Boltzmann Definition and 192 Threads

  1. 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...
  2. 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 =...
  3. 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...
  4. S

    How to Show Average Energy at Low Temperatures?

    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...
  5. 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...
  6. 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...
  7. 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?
  8. 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?
  9. 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) =...
  10. 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...
  11. 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...
  12. 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...
  13. F

    How Do You Derive Particle Distributions Using the Boltzmann Factor?

    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} =...
  14. 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...
  15. 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...
  16. 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...
  17. 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...
  18. 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)
  19. 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...
  20. 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. :-)
  21. 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...
  22. 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.
  23. 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
  24. 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...
  25. 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...
  26. 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...
  27. 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 ?
  28. 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?
  29. 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...
  30. 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?
  31. 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...
  32. 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...
  33. 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...
  34. 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?
  35. 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...
  36. 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...
  37. 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...
  38. 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?
  39. 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...
  40. 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...
  41. S

    Stefans Boltzmann Law: Find Star Luminosity

    how do i find the luminosity of a star
  42. 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.
  43. 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...
  44. 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...
  45. 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...
  46. 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...
  47. 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...
  48. E

    Where Is the Error in My Understanding of the Boltzmann Distribution?

    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?
  49. 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...
  50. 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...
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