Statistical Definition and 582 Threads

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?

Homework Statement A box is separated by a partition which divides its volume in the ratio 3:1. The larger portion of the box contains 1000 molecules of Neon gas, the smaller one contains 100 molecules of He gas. A small hole is made in the partition, and one waits until equilibrium is...

Hello, I am stuck on the first part of this question. There are several parts that follow that depend on this bit, and I know I can do them if I can just work this out. Any help would be gratefully received. Homework Statement Consider an isolated system of N identical spin-0 bosons...

Homework Statement The pass mark of an examination is set at 40. The following table shows some summary statistics of the marks (x) of the 200 students who took the examination. Mark Range: x >= 40, x < 40 Number of students: 160, 40 Mean: 64.0, 32.0 Standard deviation: 6.0, 4.0 The...

What is the physical or statistical meaning of the following integral \int^{a}_{o} g(\vartheta) d(\vartheta) = \int^{\infty}_{a} g(\vartheta) d(\vartheta) where g(\vartheta) is a Gaussian in \vartheta describing the transition frequency fluctuation in a gaseous system (assume two-level and...

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?

Greetings Next semester I'll have solid state physics, statistical physics and and introductionary course in elementary particles. So I was wondering maby those of you who had those subjects could recommend me some books. I really liked books by Griffiths so far. Especially the one on...

Hi! I am a software programmer and I would like to make a performance analysis of my software. One of the objectives that we need to achieve is to create a module for accurately computing the payment. Now, my expected result is that all computations are accurate. What statistical tool should...

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...

is there any video lectures source which is about statistical physics or quantum physics like MIT Lectures. I found some lectures about quantum physics but these are only related with it and it couldn't be considered as essential source.

Homework Statement Flip N fair coins. The distribution for different numbers of heads and tails should be peaked at N/2. When N is very large, the peak will be very high. Let x = N(head)-N/2, required to find an expression for this distribution near the peak, i.e. x<<N. Homework Equations...

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...

I came across this interesting Havard article at http://www.cfa.harvard.edu/~huchra/hubble.plot.dat listing over 600 Hubble survey results dating back to about 1929 and up to 2008. I put all the data into into a spreadsheet and using over 500 Hubble estimates from 1960 onwards I got an average...

Hi, I was having a discussion with a friend about the probability of life in the universe outside of earth. From what i know, there are 70 000 000 000 000 000 000 000 stars and god knows how many planets. Given the low probability of life spawning on a single planet but the huge amounts of...

I'm planning on taking a statistical thermodynamics grad course this Fall. Being an ME I am very familiar with classical thermo but what other topics should I be keen on? Any specific field of mathematics like abstract alg(only math I have not taken) I should be worried about? Also, I am...

I've recently gotten interested in statistical physics. Notions derived from this area are frequently applied in learning theory and other areas of biology which are of interest to me. I'm wondering if anyone knows of a good book or web resource for learning about statistical physics that...

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...

Does anyone know of any research programs out there that are considering physical structure formation in terms of emergent, self-organizing statistical manifolds, and does so without starting from some reasonable first principles without any structure or preconception of manifold, or ad hoc...

Hello This attachment is a practice paper I am doing. I know how to do everything except for questions 11, 12 and 13 so I would appreciate it if someone could please show me the process for working them out. thanks in advance.

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...

I'm having some difficulties with a problem. Based on the constraints, I have found that the average energy per particle is u = (Eo + E1 e^(-B deltaE)) / (1 + e^(-B deltaE)). I know this is correct. However, I am having problems solving as T approaches 0 and infinity. B = 1/T It tells me the...

Hi all, I am hoping someone can recommend a useful statistical test. I have a set of data on an x-y plot which varies about the y=0 line in a seemingly random way. Each data point has a y error bar, which appears to be, in general, smaller than the standard deviation of the data. I would...

[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...

