from the Boltmann...
  8. S

    The boltzmann transport equation double integral

    hi, i've never posted on here before but would appreciate any help given for this question. The scattering term (4th term) in the Boltzmann transport equation contains a double integral. What are you integrating over in each case and why is this? this may be a simple question but...
  9. E

    Boltzmann distribution - error?

    I read http://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution#cite_note-0 In formula 7 we obtain proportionaly to E^1/2 and exp(-E). But I expect proportionaly to E^-1/2 and exp(-E). Where I am wrong?
  10. P

    HELP Boltzmann law in terms of classical physics?

    The Stefan-Boltzmann law is as follows: The energy radiated by a black body radiater per second per unit area is directly proportional to the fourth power of the absolute temperature. Equation: I = σT^4 Is it possible to explain this law by means of classical physics only? If so...
  11. L

    Is the Boltzmann Brain Paradox a valid explanation for our existence?

    Hi guys. I'm new here and pretty much a layman when it comes to physics and astronomy. I came across this hypothesis a few months ago, but have been looking at it the last few days. Anyway, I'm hoping you guys know about this so you can help me. Search wikipedia for it if not. I'm not...
  12. K

    When can Boltzmann distribution be used?

    What conditions are needed?
  13. Z

    Show how the Boltzmann entropy is derived from the Gibbs entropy for equilibrium

    Homework Statement Show how the Boltzmann entropy is derived from the Gibbs entropy for systems in equilibrium. Homework Equations Gibbs entropy S= - \int \rho(p,q) (ln \rho(p,q)) dpdq where \rho(p,q) is the probability distribution Boltzmann entropy S= ln\Omega where \Omega is...
  14. A

    How did Ludwig Boltzmann develop the Boltzmann distribution and define entropy?

    So this guy came up with the Boltzmann distribution and the statistical definition of entropy, where particles occupy discrete energy levels (or states) before the advent of quantum mechanics. How the hell did he do that, does anyone have any knowledge on how Boltzmann came up with the stuff he...
  15. L

    Boltzmann collision term irreversibility

    Hello, Here is the Boltzmann collision term as it is expressed on http://en.wikipedia.org/wiki/Boltzmann_equation" : Deriving the H theorem from this equation is the way to usually prove of the irreversibility of this term. Of course, this collision term should not be symmetric by...
  16. Q

    Derivation of Boltzmann Equation

    Hi: How do you derive the Boltzmann equation? Thanks.
  17. J

    Strange maxwell boltzmann statistics, what is it actually?

    Originally, it is derived from the weight of a confuguration,i.e. how electrons are distributied in different energy level:n=gexp(a+be) It gives the number of electrons in each energy level.However suddenly it can be apply to a cloud of gas?? By dividing a box of gas into different energy and...
  18. F

    Know of an open source Boltzmann solver for photon transport?

    Many groups have created Boltzmann solvers for photon/neutron transport simulations of reactors over the years - but has anyone released their code? I am specifically interested in Boltzmann solvers, not Monte Carlo based calculations. If you know of any open source projects, please let me know...
  19. W

    Boltzmann Factor/predicting energy levels

    I'd like to just preface this by saying I'm a non-science major in a science course. The professor mentioned we might need another textbook besides the ones for this particular class. Unlike all of the science/engi majors in the class, I don't have it. Homework Statement Using the...
  20. S

    Physical Chemistry- Maxwell Boltzmann Distribution

    Homework Statement Use the maxwell Boltzmann distribution to derive an expression for <v^3> Homework Equations <v>=(8RT/piM)^1/2 The Attempt at a Solution I know that you have to integrate from 0 to infinity v^3p(v)dv.. but I don't really know how to integrate this. I just need to...
  21. D

    Understanding Freeze-Out in Semiconductors at Low Temperatures

    Studying the semiconductor in equilibrium, i found a sentence which i don't understand. "At the very low temperature, freeze-out occurs; the Boltzmann approximation is no longer valid." I know that freeze-out occurs at the very low temperature, but why is it that the Boltzmann...
  22. M

    Average Energy of Boltzmann Distribution

    The question is: Write an expression for the average energy of a set of particles obeying Boltz- mann statistics and each having energy E = bz2, where b is a constant and z is a variable. Hence, show that the average energy per degree of freedom for each particle is 1 2kBT; where kB is...
  23. M

    Question about integral used in Lattice Boltzmann text

    I would have asked in math, but I was hoping the context of lattice Boltzmann may make my question clearer. Given f is the number density of particles, v velocity, and u equilibrium velocity. In a book(http://www.ndsu.edu/fileadmin/physics.ndsu.edu/Wagner/LBbook.pdf equation 3.14), he...
  24. L

