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. WannabeNewton

    Boltzmann equation for photons

    Hi there. I have a couple of questions regarding the derivation of the Boltzmann equation in Dodelson for photons when given scalar overdensity perturbations to the FRW metric. To start with, let ##\Theta(\vec{x})## denote the temperature perturbations to the Bose-Einstein distribution of the...
  2. T

    Bibliography to understand Fermi, Bose and Boltzmann statistics?

    I'm studying by Statistical Mechanics (Huang, page 180) but can't understand many things there, can anyone provide a good bibliography to study this? I don't understand what's an occupation number of a given momentum: if it's the number of particles with that given momentum, why can it only be 0...
  3. vead

    Boltzmann equation for carrier transport

    I am little bit confused about derivation for Boltzmann equation for electron look at this link http://relativity.livingreviews.org/Articles/lrr-2008-10/articlesu25.html which is final boltazmann equation ?
  4. T

    Boltzmann Distribution: Solving 1D Ideal Gas Homework

    Homework Statement I have to find the Boltzmann ditribution of a 1 dimensional ideal gas. The answer is given as: \frac{dn}{n}=\sqrt{\frac{m}{2piKT}}e^{(\frac{-mc^2}{2KT})} For the second part I have to find the mean kinetic energy. 2. Homework Equations / Attempt For part 1...
  5. T

    Maxwell Boltzmann Distribution

    I don't know how to integrate the Maxwell-Boltzmann distribution without approximation or help from Maple. Given the Maxwell-Boltzmann distribution: f(v) = 4\pi\left[\frac{m}{2\pi kT}\right]^{3/2}v^2\textrm{exp}\left[\frac{-mv^2}{2kT}\right] Observe the appearance of the Boltzmann factor...
  6. T

    Maxwell Boltzmann Distribution

    I don't know how to integrate the Maxwell-Boltzmann distribution without approximation or help from Maple. Given the Maxwell-Boltzmann distribution: f(v) = 4*pi*[m/(2*pi*k*T)]^(3/2)*v^2*exp[(-m*v^2)/(2*k*T)] Observe the appearance of the Boltzmann factor exp[(-m*v^2)/(2*k*T)] with E =...
  7. A

    Understanding the Boltzmann Equation Derivation in Electric and Magnetic Fields

    Below is part of derivation of the Boltzmann equation in an electric and magnetic field. I don't understand how to arrive at the bottom equation though. It is known that the dependence of the original distribution function is the given. My idea is to use chain rule but I don't see how to get a...
  8. S

    Boltzmann distribution problem

    A system has two non-degenerate energy levels E1 and E2, where E2>E1>0. The system is at tempreture T. The Average energy of the system is = E1+E2e^(-B*deltaE) / 1+e^(-B*deltaE) where deltaE= E2 -E1 and B=1/kT (k=Boltzmann constant). show that for very low temperatures kT<<deltaE, average...
  9. S

    Boltzmann Distribution: Calculate Probability of Particle in 4 States

    A certain particle is interacting with a reservoir at 500 k and can be in any four possible states. The ground state has energy 3.1 eV and three excited states all have the same energy. what is the probability that the particle is in ground state? what is the probability that the particle is in...
  10. tom.stoer

    Boltzmann vs. Gibbs entropy, negative energy

    This article insinuates that the physics community had forgotten Gibbs entropy long ago and has used Boltzmann entropy since. Isn't this nonsense? For me it was always clear that Boltzmann entropy is problematic...
  11. M

    Maxwell boltzmann distribution

    The question is in the image file. I am stuck, I don't know how to start. Can someone guide me please?
  12. lonewolf219

    Planck and Boltzmann Distribution

    Does anyone know if Max Planck knew about the Boltzmann distribution before he published his results in 1900? Also, when Planck introduced h, did he also give the value?
  13. J

