Statistical mechanics Definition and 356 Threads

Homework Statement If ##Z## is homogeneous function with property ##Z(\alpha T,\alpha^{-\frac{3}{\nu}}V,N)## and you calculate Z(T,V,N). Could you calculate directly ##Z(\alpha T,\alpha^{-\frac{3}{\nu}}V,N)##. Homework Equations ##Z(T,V,N)=\frac{1}{h^{3N}N!}(2\pi m k...

I've been reading, in my own time, a first course in thermodynamics and they present a quantum treatment of statistical mechanics (discrete energy levels), but on the article for the partition function on wikipedia, I find out that there is a classical treatment of statistical mechanics as well...

That's the only equation I know on the topic so far. I'm an undergrad physics major and one of my courses this term is statistical mechanics which I am finding to be overwhelmingly difficult to understand. Apparently the course is considered "graduate level," although they still require us to...

Homework Statement A system of N particles has three possible energy levels namely; 0, E and 4E. How many particles does one expect in the second state at temperature T? Homework Equations It's a sample problem for our finals. Our Text book is Statistical Mechanics by Roger Bowley and...

Homework Statement A system of N distinguishable particles is arranged such that each particle can exist in one of the two states: one has energy \epsilon_{1}, the other has energy \epsilon_{2}. The populations of these states are n_{1} and n_{2} respectively, (N = n_{1}+n_{2}). The system is...

We don't have rigorous approach to statistical mechanics but have an intuitive one.We follow Concepts of Modern Physics by Sir Arthur Beiser. It is given that n(ε)=g(ε)f(ε) Here ε is the energy state. where according to my understanding n(ε)=number of particles which are present in an...

I am planing to study thermal physics on my own as I got an incompetent faculty who doesn't know anything about this subject. I want to have a detailed understanding about the topic. So can somebody suggest me which book I should follow from the following list. 1. Schroeder, Thermal...

I'm taking stat mech right now (Kittel book) and...I might hate it. I love e&m, quantum, classical, relativity, but I like almost none of what we're doing in this class. It's not the type of physics I'm interested in and it's abstract in a way I don't like (I normally like abstraction). I know...

Prove that the following two statements of the second law are equivalent (each one can be derived from the other): (a) “It is impossible for heat to flow spontaneously from a colder to a warmer body without causing other changes” (b) “It is impossible to convert all the heat taken from a...

I'm taking Stat Mech at the graduate level and I find the course incredibly frustrating in that it just feels like a whole lot of mathematical formalism without any examples. I've looked in Paritha, Huang, and Salinas and all these books seem the same in that they just looks like a bunch of...

An Introduction To Thermodynamics And Statistical Mechanics by Stowe is the course textbook for my Statistical Physics course I am having trouble with the book as it does NOT provide good examples and explanations nor does it have solutions just answers. I was wondering if there is Schaums or...

In a aislate system, the probability on a microcanonical state \Gamma is p(\Gamma ) = 1/K , if E<H<E + ΔE, and 0 on otherwise with K = \int_{\Gamma : E<H<E+ΔE} d \Gamma a) Show that ΔE →0, then p(\Gamma) = \frac{\delta (E-H)}{\int_{\Gamma : H=E} \delta(E-H)} b) Show that if...

Homework Statement Consider a system consists of two subsystem A and A' in which A contains 3 spins and A' contains 2 spins. Suppose that, when the systems A and A' are initially separated from each other, measurements show the total magnetic moment of A to be - 3{\mu _0} and the total...

I'm looking for a book on statistical physics. One's I've used already are Huangs Intro one and Sachs/Sens/Sexton. They're both great and the problems are great but neither provide answers nor are there any solutions to be found online so I have no idea if I understand the material. Could...

Homework Statement \frac{dq}{dT}=\sum_{i} g_i \frac{dq}{dT} e^{-\frac{ε_i}{kT}} = \frac{1}{kT^2}\sum_{i} g_i ε_i e^{-\frac{ε_i}{kT}} = \frac{1}{kT^2} \bar{ε} q Homework Equations q=\sum_{i} e^{-\frac{ε_i}{kT}} or for degenerate states, q=\sum_{I} g_i e^{-\frac{ε_I}{kT}} The Attempt at a...

