Statistical Definition and 582 Threads

1. A gas molecules of mass m are in thermodynamic equilibrium at a temperature T. If v_{x},v_{y},v_{z} are the components of velocity v, then the mean value of (v_{x}-{\alpha} {v_{y}}+{\beta} {v_{z}})^2 is: a.(1+\alpha^2+\beta^2)\frac{k_{b}T}{m} b.(1-\alpha^2+\beta^2)\frac{k_{b}T}{m}...

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...

This is a continuation of discussions from another thread: https://www.physicsforums.com/showthread.php?t=490677&page=2 I believe it deserves its own thread instead of hijacking the other one. "Ref 3" in what follows is this paper: L.E. Ballentine, "The Statistical Interpretation of...

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?

How can you write numbers (1,2,3,...) in statistical way?

In the book of Pathria (p.15), Cp =: T (ds/dt)N,P = (d(E+PV)/dT)N,P S=S(N,V,E) I don't know how it comes the 2nd equal sigh. Does anybody can help me? Thanks in advance!

I have a 2x2 contingency table, and I want to discover how likely it is that the two events are dependent. The top-left cell is usually in the range of 1-10. The bottom-right cell can be over 3 billion. The other two cells are in the hundreds or millions (exclusively). I have tried Pearson's...

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?

Hi, I am just wondering if anyone knows of any website that offers raw statistical data. This may be a major request but the data also has to contain dummy (indicator) variables. Thanks

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.

Homework Statement A paramagnetic crystal of N ions of spin 1/2, at constant temperature T, is subjected to a magnetic field B. Using the fact that the Helmholtz Free Energy is minimized show that the mean magnetic moment M is: \mu tanh\frac{\mu B}{kT} Homework Equations Magnetic...

i'm looking for two reports with headings approx. as below (1) world market and trends in Switch Mode Power Supplies, SMPS (2) world market and trends in ferrite cores the material should be free of cost thanks

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 A system of 10 oscillators, characterised by a \beta^ parameter of ln(3/2) is in equilibrium with a heat bath. Determine the probability that the system should possesses Q quanta.Homework Equations p(Q) proportional to e^(-Beta*Q)The Attempt at a Solution I have seen a...

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...

Suppose you build a heat engine. On one side you have a hot body, on the other side you have a cold body. Between the 2 you have the heat engine but on a parallel path you have a simple heat conductor. What will happen is that some of the heat will travel through and power the heat engine...

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>?

This thread is motivated by this thread: https://www.physicsforums.com/showthread.php?t=461228 The effect of this fraudulent study is relatively clear from a scientific perspective: it resulted in a markedly reduced vaccination rate in the UK with an accompanying substantial increase in...

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...

Homework Statement Consider a system of N particles, with two available energy states, 0 and E. What is the ratio of particles occupying the first state, n0, to particles occupying the second state n1?Homework Equations single particle partition function Z=\Sigmaexp(-ei/kt) system partition...

I am sure probably everyone has seen the news about the flocks of birds and fish that are dying off at different places in the world. The point of my question here is not to somehow explain why they died or if it's the beginning of the apocalypse. Rather I am curious about whether there is a...

My goal is to implement a web based software to provide a soccer forecast table like http://www.gymex.com/Predictions.html" as an interesting feature for visitors. I don't have any problem with coding the application but I need a set of clear instructions to start coding. I read an article by...

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...

Suppose I have N ideal particles in an enclosure, be it a ball or a cube or some other form. The particles shall bounce off the walls of the enclosure and against each other without losing speed. The velocity of each particle i shall be such that it fullfills |v_i|=\rho, where \rho is constant...

Statistical "Error" of Centroid of Gaussian Distribution If I have L data samples, distributed randomly (3D real Gaussian distibution, unity variance) about the origin in 3D real space, how can I derive an expression for the "origin estimation error" (i.e. the distance between the true origin...

Hello, I'm (only) receiving an introduction to Quantum Physics atm, and today our professor argued that the uncertainty principle doesn't have a definite form: the right hand side of the inequality is dependent on the confidence measure/certainty you choose, in other words 95%, 99% certainty...

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...

A roadway construction process uses a machine that pours concrete onto the roadway and measures the thinckness of the concrete so the roadway will measure up to the required depth in inches. The concrete thickness needs to be consistent across the road, but the machine isn't perfect and it is...

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...

Hi! I am for the moment reading a course in statistical physics where the author has definied not less then three diffrent partitionfunctions. W, Z an Z which are called the microcanonical partitionfunction, canonical partitionfunction (?) and the grand canonical partitionfunction. I...

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...

Hi all. I was perusing the grad course options for mechanical engineering at a local school when I noticed a course in statistical thermodynamics. I know the difference btw classical, chemical, and statistical thermodynamics, and that MEs generally learn classical. What are the ME...

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...

Homework Statement A square well of length L= 0.6 mm is to be used as a trap for He atoms at 20 K. Consider the values of some of the lowest energy levels of He atoms in a 1-D square well. Explain if it is valid to use the Boltzmann distribution in this situation Homework Equations...

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...

Can anyone give me some intuitive arguments about why all the accessible microstates of the system are equally likely in equillibrium state.

Can anyone advise me about Greiner's Thermodynamics and Statistical Mecahnics ? I want to master that subject and want a book that I can work through from cover to cover in detail. I can say that my command of maths, quantum mechanics and classical mechanics is at the level of Kreyszing and...

Hi There, My maths used to be a lot better than it is these days, i gave up being a computer geek to set up my own business about 7 years ago and i can't work out the following as probability due to this and I'm rather stressed/angry, my attempts with excel are getting me nowhere tonight...

Homework Statement I will present a vary simplified version of the problem I am trying to model. Essentially I took 100 people and split them into 10 groups. To each group I tried to sell them a product. To the first group I priced the product at $5, to the second I priced it at $15, to the...

More on http://www.rand.org/news/press/2008/07/29/ Free e-document: http://www.rand.org/pubs/monographs/MG741-1/ (at the bottom of the page). "RAND makes an electronic version of this document available for free as a public service. If you find this information valuable, please consider...

Please help me solve this problem: Homework Statement http://img688.imageshack.us/img688/8140/86617607.jpg The attempt at a solution http://img63.imageshack.us/img63/9531/79093945.jpg This is my whole procedure...

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...

Hello All, I am stuck on this statistical Analysis. I am wondering which statistical method to use, any suggestions and why? The scenario is as follows Since the 1960s there has been an ongoing campaign among Quebecois to separate from Canada and form an independent nation. Should...

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