Statistical mechanics Definition and 355 Threads

could we use three ensembles(microcanonic, canonic, grandcanonic) in cases of each problems? or can we solve any problem by using every one of these ensembles?

Statistical Mechanics -- Maximum Temperature We know that at zero degrees kelvin the only energy is zero point energy. As we heat a substance, the atoms move faster and faster. The question is, is there a maximum temperature since the fastest a atom can move is the speed of light?

why do we say that a classically behaved gas is non-degenerate and a quantum behaved gas is degenerate? I can't get why the word of "degeneracy" here can distinguish two kinds of behavior of gas.

Having learned the fundamentals of quantum mechanics from Ballentine, I am now looking around for books on quantum statistical mechanics. However, I find most of them in-complete. I don't want to fuss, but I really liked Ballentine's approach and would like to continue with something similar. Do...

Homework Statement I'm working through an example from class and the textbook, but I'm confused about how the steps progress mathematically. The example involves the Gibb's partition for a paramagnet. \sum_{s} exp(\beta \mu B \sum_{i}^{N} s) Where s = -a,-a+1...a for each spin...

1. Homework Statement Given y = xz5 and x = zg find : (∂y / ∂x)z (∂y / ∂x)g 2. Homework Equations 3. The Attempt at a Solution I understand the concept of a partial derivative, but I've never seen one such that there is a variable held fixed, or one where ∂x is not changing...

What are the classics in the area of (classical) statistical mechanics / kinetic theory? Is there anything as universally-lauded as, say, Jackson's Classical Electrodynamics or Goldstein's Classical Mechanics are in their respective fields?

Homework Statement Neutrinos are massless spin-1/2 particles (ignore their tiny finite masses). There are 6 types of neutrinos (3 flavours of neutrinos and 3 of anti-neutrinos), and each has just one possible polarization state. In the early universe neutrinos and antineutrinos were in...

I was reading the solution to a statistical mechanics problem and this showed up: http://imageshack.us/photo/my-images/196/grddar.jpg/ S2N-1 = the area of the 2N-1 dimensional unit sphere. Could anyone shed some light on how these expressions equal each other, I am quite dumbfounded :(.

Homework Statement Consider a system composed of 2 harmonic oscillators with frequencies w and 2w respectively (w = omega). The total energy of the system is U=q * h_bar * w, where q is a positive negative integer, ie. q = {1, 3, 5, ...}. Write down the number of microstates of the system...

Homework Statement Give an physical explanation to why the specific heat capacity goes to zero as temperature goes to zero. Homework Equations The Attempt at a Solution I was simply thinking that around absolute zero the average kinetic energy of the particles should be zero...

Im having a hard time visualizing the 2 level energy state that my professor is lecturing about in our discussions on the Maxwell-Boltzmann Distribution within our Thermodynamics section. He keeps saying the "molecule will jump up to the next level at a higher temperature" What exactly is he...

Homework Statement You have a latice of particles that all have spin 1, but they can change the direction of their spin so constraint \left|S_j\right|=1. There is only interaction with the closest neighbours so we have the following hamiltonian: H = -J \sum_{\left\langle ij \right\rangle}...

Homework Statement Please look at P9 in http://panda.unm.edu/pandaweb/graduate/prelims/SM_S09.pdf "Now consider a metal surface in which the M adhesion sites are comprised of equal populations of sites of two different types..." Homework Equations The entropy and the chemical potential of a...

Homework Statement Trying to solve 2(a) on this problem set...

Homework Statement A box of volume .5m^3 contains air pressure 3*10^5 n/m^2, and air composition of 80% N2 and 20% O2. There is a small hole of area 1*10^6 m^2 in one face. The exterior of the box has air of the same composition and temperature but pressure of 1*10^5. How long will it...