Homework Statement In a large system of distinguishable harmonic oscillators, how high does the temperature have to be for the probable number of particles occupying the ground state to be less than 1? Homework Equations N(E_{n})=NAe^{\frac{-En}{K_{B}T}} E_{0}=0 (the textbook...

For the people who are in either of these fields, which math did you encounter most frequently in the field? Abstract Algebra, Analysis, Probability, Statistics, Calculus, or other? I have taken introductory courses for both topics at university and both seem to involve a wide range of math...

Hello, i need solve de following integral \int ^{\infty}_0 \frac{x^3}{e^x+1} dx i tried with the fermi function but the factor e^x is different to e^{x-\eta}, and with the gamma function but the factor e^x+1 is different to e^x-1. Help please

I am specifically referring to textbook "Statistical Mechanics" by Kerson Huang. It is not a general physics question, I am just trying to understand what is written in this specific book. So you can only really help if are familiar with it and have it at hand. I'm having trouble following...

Homework Statement I am supposed use stat mech to find the particle density in Earth's atmosphere given only the particle mass, and temperature, and the planet's mass I guess. And I don't really know where to begin. Obviously I need to use the grand canonical ensemble but I don't know where to...

This topic is about history of physics so I decided to post it in general physics section but it would be nice to have a history of physics(or maybe science)section. Anyway,during my statistical mechanics course,I realized QM is being used from the beginning,in contrast to other parts of...

[hi] can you help me to solve these problems from statistical mechanics by pathria?? these problems are 7,8,11,13 and 14 in page 27 thank you

Author: Mark Tuckerman Title: Statistical Mechanics: Theory and Molecular Simulation Amazon Link: https://www.amazon.com/dp/0198525265/?tag=pfamazon01-20

Author: Donald McQuarrie Title: Statistical Mechanics Amazon Link: https://www.amazon.com/dp/1891389157/?tag=pfamazon01-20

Homework Statement Imagine a system with N distinguishable particles. Each particle may be in two states of energy: -ε and +ε. Find the the partition function of the system Homework Equations The Attempt at a Solution I know that I have to find the partition function for a...

I have gone through two volumes of Cohen (Quantum Mechanics). Now I need a book on Quantum Statistical Mechanics. The book should use axiomatic formulation using density matrix. Please give me a suggestion. ( I'm also introduced with 2nd quantization slightly) Thanks for any help in advance.

Homework Statement An isolated system has N=3 distinguishable particles A, B, C with single particle states equally spaced at intervalsof E and a total energy U=3E. ie the macrostate is defined by N=3, U=3E. The system has single particle levels 0, E, 2E, 3E. Homework Equations...

can someone please explain "Postulates of Classical Statistical Mechanics" , "priori probability" , "equilibrium" ..i m a post graduatation student .and in physics these chapters are seem very difficult i need some step by step explanation ..

Homework Statement A quasi-3 level solid-state laser gain medium consists of a ground state manifold containing two energy levels within which a single electron can be promoted, with the second energy 10meV above that of the lowest level. A. Where the gain medium is not optically pumped...

I was wondering if it's common in undergraduate studies for statistical mechanics to be covered in the last 3-4 weeks of a thermodynamics course? I feel like the same is done for infinite series in a 2nd semester of calculus. Needless to say, both topics deserve much more time to fully do them...

I'm looking for a first-year graduate level stat mech textbook. What are the best ones out there?

My advanced statistical mechanics prof told me that it wouldn't make any physical sense to allow N (the number of particles in a system) to be negative. But, somehow, I think that this possibility should be theoretically left open; perhaps there are some systems whose statistical behavior would...

Hi. I'm reading my third year of a Swedish engineering degree and we are about to read Statistical Mechanics. The scope of this course is Thermodynamics (although we have already had a small course in it), Statistical Mechanics and some Quantum statistics. The course book is "Concepts in...