    The background measure in Boltzmann measure

    Suppose a set X describes the possible states of some system, and suppose a function x\mapsto E(x) tells the energy level of each state. At temperature T the Boltzmann-measure, which will be the probability measure describing the state of the system, is obtained by formula dp(x) =...
  14. L

    Calculating the probability of a Boltzmann Brain

    Can anybody point me to a rough calculation of the probability of a disembodied brain appearing from a random fluctuation vs the probability of a brain evolving in a vary large random fluctuation? I'm an eternalist. I find it easier to accept the ridiculous idea that the universe was always...
  15. D

    Using Maxwell Boltzmann distribution to find number of atoms

    Homework Statement You will recall from our discussion of the Franck-Hertz experiment that the energy difference between the first excited state of mercury and the ground state is 4.86 eV. If a sample of mercury vaporized in a flame contains 1.06×1020 atoms in thermal equilibrium at 1563 K...
  16. A

    Boltzmann distribution for particle energy

    I'm puzzled by the appearance in the literature of 2 conflicting forms: P(E)=√(E)*exp(-E), which I understand as derived from the Maxwell distribution for speed. It is a chi -square distribution with 3 degrees of freedom. P(E)=exp(-E), which seems wrong to me. But it is not simply a...
  17. F

    Boltzmann Factor Type Question

    Homework Statement A system in thermal equilibrium at temperature T consists of N particles that have two energy states separated by an energy Δε. If the number of particles in the two states is N1 and N2, show that: N{1} = N(\frac{1}{1+exp(-Δε/k{B}T})) and N{2} =...
  18. U

    Boltzmann equation with collision term

    Homework Statement Solve the Boltzmann equation for a homogeneous plasma with not external forces present when the collision term is \frac{\partial f(v,t)}{\partial t} = -\nu (f(v,t) - f_0(v)), where \nu and f_0 are constants. Homework Equations Boltzmann equation \frac{\partial...
  19. S

    Probability distribution using the Maxwell Boltzmann formula

    According the the kinetic theory of gases, molecules moving along the x direction are given by Σx= (1/2) mv^2, where m = mass and vx is the velocity in the x direction The distribution of particles over velocities is given by the Boltzmann law p(x)=e^[(-mv^2)/ekT] where velocities range from...
  20. D

    Getting to the Boltzmann Equation from a Nonequilibrium Distribution Function

    Homework Statement Hi. I have a course where I am supposed to show how to get to the Boltzmann equation from a nonequilibrium distrubution function. At the moment I'm kinda lost to how this is done, so hopefully a hint or two would be of some help :)Homework Equations The nonequilibrium...
  21. B

    Thermodynamics involving escape velocity and Boltzmann factor

    At 293K, helium atoms have a root mean square speed of about 1.35 km/s, whereas escape velocity at the Earth's surface is about 11km/s. Explain why is it nevertheless possible for helium atoms to escape from the Earth into space. Is it because near the top of the atmosphere the temperature...
  22. K

    Boltzmann Distribution (Chemistry/ Physics)

    Homework Statement Okay i want to ask 2 questions. Question 1 Hyperstoichiometric compound Al3O has a vibrational energy spacing of 3.08x 10^-21J how many molecules are present in the ground state at 300k and 3000K Question 2 Calirimetric data for protein unfolding yielded following...
  23. T

    How to derivate Maxwell Boltzmann Distribution

    Hi PFers. I am interested in Maxwell Boltzmann Distribution. I have searched in Internet for the derivation but I am not satified with them. Can somebody show me the way to derivate it? Thanks. ψ(v)=(m/2*pi*kT)^(3/2) e^(-mv^2/2kT)
  24. B

    Boltzmann Entropy for micro state or macro state?

