Statistical mechanics Definition and 398 Threads

In my notes, http://www.ph.ed.ac.uk/~pmonthou/Statistical-Mechanics/documents/SM3.pdf on page 1 we are told we're dealing with systems of fixed total E but in the expilicit example on page 3, do we not find 4 different values for the total energy. how is this possible?

I have to take that next year and am nervous about it. I took it as an undergraduate, but most of it went right over my head. Now I have to take the graduate-level course. Can anyone recommend a good book for me to read in preparation for that class?

In adjacent containers of volume V1 and V2, there contains a gas of N molecules. The gas is free to move between the containers through a small hole in their common wall. What is the probability to find k molecules in the V1? Probability of one molecule to be in V1 is given by...

I am trying to show that the change in number of accessible microstates, and therefore the change in the multiplicity function g of a simple system is g=\left( \frac{\tau_F^2}{\tau_1\tau_2}\right)^{\frac{mC_V}{k_B}} where the system is two identical copper blocks at fundamental...

Imagine a jet of fluid (perhaps air) impinging on a flat plate. It could be said that the jet has a slightly higher mean velocity in the direction normal to the flat surface (we'll arbitrarily call this X). From a classical thermodynamic point of view it could be said that the gas has a higher...

Homework Statement Hi all. I've read some about the MaxEnt method (maximum entropy), and one question of mine is still unanswered: Why is it that we wish to maximize the entropy? When looking at a gas with average energy U, the higher the entropy, the "less" we know about the gas because...

Hi, This question is probably a dumb one but I admit that I am quite perturbed with this issue. Indeed, I don't understand why canonical ensembles like the microcanonical ensemble or the canonical one are called "equilibrium ensemble". I do agree that they correspond to steady measures of...

Dear all, I'm reading "Equilibrium Statistical Mechanics" by Atlee Jackson (Dover) which is very good. What could be a next step? In the web everybody speaks highly of "Introcution to modern statistical physics" by Chandler. What about the books by Hill (Dover) or Principles of Statistical...

Please help: Homework Statement A simple model of a Geyser is an underground huge lake connected to the surface by a small tube. let the depth (and the tube length) be 90m. proove that the ratio between the mass of the water in the lake and the gas which sparks from the geyser is...

statistical mechanics -- why is temperature not a mechanical variable Hi, I have heard that temperature is not a mechanical variable. That is, that even if you knew the positions and momenta of all the particles in some system, you still couldn't calculate the temperature, because temperature...

hello, I'm trying to learn statistical mechanics with feynman's book he seems to have a lot of times where he thinks something is very clear and then it will take me a few pages of working things out to get what he has jumped to. i'm having one of those moments on page 15. i was wondering if...

Homework Statement Given the width of an energy band of electrons is typically ~10eV, calculate the number of states per unit volume within a small energy range KT about the centre of the band at room temperature. K is boltzmanss constant = 8.617*10^-5 eV/K Homework Equations volume...

Homework Statement The neutnral carbon atom has a 9-fold degeerate ground level and a 5-fold degenerate excited level at an energy 0.82 eV above the ground level. Spectroscopic measurements of a certain star show that 10% of the neutral carbon atoms are in the excited level, and that the...

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=...

Homework Statement average energy per particle u = (Eo + E1 e^(-B deltaE)) / (1 + e^(-B deltaE)) B = 1/T Homework Equations Possibly relevant: e^x = 1 + x^2 / 2! + x^3 / 3! ... The Attempt at a Solution It tells me the average energy is about u = Eo + (deltaE)e^(-B delatE) as...

Homework Statement Find Condensation Temperature of ideal Bose gas with internal degrees of freedom. Assume only ground and first excited state of internal spectrum need to be taken into account. Homework Equations The Attempt at a Solution I know j(T) for internal degrees of...

[SOLVED] statistical mechanics 6.1 Homework Statement http://ocw.mit.edu/NR/rdonlyres/Physics/8-044Spring-2004/00E63135-AD4E-4F76-9917-349D5439ABF4/0/ps6.pdf The answer to Problem 1 part c is 2N. I disagree. I think it should be N because if you specify the z component of the system then you...

A complete set of lecture notes for an upper-division thermodynamics and statistical mechanics course. Topics covered include elementary probability theory, classical thermodynamics, the thermodynamics of the atmosphere, heat engines, specific heat capacities of gases and solids, the Maxwell...

I am looking for educational derivation( or any available and detailed) of the key principle of statistical mechanics: If a system in equilibrium can be in one of N states, then the probability of the system having an energy En is (1/Q) e-En/κT Q is the partition function. I have looked it...

Hey everyone, I'm about to take a senior-level undergraduate course in statistical mechanics What preparation in terms of mathematics and statistics knowledge do you think I'll need? Is there any material in math/stats you would recommend for reading before the course starts? Thanks...

Hi everyone, I'm finishing up my undergrad with a double major in chemistry and physics. My interests are right at the cusp of the two, in chemical/statistical physics. I've been doing research for over a year in molecular dynamics with a well-known prof in the chemistry department...

The partition function in the classical theory is an integral over phase space. Thus, the partition function is often not dimensionless. Then the formula F = -T \log Z can no longer be valid, as you can only take the logarithm of a dimensionless number. In the quantum theory, this...

Does anyone understand thermodynamics? There are so many terms that I feel that I am doing the maths but not really understanding the physics. Is it better to do stuff from a stat physics way (which makes more sense) and derive the thermodynamic relations from there?

Homework Statement describe one significant success and one troublesome failure encountered when classical statistical mechanics is used to explain the properties of gases. (7 marks) Homework Equations The Attempt at a Solution success- it is simple to and it would fit the...

