Boltzmann Definition and 192 Threads

What conditions are needed?

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...

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...

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...

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

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...

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...

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...

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 "At the very low temperature, freeze-out occurs; the Boltzmann approximation is no longer valid."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...

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...

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...

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

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...

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...

***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...

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...

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

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...

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...

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...

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?

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)...

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...

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...

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...

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...

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=...

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...

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...

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...

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...

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...

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...

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...

Hi I'm new here with new problem. I have to show how can the Planck average energy reduce to Boltzmann energy in the limit of no quantization, but I have some problems to understand how should I solve this. If you have any ideas or answers or maybe some materials please send me a MAIL or...

We know the Maxwell-Boltzmann distribution for the energy and the speed of a molecule of an ideal gas. Using derivatives it is easy to see that the most probable speed for a gas molecule is given by sqrt(2kT/m), which corresponds to kinetic energy kT. Calculating the most probable energy, we get...

I need to answer the following question: A simple energy level system has two energy levels. These are the energy levels matching the spin of a proton in a magnetic field. This is important for NMR. In that case the energy difference depends on the used magnetic field, but for a typical NMR...

I have a homework problem that asks me to interpret the two curves for when the Fermi level (Ef) is 0.25 eV. I ploted the two graphs and both of them look nothing alike when E < Ef. But both plots predict a probability of essentially zero when E > Ef. I was wondering why is there such a large...

I got a problem by finding an proper explanation. The Boltzmann factor is defined as P_j=\frac{1}{Z}e^{-\beta E_j} I know, this is a probability distribution. but what exactly does it mean? Wikipedia says: "The probability Pj that the system occupies microstate j" (link) But that doesen...

Boltzmann Equation--where'd the 3 come from? Greetings, I'm a little bit confused about the derivation for the Boltzmann equation for a particle in thermal equilibrium in the Friedman-Robertson-Walker metric. I've been following the exposition in Kolb and Turner, The Early Universe p. 116. I...

According to Max Planck : Planck's seven (7) primary universal base unit values 1) Planck intensity : (bar-hG/c^5)^1/2/sr = 7.8672231(80) x 10^-46 cd 2) Planck time : (bar-hG/c^5)^1/2 = 5.3904639(43) x 10^-44 s 3) Planck length : (bar-hG/c^3)^1/2 = 1.6160204(35) x 10^-35 m 4) Planck...

from callen, equation 16.10 reads Z = sum(e^-BE) the text later says that F = -kT ln Z, and states that it gives the helmholtz potential as a function of B, V, N where B = 1/kT my question is, what part of this relationship characterizes the volume?