    From theory, we know that Boltzmann entropy for a given distribution, defined through a set of occupancy numbers {ni}, of the macrostate M, is given by: S=k log(Ω{ni}) where omega is the number of microstates for the previously given set of occupancy number, {ni} . Assuming that the system...
  25. S

    Generalized Boltzmann dist. (insights to share)

    I was reading about the thermodynamics of the free-electron gas last night, and my mind veered to fundamental concepts of statistical mechanics. I was able to reorganize my knowledge in a way that made everything clearer. In it, energy does not play a role more privileged than any other...
  26. S

    Free electron Theory and Boltzmann Transport equation

    Hello! I have two questions for knowledge. Q) Explain under what conditions Maxwell Boltzmann and Fermi Dirac statistics are applied on free electrons. Q) Explain each parameter of Boltzmann Transport's equation. Thank you in advance. :-)
  27. R

    Maxwell Boltzmann Speed Distribution

    Homework Statement The three quantities Vmost probable, Vaverage, and Vrms, are not the same for the Maxwell speed distribution in 3D. If you restrict the gas to only be one dimensional, are these three quantities equal to each other? Justify your answer with a short explanation. Homework...
  28. N

    Boltzmann and Fourier for biologist

    Hello, Please could someone explain to me about Boltzmann distribution and Fourier transformation? or point me in the direction of some really really easy-to-understand guide? I need to understand it for biology - to understand NMR and mass spectrometry. Thanks.
  29. L

    Units of Volume in Deriving Boltzmann Constant

    Im recently studying Boltzmann Constant for Landauer's principle. I wondered is there a volume for that? What's the units they use(cm or m) when we derive the Boltzmann constant? I've been looking through the internet but I found nothing. Any Help? Thanks
  30. K

    Thermal equilibrium through radiation and Stefan Boltzmann

    Hey Guys, so I had a longish discussion with colleagues and on reddit about thermal equilibrium and the sun and how you cannot heat up anything above the surface temperature of the sun using clever mirrors and stuff. However, somebody came up with Napkin calculations of the Stefan Boltzmann...
  31. J

    Application of Maxwell Boltzmann velocity distribution to nanoscale systems

    Dear All I have a question about the validity of Maxwell Boltzmann velocity distribution in the case of nanoscale systems. When you consider a nanoscale system such as flow of water molecules (less than 100 molecules) through a carbon nanotube or graphene sheet, is it possible to expect a...
  32. P

    Why are there two Stefan Boltzmann Laws in Reif's book?

    In Reif's book Fundamentals of Statistical and Thermal Physics, he labels two formulas as the Stefan-Boltzmann Law. They are both involve T^4 but the constant is different. In one, on page 376, the law is given as (pi2/15)*(kT)4/(c*hbar)3. The other, on page 388, is...
  33. A

    Boltzmann constant in formulas

    Hi, I see that Boltzmann constant comes in different forms like: k=8.62*10-5 eV/K and also k=1.38*10-23J/K. Which one should I use in , say formula for intrinsic carrier concentration ni = sqrt(Nc*Nv)*e-Eg(T)/2kT ?
  34. A

    I remember I read somewhere about the boltzmann distribution that it

    I remember I read somewhere about the Boltzmann distribution that it is only valid for high temperatures. Why is that?
  35. A

    Boltzmann Distribution: Exploring Energy in High Density Reservoirs

    Consider a resevoir of N atoms in contact with a single atom. Obviously, if the atom is in a high energy state then the multiplicity left for the resevoir is significantly lower. So this is in agreement with the fact that looking at the single atom, the probability for the ground state is very...
  36. A

    Why Does Boltzmann Distribution Depend Only on Temperature?

    Why is the Boltzmann distribution for a collection of atoms independent of their total energy? (it only depends on their temperature) One would assume that if the energy is high there'd be a greater tendency to be in excited states or am I wrong?
  37. A

    Deriving the boltzmann factors

    My classmate has already asked about this I think, but since I can't find the post I'll ask again.. Take a single atom with degenerate energy levels E1, E2 etc. We place the atom in a resevoir and want to find the probability of probability for finding the atom in the different energy states...
  38. I