Can anybody tell if i can get solutions to the end of the chapter problems in "Statistical Mechanics" by R k Pathria?

1.Homework Statement A lattice in one dimension has N sites and is at temperature T. At each site there is an atom which can be in either of two energy states Ei = +/- E. When L consecutive atoms are in the +E state, we say they form a cluster of length L (provided that the atoms adjacent to...

is anyone of you learning Statistical Mechanics ? come and let's learn together! :biggrin: haha, I am currently taking statistical mechanics in my undergraduate 2nd year. This subject is so interesting! I would like to invite you all to discuss and debate about the our understanding of...

Just a quick ponderance on a statistical mechanics problem. "How many distinct spin quantum states has the orthohydrogen molecule?" Does one include the electron spin states in the calculation? I'm inclined to say yes, as they most definitely have spin and most definitely are a different...

Hi, 1- In the introduction of the concepts of partition function and canonical ensemble, a system is assumed to be in direct contact with a heat bath (a thermal reservoir) where energy can be transferred between them. All thermodynamical properties of the system can be deduced from the...

(I didn't know where to put this one, so somebody will eventually move it, I predict...) This is a absolute newbie-question, so don't be evil! Why does statistical mechanics deal with probabilities? ASAIK, statistical mechanics is built on classical mechanics, where it is possible to predict...

1. The problem Statement A cubic box of volume V=L^3 contains energy in the form of photons in equilibrium with the walls at temperature T. The allowed photons energies are determined by the standing waves formed by the electromagnetic field in the box. The photon energies are (h/2pi)Wi =...

I have a homework problem that is kinda driving me nuts... Consider the case of an anharmonic oscillator with microsystem quantum states given by Ej = jhf - (lambda)(jhf)^2. Using the known harmonic expressions as a starting point, determine the corresponding expression for F1 and for F...

Below 0.6K the heat capacity of liquid He is well represented by the equation Cv=(9.819 x 10^-3 K^-3)NkT^3 Given that transverse shear waves cannot propagate in a liquid, predict the phonon contribution to the heat capacity of He from the data c=238 m/s (speed of sound in liquid He) p=0.145...

Hi all, I have this problem which I don't even know how to start it! Any hint will be appreciated. "A set of telephone lines is to be installed so as to connect between town A and town B. The town A has 2000 telephones. If each of the telephone users of A were to be guaranteed instant access...

This shouldn't be too hard but I'm struggling. Consider N identical particles in a box of volume V. The relation between their linear momentum and kinetic energy is given by E = c\left|\overrightarrow{p}\right|, where c is the speed of light. So, the Hamiltonian of the system is...

I've seen an approximation in a statistical mechanics book, given without any proof: \frac{<N!>}{<(N-n)!>} = <N^n> (1 + \mathcal{O}( \frac{1}{<N!>} )) I've been trying to work out a proof, but I'm simply stuck any ideas how it can be proved?

I am trying to make the connection from statistical mechanics to thermodynamics for the isothermal isobaric ensemble. Partition function = (sum of)exp(-BEj-gamma*Vj). I have followed T.L. Hill [Statistical Mechanics, p. 67] but can not understand how he justifies dE=(sum of)EdP, rather than...

I understand that a microstate is one possible distribution of energies that make up the system's total energy. But I can't understand why, in a monatomic gas for example (where there is only translational kinetic energy of atoms), there is a finite number of states. Surely that would mean that...

it's just not sinking in.. i know a cell in phase space has 6 dimensions, 3 for momentum and the other 3 for position. but i'd like to understand it(phase space). can someone give me an example maybe or tell me why this constuct is needed?? or a link to a very good description?

Can anybody in the forum direct me as to where I can get the solution manual for "Statistical Mechanics" - by Pathria. Thanking you in advance.

Hi, I am just starting a 3rd year course in Statistical Mechanics, and am a bit confused about the operator trace, Tr. I know there is a trace for quantum operators, as well as one in classical physics, but i am not sure how to calculate either, or their physical meaning. Any help would be...

I'm searching for a statistical mechanics textbook. It should be roughly at or above the advanced undergraduate level, have a decent set of problems, be reasonably thorough, and be ideal for self-study. I would be grateful for any recommendations.

I wish to know about web sites or other resourses from where i can get solutions for all the end of the chapter problems for the book on statistical Mechanics by R K Pathria

Does "equilibrium" imply max. entropy in statistical mechanics? I've gotten myself confused thinking about the meaning of "equilibrium" in statistical mechanics. I thought I remembered that an isolated system at equilibrium is equally likely to be in any possible microstate, which means there...

In my Statistical Physics and Entropy module, we did something about atoms in a box with an imaginary partition down the middle, so atoms could either be on the left or the right. If there were 4 atoms in the box, the system would have 5 macrostates. If there were 8, there would be 9. Is is...

Please Help- A problem in statistical mechanics In a gas at STP, let p(r)dr be the probability that an atom has a nearest neighbor between distances r and r+dr. Find p(r). I am struggling with this question. For STP I can find the particle density. But where do I go from there? Do I need...

I got into a discussion about the "arrow of time" recently, and one point I brought up is that for a system governed by time-symmetric laws, if you place no special restrictions on the initial conditions but instead pick an initial state randomly from the system's entire phase space, you will be...

I'm planing on learning Statistical Mechanics by myself. I would like to hear recomendations on what you think are the best Statistical Mechanics books. My interest right now would be books that are on a undergraduate level, with detailed explanation, examples and problems, but you could also...