Homework Statement http://ocw.mit.edu/NR/rdonlyres/Physics/8-044Spring-2004/85482B93-6A5E-4E2F-ABD2-E34AC245396C/0/ps5.pdf I am stuck on Problem 5 part a. They say that the relevant state variables are H,M,T, and U. Obviously the first law of thermodynamics still holds: dU = dW+dQ (does...

[SOLVED] statistical physics Homework Statement http://ocw.mit.edu/NR/rdonlyres/Physics/8-044Spring-2004/85482B93-6A5E-4E2F-ABD2-E34AC245396C/0/ps5.pdf I am working on number 3 part a. I am trying to calculate C_P. From the first law of thermodynamics: dQ = dU -dW = dU +PdV (does anyone...

[SOLVED] statistical physics Homework Statement http://ocw.mit.edu/NR/rdonlyres/Physics/8-044Spring-2004/AC9B128C-9358-4177-BFE6-A142E0FD897B/0/ps4.pdf I am working on Problem 3. So I want to calculate the integral of dW along each of those paths. But how can I relate dW to dV? dW is equal...

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...

[SOLVED] statistical physisc Homework Statement http://ocw.mit.edu/NR/rdonlyres/Physics/8-044Spring-2004/AC9B128C-9358-4177-BFE6-A142E0FD897B/0/ps4.pdf I am working on Problem 1a. I am really confused about this question. Do I set the two equations equal to each other and solve for something...

Homework Statement A spaceship that is cylindrical of area A and Length L decelerates at a constant rate a. The air treated. What is the difference in pressure due to the motion from the front to the back of the ship. The acceleration is parallel to L and air was in thermal...

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...

Hello! I have a question arising from my course in statistical physics: Describing microcanonical, canonical and grandcanonical ensemble you take three variables (like E,V,N for microncanonical) and get the "rest" from derivatives of the free energies. Is there a deeper meaning why there are...

The basis of inferential (testing) statistical analysis is that data are composed of two elements, a. theoretical expectation + error b. mean + standard error Would the two correct elements be listed in choice a.? The mean of a sample and the standard error (which is the sample’s...

I have a large sample of vectors in 3-space, and I would like to how uniformly they are distributed. Ultimately I'd like to know how uniform the angular distribution as a function of magnitude. What I mean by that is that if I divide the space into spherical shells, will the vectors whose...

how do I use the 50g to solve this one ? in a 80 battery lot there are 13 defectives; then, if it is taken a sample of 7 batteries. Which is the probability to find exactly 3 defectives batteries?

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 can't remember which statistical tests are needed for the following two tests. I thought maybe the null hypothesis test but wanted to check on here first... Maybe something Bayesian? Consider you have a plot of y against x with several data points on it, each with y error bars...

I apologize if this is the wrong thread but since this relates to thermo I figured this would be a good place to post this question. This is a problem that was assigned to us for physical chemistry but I can't find a good justification for one of the problems. 1. A system containing 38...

[SOLVED] Basic Statistical Thermodynamics Homework Statement Two distinguishable particles are to be distributed among nondegenerate energy levels 0,e,2e,3e... such that the total energy is U = 2e If a distinguishable particle with zero energy is added to the system show that the entropy...

I found a statistics question and am wondering how its figured out, the way its worded is hard to understand what everything means. anyhow.. If a coin is flipped N times, one expects to get "heads" roughly half the time. More precisely, Number of heads=N/2+Δn where Δn is the statistical...

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...

Hello, I've been running a model with different combinations of imput parameters. Let's just assume they look like this: 1,2 1,3 1,4 3,4 1,2,3 2,3,4 1,2,3,4 As a result I receive a certain numerical value. Jus by looking at that value I can see if the result is good or not. But...

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...

1. A system of 7 objects each have one measurement taken of them. These measurements are to be compared with two theoretical models, which theoretical model does the data fit best?[br]The machine used to measure the values has an extremely small error, so the data gathered does not have...

can somebody help me answer the problems 4.4 and 4.2 in statistical and thermal physics by reif. thanks in advance

http://physicsworld.com/cws/article/news/30711 Also here