Statistical mechanics Definition and 356 Threads

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...

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 + 1) , where β is thermodynamic beta, 1/KbT. How do I convert this to an expression for the variance of the...

So I didn't start my physics major until my sophomore year which means I'm a year behind. Because of this I won't be able to take quantum mechanics until the first semester of my senior year which is also when statistical mechanics is offered. I'd really like to take statistical mechanics but...

Consider an ideal gas of oxygen atoms in equilibrium with oxygen atoms absorbed on a planar surface. here are N_s sites per unit surface area at which the atoms can be absorbed, and the energy of an absorbed atom is -e compared to one in the free state. The system is under 1 atm and at 300K...

I am quite well versed with the random walk problem and am interested in finding out more about Brownian motion. Does anyone have any suggestions for books that explain Brownian motion in detail? I suspect these will be books on statistical mechanics.

Hi! I'm a graduate student in solid state physics and I have to follow a graduate course on equilibrium statistical physics, and we're using Plischke and Bergersen's book on "Equilibirum Statistical Physics". Presently, we're seeing Mean Field Theories and Ising model, but somehow, I'm not...

Given a macro-state M of a system, let S denote the potion of the phase space that has the macro-state M. A micro-canonical ensemble is one in which the probability of finding the micro-state in any part of S is equally likely (the density function is constant over S). In Pathria's...

I'm not sure if this is the proper location for this thread, but its for a math course and I think my issues concern the math portion of the problems. If it should be moved please do so. Note: I know the post is quite long, so I'll just pull out my few main issues from all the junk. 1)...

I've been refreshing myself on some of the statistical mechanics I learned a couple years ago, using Kittel and Kroemer as a guide. However, I've come across a couple things that bother me: 1. When the Boltzmann distribution is derived, no real physics enters the picture. Essentially, the...

Hi guys, I am reading Reif's book on statistical mechanics and have a question on the H theorem. In section 2.3, Reif gives (on page 54) both the definition of equilibrium as well as a fundamental postulate. Definition: "An equilibrium situation is characterized by the fact that the...

I have of late been reflecting on something. Generally as a rough approximation we may divide physics into classical mechanics, quantum mechanics, classical field theory (like E/M, fluid mechanics...), quantum field theory, and then statistical mechanics. All the classical and quantum...

I am currently trying to get my head round RG in the context of statistical mechanics and am not succeeding! I would be grateful for any help. I have a specific question, but any clarification of RG in general would be useful. Here is my understanding of the main ideas: 1. Define...

I have my main UG exam on Sat & i dnt have answer to these questions . Help me out Q. Distinguish b/w degenerate energy level & a degenerate gas ? Ans : Degenrate level : A single energy level can be degenerate with another energy level , no difference b/w their energies . Degenerate...

Homework Statement N weakly interacting distinguishable particles are in a box of volume V. A particle can lie on one of the M possible locations on the surface of the box and the number of states available to each particle not on the surface (in the gas phase) is aV, for some constant a. 1...

http://www.ph.ed.ac.uk/~pmonthou/Statistical-Mechanics/documents/SM15.pdf At the top of page 59 in the above link, I can't see where the first three bullet points that follow E(T=0)=\int_0^{\epsilon_f} g(\epsilon) d \epsilon come from? can anyone help?

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?

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...

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...

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...

[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?

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.