Hello,I'm studing the fundamental principles of statistical mechanics and I don't understand the "principle of equal a priory probabities" for this reason: the principle states that all states in the representative emsemble have the same probability which means that the density \rho(p,q) should...

Hi all, I am thinking of doing a PhD in theoretical statistical mechanics and would like to do it in Europe. I am having trouble finding institutes with a focus on SM or Physics/Mathematics departments strong in the field. Some guidance would be really appreciated. Thanks, and best...

I'm a junior chemical engineering major. How much overlap is there between stat mech and engineering theromdynamics? I was thinking about taking both next semester assuming they are not too similar. Are the topics different enough to warrant taking them at the same time?

Hallo Everybody, I am following Professor Susskinds lectures on statistical mechanics, but can't find an appropriate book that is in line with what is presented in the lectures. Can anyone recommend a book that the lectures follow or which presents the same ideas as in the lectures? Your...

I'm taking Statistical Mechanics this semester. I already took Thermodynamics, covering the first three laws (0,1,2) at the level of Fermi's Thermodynamics book (and other similar ones). My Stat. Mech. teacher is a condensed matter experimentalist and he's boss at what he does, no question about...

I'm reading through Reif's "Statistical Mechanics" to prepare for the upcoming semester. Basically, a drunk guy takes N total steps, n1 to the right and n2 to the left. The probability that the current step will be to the right is "p," while the probability that the current step will be to the...

Hi, I'm looking for a good book on statistical mechanics (to go with a course) and I've been considereing Tolman's book http://books.google.be/books?id=4TqQZo962s0C&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false Is this book still up to date with the quantum mechanics...

I see a lot of talk about QM, relativity, particle physics, classical mechanics, electrodynamics, etc. But I hardly see statistical mechanics (or pure thermodynamics, for that matter) related matters, beyond the pure basics, that is. What's the reason for this? Is it perceived to be less...

hi! i study statistical mechanics from this book at the moment and I'm a little bit confused somtimes. i thougt if anybody else is using this book, we could discuss and clarify confusions (or errata) here. please let me know if anyone is out there... greetings!

I am reading chapter three of Huang's Statistical Mechanics and I have a problem with equation (3.22). Having discussed the derivation of the classical cross section for a scattering process, Huang moves on to the quantum version of it. He states that in quantum mechanics the fundamental...

Right now I have Schroeder, and I'm not a fan of it, despite some of the rave reviews I have read. I'm thinking I need another text to learn from while taking this class. I have a copy of Fermi's Thermodynamics (somewhere), but I'm not exactly sure what's in it. I just think it's silly that I'm...

According to quantum mechanics, every particle has an uncertainty of position and momentum. Particles have quantum vibrations. So is it possible for all the atoms in an object to vibrate at the same time in the same direction making the object as a whole move? If so, what kind of energy would...

Homework Statement 500 blue and 500 orange bacteria are placed in a growth medium. Each bacterium divides every hour. A predator eats exactly 1000 bacteria per hour irrespective of color. a) What is the ultimate probability distribution for the colors of bacteria in the growth medium? b) How...

Homework Statement We have N particles, each of which can either be spin-up (s_i = 1) or spin-down (s_i = -1) with i = 1, 2, 3...N. The particles are in fixed position, don't interact and because they are in a magnetic field with strength B, the energy of the system is given by: E(s_1...

Homework Statement A classical particle with mass m is in thermal equilibrium with a fluid at temperature T. The particle is stuck to a harmonic ('Hookean') spring and can only move on a horizontal line (-\infty < x < \infty). The position of the particle is x = 0 if the spring is in its...

I'm starting a self teaching in statistical mechanics, so I would appreciate suggestions about the most appropriate textbook for this purpose. Thanks.

Homework Statement We have a surface that can adsorb identical atoms. There are N possible adsorption positions on this surface and only 1 atom can adsorb on each of those. An adsorbed atom is bound to the surface with negative energy -\epsilon (so \epsilon > 0). The adsorption positions are...