I just want to ask why Causal Dynamical Triangulations use a partition function for describing the dynamics of the whole theory. Does the theory have some deep relation to statistical mechanics because of this formulation of the theory? Or is the partition function also a usual terminology to...

why phase transitions and points in phase diagrams important?

Hi there PF. I just want to ask, whether Quantum Statistical Mechanics is a Quantum field theory. If not, is there anything else that describes entropy and thermodynamics in terms of a Quantum field theory?

Dear Colleagues, I would like to submit to your court the article in which we attempt a physical analysis of living matter. Biology is a very difficult field for physics as a result errors are very likely. We would appreciate guidance on possible errors. Prokhorenko DV and Matveev VV. The...

Are they different in any significant ways? Are they frequently confusing? For whatever reason, I find pchem books somewhat hard to read (for now) because something with the notation is confusing me. Statistical Mechanics books are much more readable. Okay, for some reason, I understand things...

As the title suggests, does anyone know any good books for (introductory) Statistical Mechanics and/or Nuclear Physics? Any input is greatly appreciated :-p.

One of the things I've learned about probability is that it seldom = 0. For example, the probability of a giant meteor hitting Earth is incredibly low, but it isn't zero. Thats why it happened (eventually). So let's extend this to statistical mechanics. My understanding of (say) a thermometer...

Homework Statement Suppose that by some artificial means it is possible to put more electrons in the higher energy state than in the lower energy state of a two level system. Now it is clear that this system cannot be an equilibrium situation, but, nevertheless, for the time that the system is...

Homework Statement Suppose that by some artificial means it is possible to put more electrons in the higher energy state than in the lower energy state of a two level system. Now it is clear that this system cannot be an equilibrium situation, but, nevertheless, for the time that the system...

If I have a container containing a liquid mixed with some other substance that has much a higher boiling point (i.e. water and salt). This liquid will be in equilibrium with its vapor (the salt vapor pressure is negligible). Now I quasi-statically adiabatically expand this vapor. Isentropic...

Homework Statement Please see attached Homework Equations The Attempt at a Solution Ok so I've done the first part okay and got S = 17.38 times the Boltzmann constant. Just don't see how to make a rough estimate of the temp.. what is epsillon>?

Hello. I read this assertion in a book: if we take at an initial time t_0 a constant density distribution \rho(p,q,t_0) in phase space, then this implies that \rho wil remain independent of time for all t>t_0 because by Liouville's theorem \frac{\partial\rho}{\partial...

Is there some kind of resolution to the Hydrogen atom problem in statistical physics, that is the fact that canonical partition function diverges for E_n = - E_0/n^2 with degeneracy n^2 since Z = \sum n^2 exp(-\beta E_0/n^2) > \sum n^2 exp(-\beta E_0) , which makes the H atom problem seem...

I'm kind of stuck on this problem, if someone could help me out that would be appreciated. Consider 2 blocks treated as collections of Einstein oscillators. The first block has N1 oscillators of frequency omega. The second block has N2 oscillators of frequency 2omega. Initially the first...

Statistical Mechanics preparedness...? Hello, I am a third year physics major having trouble deciding wether to take Statistical Mechanics this Spring semester. The problem is that there are 2 pre-requisites, Quantum Mechanics 1 and Thermodynamics, and I am only taking Thermodynamics this...

Hi all, It's my first time to ask a question here I am now taking a Thermodynamics course and I have the authority to choose what topics to study in this course. My intention is to be able to study statistical mechanics afterward. So I need thermodynamics that will be useful when studying...

hi everyone! I am so confused about interaction energy! as you know, in many statistical mechanics books we see there are equations which are taken in a non-interacting system. for example for a two particle system, you can see the total energy is: E = E1 +E2 +E12 while E12 is the...

Homework Statement Spectroscopic data (rotational-vibrational lines) show that the hydrogen fluoride molecule has a vibrational frequency of 7.8x10^14 rad/sec and a moment of inertia of I=1.35x10^-47 kg.m^2. Find the relevant characteristic temperatures of the HF molecule. Homework...