    Boltzmann constant- temp, pressure

    Homework Statement A sealed container of volume 0.15 m^3 holds a sample of 5 × 10^1000 atoms of neon gas in equilibrium. The distribution of speeds of the neon atoms shows a peak at 2000 m s^−1. (i) Calculate the temperature and pressure of the neon gas. (6 marks) (ii) What is the...
  39. P

    Using Boltzmann distribution law to find Temperature (1% of photons> 1eV)

    Homework Statement Use the Boltzmann distribution function to calculate the temperature at which 1.00% of a population of photons will have energy greater than 1.00 eV. The energy required to excite an atom is on the order of 1 eV. The Attempt at a Solution I attached my attempt but...
  40. edpell

    Boltzmann Distribution with two gasses

    What is the Boltzmann distribution look like if we have a mix of two gasses with very different molecular weights? Say hydrogen at 2 amu and xenon at 132 amu. Do they have equal average momentum and hence the hydrogen has an average velocity 66 times the velocity of the xenon and an energy...
  41. G

    Boltzmann Transport Equation : Hall Effect in the Relaxation Time Approximation

    Hello everyone! I have been on this website for quite a while, and found some interesting answers to many questions, and I decided to create an account to seek you help with a particular issue I encountered in my assignment. Please have a read, and thank you for any input! Homework...
  42. T

    Struggling with the Boltzmann Collision Term?

    Hello, I'm working of the Boltzmann equation to simulate a partially ionized plasma, but I'm having troubles to solve the collision term. I'm using a splitting technique for the advection in the phase-space, but I'm quite stuck in the collision term. Any recommendations?
  43. O

    Boltzmann distribution of two different gases

    hi everyone, consider two different masses of ideal gases with different molar masses, we're putting them in a uniform gravitational field and wait until they come to their equilibrium states. how would the density distribution change with height in this case? ( i came out with this question...
  44. A

    Why Can't I Get the Same Answer for the Boltzmann Equation Problem?

    Why I can't calculate the same answer as the solution below? I use the value as what the below solution showed. Q: Where Nj is the number of atoms in excited state, No is the number of atoms in the ground state, Pj and Po are constants determined by the number of states having equal energy...
  45. D

    Boltzmann Distribution Relative Population of 2 atomic states

    Homework Statement The relative population of two atomic population states in equilibrium is given by Boltzmann Distribution: n1/n0 (proportional to) e^(-ε/(κT)) , where ε is the energy difference between the two states, T is the temperature and κ is the Boltzmann constant = (1.38 x...
  46. N

    Boltzmann factor (canonical) only for extensive systems?

    With an extensive system, I mean a system where energy is an extensive variable. But no need to state it so generally, since I have a specific system in mind which will make sure we don't get into a battle of semantics: if you double the size of a gravitational system, the energy is not...
  47. P

    KT where k is Boltzmann constant times the absolute temperature.what

    kT where k is Boltzmann constant times the absolute temperature. what happen if the temperature is a variable?
  48. N

    How does the coefficient in the Boltzmann equation comes from

    In the Boltzmann equation, {\bf{L}}\left[ f \right] = {\bf{C}}\left[ f \right], the right which is the collision term and in general it is{\bf{C}}[f]=\sum\limits_{p,p_1} {|Amplitiude|^2}{f(p)}. and explicitly, the collision term for decaying process is \begin{eqnarray} {\bf{C}}\left[ f...
  49. S

    Understanding the Boltzmann Distribution - Integrating N(E) from 0 to Infinity

    For N(E)=Aexp(-E/kT), I know that N(E) is the no. of particles with a certain energy E, but why does integrating N(E) from 0 to infinity equal to 1? Although I realize that it means that there is 100% probability to find a particle in this range, I want to know why summing up all no. of...
  50. M

    Boltzmann transport equation & drift-diffusion equation ~ Please help me

    Boltzmann transport equation & drift-diffusion equation ~ Plz help me! 1. From the Boltzmann transport equation, derive the energy conservation equation for mass conserving particles. Use the momentum equation to subtract the mechanical energy component, and then derive the equation for...
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