    Solving Boltzmann Equation: Guidance for Partial Differentiation

    Hi I am trying to make the following equation to get Boltzmann equation which I write below. f(\mathbf{x}+\frac{\mathbf{p}}{m}dt,\mathbf{p} + \mathbf{F}dt,t+dt) \,d\mathbf{x}\,d\mathbf{p} - f(\mathbf{x},\mathbf{p},t)d\mathbf{x}\,d\mathbf{p} = \left. \frac{\partial...
  25. F

    How Did Mathematicians Finally Solve the 140-Year-Old Boltzmann Equation?

    I've never heard of this before. Maybe I should learn more physics: http://www.upenn.edu/pennnews/news/university-pennsylvania-mathematicians-solve-140-year-old-boltzmann-equation-gaseous-behaviors http://www.pnas.org/content/107/13/5744.abstract?sid=08ced618-f372-4c0d-a80c-64786d92c3ff
  26. H

    Derivation of the Boltzmann constant

    Hey so I'm just looking through a thermal physics textbook at a quick derivation of the Boltzmann distribution. It says to consider a small 2 state system with states of energies E=0 and E= \epsilon .This system is connected to a resivor of energy U_0 when the small system is in the 0 energy...
  27. G

    Need guidance for learning lattice Boltzmann

    Hello This term i must do a project for my advanced fluid mechanics course,in this project i must solve navier stokes equations in a cavity using lattice Boltzmann method,but the problem is i have no background in lattice Boltzmann,and i need some sources like some useful pdfs or textbooks...
  28. S

    Derivation of the Boltzmann Distribution

    I'm using McQuarrie's "Statistical Mechanics" for a class, and I'm not quite understanding the the derivation of the Boltzmann Distribution. I'm going to go through it, and then ask a few questions along the way. All right. You start with a canonical ensemble with N, V, and T fixed. Heat can...
  29. P

    Elementary Boltzmann Statistics

    ***SOLVED*** Homework Statement A system of particles is at equilibrium. What is the proportion of particles in the ground state? The Attempt at a Solution P(\epsilon_{s})=\frac{exp(-0/\tau)}{1+exp(\frac{-\epsilon_{s}}{\tau})+exp(\frac{-2\epsilon_{s}}{\tau})} Is that right? This is a...
  30. haushofer

    Derivation of Boltzmann distribution, heatbaths

    Hi, I have some questions about the derivation of the Boltzmann distribution, for instance as in Mandl's "statistical physics". Put a system (1) in a heatbath (2) with temperature T. In thermal equilibrium system 1 will also then have temperature T. The energy of system (1) is not fixed due to...
  31. 0

    Unraveling the Mystery of Boltzmann Brains & Landscapes

    Could someone give me a quick explanation what Boltzmann brains are? Does it have something to do with the landscape?
  32. T

    Inflaton and the boltzmann equation's density/velocity sources

    Hi, I'm looking for a resource which explains how the inflaton (and metric) perturbations are related to the CMB; in particular a lot of common sources (Dodelson in particular and some reviews I found on arxiv) simply state that the photon-baryon fluid has a 'monopole' (density perturbation)...
  33. M

    Introduction to Lattice Boltzmann for Non-Physicists: Q&A on Basics

    I want to use Lattice Boltzmann methods for a game-like simulation, and I need a good introduction. I am weak on the physics side, so any introduction that starts tossing around physics variables and equations without defining them is going to lose me. Any ideas for a good source? Some...
  34. X

    Study Kinetic Theory: Deriving Boltzmann Equation from Liouville

    I am studying kinetic theory. The Boltzmann equation can be derived from the liouville equation, I want to know how to deduce it , which books explore the question. I am reading a book( the title is kinetic theory, the author is R.L.Liboff), in this book the method proposed by Prigogine is used...
  35. P

    Derivation of the Boltzmann Distribution

    I have a question about the Lagrange Multiplier method used to derive the Boltzmann distribution. I'm following the first http://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_statistics" . I can get to this equation fine: And I understand how they get the next line...
  36. C

    Maxwell Boltzmann Distribution Question

    Hello everyone Homework Statement The equivalent of the Maxwell-Boltzman distribution for a two-dimensional gas is P(v) = Cv e^-\frac {mv^2}{kt} Determine C so that \int_0^\infty P(v)dv = NHomework Equations Not really sureThe Attempt at a Solution I wasn't really sure how to tackle this...
  37. B