So I'm not asking if thermodynamics has, but specifically statistical mechanics, because it seems so unlikely that by probabilistic and mechanical reasoning, the phenomenon of self-organization would arise -- and if it has happened, I'd love to find out. I'm not looking for specific papers, as I...

Hello, so I was watching Susskind's lectures on Statistical Mechanics: He explained Liouville's Theorem qualitatively in the following two ways: No Merging: Two trajectories in phase space will never merge; this seems obvious using the time-symmetry and determinism in classical mechanics...

Hello, I've finished the topics about statistical mechanics in Feynman Lectures,and I'd like to study the topic in a deeper aspect. I've had a look at Berkeley Course vol 5(by Reif),I liked it,but I find it rather too introductory. I also had a look at Huang,but I think it is too advanced for...

A simple websearch reveals many textbooks, lecture notes and articles about Non Equilibrium Statistical Mechanics. Comments please?

I have some questions that my teacher was unable (and unwilling) to answer in class, so I thought I'd ask them here. The chemical potential \mu=\left(\frac{\partial U}{\partial N}\right)_{S,V} is given by the derivative of the energy with respect to particle number at constant volume and...

Homework Statement In a system of N weakly interacting particles each particle can be in one of M energy states: E_1 < E_2 < ... < E_M At T=300K there are 3 times as many particles in E_2 as in E_1. Calculate E_2 - E_1 Homework Equations This is not my homework, just a tutorial question, I'm...

Does anyone have any recommendations of a good book(s) for a first undergraduate-level course in Statistical Mechanics?

I took stat mech as an undergrad but the textbook we used (statistical and thermal physics by sturge) was over my head. Can someone provide a good and readable (as readable as stat mech can get) textbook for stat mech? I am switching to a different research group in grad school that deals with...

When I learned statistical mechanics, it followed the lines of the maximum entropy principle from information theory as laid out by Jaynes which can also be seen as a Bayesian statistical theory. I wonder whether there exist some orthodox frequentistic interpretation of statistical mechanics...

I was thinking of taking the statistical mechanics course for PhD candidates that's being offered next term at my school. My background is pretty typical, I've had Calc 1-3, linear algebra, differential equations, classical mechanics, e&m, thermodynamics with statistical mechanics, all at the...

Homework Statement a) Derive an asymptotic expression for the number of ways in which a given energy E can be distributed among a set of N, one-dimensional harmonic oscillators, the energy eigenvalues of the oscillators being (N+\frac{1}{2})\hbar\omega, n=0, 1, 2, .... b)Find the corresponding...

Homework Statement Consider a particle confined within a box in the shape of a cube of edges Lx=Ly=Lz. The possible energy levels of this particle are then given by the quantized energy for a particle in a 3D box. Calculate explicitly the force per unit area (or pressure) on this wall...

Homework Statement Consider a particle confined within a box in the shape of a cube of edges Lx=Ly=Lz. (a) Suppose that the partice is in a given state specified by particular values of the principal quantum numbers nx, ny, nz. By considering how the energy of this state must change when...

I am currently enrolled in PHY4523 - Thermodynamics and Statistical Mechanics where we are currently using "Fundamentals of Statistical and Thermal Physics" by F. Reif and I was wondering if there were any good recommendations as far as supplemental texts that I could use in helping me...

Homework Statement From Landau and Lifgarbagez: \langle (\Delta f)^{2} \rangle = \overline{f^{2}} - (\overline{f})^{2} This isn't derived, just stated, and I'd like to understand how it comes about. f is a generic quantity "relating to a macroscopic body or to a part of it."...

I posted this once already without seeing the rule that HW questions must go here--sorry :redface: So, the problem: I'm really lost on where to get started here. It's a two state system, one with energy 0 and the other with energy ε. I already have ensemble average, <E>, found to be: ε / (e^βε...