    Equivalence of Boltzmann and Clausius entropy

    I can't figure out how to show that the Clausius entropy \Delta S= \int_{T_1}^{T_2} \frac{dQ}{T} is equivalent to the Boltzmann entropy S=kln \Omega at thermal equilibrium. Does anyone know how to do this?
  38. V

    Maxwell Boltzmann distribution

    Homework Statement The energy difference between the first excited state of mercury and the ground state is 4.86 eV. (a) If a sample of mercury vaporized in a flame contains 10^20 atoms in thermal equilibrium at 1600K, calculate the number of atoms in the n=1 (ground) and n=2 (first-excited)...
  39. J

    Boltzmann Probability: Calculating Probability of Bound States for Hemoglobin

    Homework Statement Simplistically, hemoglobin can exist in 5 states (0,1,2,3 or 4 bound O2). Name each state accordingly as UB (unbound) and B1, B2, B3, and B4 (for the four bound states). Using Boltzmann's Law, write down the probability that the molecule exists in a bound form...
  40. J

    Boltzmann statistics - finding the number of particles

    Boltzmann statistics -- finding the number of particles Homework Statement A column of water contains fine spherical metal particles of radius 2 x10-8m, which are in thermal equilibrium at 25C. If there are 1000 particles per unit volume at a given height, how many particles would be found...
  41. A

    Boltzmann Factor in QM Language

    Hi, I'm stuck on "the summit of statistical mechanics" (as Feynman calls it): the definition of the Boltzmann Factor. The probability of measuring the system with energy E is P(E) = 1/Z * e^-E/kT. I've taken courses in QM and can't understand why P(E) does not depend on the ket of the...
  42. M

    Boltzmann Brains: NY Times Article Explained

    Hi guys - long time lurker. I just wanted the esteemed members of this forum's thoughts on an article in the NY Times about Boltzmann Brains which I found very interesting. http://www.nytimes.com/2008/01/15/science/15brain.html" I think the general gist of it is that a Universe is so...
  43. S

    Boltzmann equation/ Statistical Mechanics

    Homework Statement If we assume entropy is a function of the multiplicity, \Omega, (S=k*f(\Omega)) show that that function f(\Omega) is ln(\Omega).Homework Equations The Attempt at a Solution \Omega can be written as N!/ni!. By using stirling's approximation, this becomes \Omega=...
  44. C

    The Boltzmann distribution of uniformly spaced energy levels

    The question states: A system has energy levels uniformly spaced at 3.2x10^-10 J apart. Thepopulations of the energy levels are given by the Boltzmann distribution. What fraction of particles is in the ground state at T=300K. I know that the Boltzmann distribution is: _{}p*j=probability...
  45. C

    Universal Acceleration and Boltzmann Brains

    Something has recently occurred to me which I think I should mention here. Boltzmann brains have a definite probability of "popping up" anywhere in the universe as fully formed, sentient beings. Although the odds against such a thing happening are astronomical, there is a probability which can...
  46. T

    Boltzmann distribution vs. Distribution of energy

    Hi folks! i'm a biologist trying to understand some basics of statistical mechanics. :wink: unfortunately, i cannot get over the following problem(s). A) in the Boltzmann distribution the fraction of particles with energy Ei is given by: \frac{Ni}{N} = \frac{exp(-\beta Ei)}{\sum...
  47. A

    Help me convert Boltzmann distribution/partition function into Geometric series

    Homework Statement 3. The following calculaltion shows how the ratio of e to kT affects the populations of different energy levels. kT is sometimes called the thermal energy; if it is small relative to e, a particle will not be able to access higher energy states. Consider a harmonic...
  48. B

    Temperature at which ground state and first excited state have equal populations

    Homework Statement Consider a pure hydrogen hydrogen gas ata tempeature of 10080 K. What is the ratio of the populations of the ground state(n=1) to the first excited state(n=2). Note that the energy difference is 1.634e-18 joules between these two states. At what temperature would both...
  49. M

    Entropy of relativistic Boltzmann gas?

    Homework Statement I'm given a relativistic Boltzmann gas and told to find the entropyHomework Equations \epsilon = pc p = 3d momentum c = speed of light The Attempt at a Solution I tried to start by finding the partition function, from which I can just take the derivative, but I don't know...
  50. U

    Thermodynamics Boltzmann Statistics

    Homework Statement Consider a classical particle moving in a one-dimensional potential well u(x). The particle is in thermal equilibrium with a reservoir at temperature T, so the probabilities of its various states are determined by Boltzmann statistics. Show that the average position of the...
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