Statistical thermodynamics Definition and 36 Threads

Suppose we have a gas of bosons with spin 0 and the grand potential is ##\Phi =\frac{kTV}{h^3} \int ln(1-e^{-\beta(p^2/2m -\mu})d^3p## we already integrated the function in the coordinate space and the result is the factor V (volume). Now, we know that ##\epsilon = p^2/2m## and ##d^3p = 4\pi...

Assume you have a microscopic pendulum you can suppose is like quantum harmonic oscillator. If the length of pendulum has variation of ##dl##, calculate the work on the pendulum and thermodynamic generalized force. Find also the variation of mean number of extitations. My Attempt Firstly, I...

Hi, as in a previous thread I would like to better understand the Feynman's analysis of brownian ratchet as described here: https://www.feynmanlectures.caltech.edu/I_46.html https://en.wikipedia.org/wiki/Brownian_ratchet Consider the case in which the two boxes (i.e. heat baths) are at the same...

Hi, I've a question about the concept of ensemble is statistical physics. Take a conservative system in a given macrostate (e.g. with a given energy): there will be a number of phase space's microstates compatible with the given macrostate. If I understand it correctly, basically the...

An insulated container (constant volume, adiabatic) contains an Ideal gas with pressure P1 and temperature T1. We open the container's hatch for a few seconds and let some particles escape from the container, then we close the hatch again. We know container's pressure has reduced by exiting...

Canonical ensemble can be used to derive probability distribution for the internal energy of the closed system at constant volume ##V## and number of particles ##N## in thermal contact with the reservoir. Also, it is stated that the temperature of both system and reservoir is the same, i.e...

Canonical ensemble is the statistical ensemble which is applicable for the closed system in contact with the reservoir at constant temperature ##T##. Canonical ensemble is characterized by the three fixed variables; number of particles ##N##, volume ##V## and temperature ##T##. What is said is...

One of the common derivations of the canonical ensemble goes as follows: Assume there is a system of interest in the contact with heat reservoir which together form an isolated system. Heat can be exchanged between the system and reservoir until thermal equilibrium is established and both are...

Boltzmann entropy definition is given by: $$ S = k_B lnW $$ where ##W## is the weight of the configuration which has the maximum number of microstates. This equation is used everywhere in statistical thermodynamics and I saw it in the derivation of Gibbs entropy. However, I can't find the...

I have a question about a sentence in the book Introduction to Thermal Physics (Daniel v. Schroeder). So in chapter 6, Schroeder talks about an atom isolated. This means its energy is fixed. The atom is in some state. The energy states of the atom have degenerated. All microstates with that...

iam not getting why in bose statistics the number of ways to arrange ni particles in gi degenerate states is = (gi+ni-1) ? and why do we divide by ni factorial , and gi factorial .

Homework Statement Show that, in the Debye theory, the number of excited vibrational modes in the frequency range ##\nu## to ##\nu+d\nu##, at temperature T, is proportional to x2e-x, where ##x=h\nu/kT##. The maximum in this function occurs at a frequency ##\nu'=2kT/h##; hence ##\nu'→0## as...

Homework Statement The actual question was deriving Bose-Einstein, but I got confused on the F-D example. I'm basically following the method given here. Homework Equations [All taken directly from the above link] Taylor series: The Attempt at a Solution So after that third equation...

Integral constant for internal energy of ionic liquid I have a question, and I will be really grateful if someone helps me. I have a polynomial equation for internal energy which I calculated by integration an equation of state formula, which is based on density. But, because I calculated this...

Does anyone have any good books, or other references, that they would recommend for studying for the thermodynamics & statistical mechanics portion of graduate qualifying exams? I didn't have any undergrad Stat Mech and my grad prof/class was really not good, to the point that I didn't really...

So I worked through the Boltzmann distribution and got: $$ P\propto e^{\frac{-E}{k_BT}} $$ Where $E$ is the energy. So surely this means the kinetic energy (and therefore speed) of particles is distributed over a Boltzmann distribution. Or in equation: $$ P\propto e^{\frac{-mv^2}{2k_BT}} $$...

Homework Statement Consider a model thermodynamic assembly in which the allowed (nondegenerate) states have energies 0, ε, 2ε, 3ε.The assembly has four distinguishable (localized) particles and a total energy U = 6ε. Tabulate the nine possible distributions of the four particles among the...

I have a simulation with a bunch of particles with volume bouncing around in a box with no interaction between them, a hard-sphere gas. Initially, they all have the same momentum |p|=√(2⋅m⋅2/3⋅k⋅T) to have the average kinetic energy 3/2⋅k⋅T. I'm asked to add a constant energy flux to the system...

Homework Statement A particular logic gate takes two binary inputs A and B and has two binary outputs A' and B'. I won't reproduce the truth table. Suffice to say every combination of A and B is given. The output is produced by A' = \text{NOT} \ A and B' = \text{NOT} \ B . The input has...

Can someone recommend me some good textbooks or articles that contain or focus on statistical thermodynamics and/or oscillatory motion (preferably with advanced math, not just stories)?

Homework Statement If the energy ##E## of a system behaves like ## E = \alpha |x|^n##, where ## n =1, 2, 3, \dots ## and ## \alpha > 0##, show that ## \langle E \rangle = \xi k_B T ##, where ##\xi## is a numerical constant. Homework Equations $$ \langle E \rangle = \frac{ \int_{- \infty}^{...

Homework Statement 1.) For N particles in a gravity field, the Hamiltonian has a contribution of external potential only (-mgh). Show that the particle density follows the barometric height equation (1). 2.) For N particles in a open system at constant pressure p and temperature T, let there...

Homework Statement Consider a classical one-dimensional nonlinear oscillator whose energy is given by \epsilon=\frac{p^{2}}{2m}+ax^{4} where x,p, and m have their usual meanings; the paramater, a, is a constant a) If the oscillator is in equilibrium with a heat bath at temperature T...

A glass bulb contains air at room temperature and at a pressure of 1 atmosphere. It is placed in a chamber filled with helium gas at 1 atmosphere and at a room temperature. A few months later, the experimenter happens to read in a journal article that the particular glass of which the bulb is...

Homework Statement Consider the case of a gas in the atmosphere. Assume that the temperature is a constant. Based on the Maxwell Boltzmann distribution, at sea level the atmosphere contains 78.1% N2, 21% O2, 0.9% Argon, and 0.036 CO2. What are the ratios at the the top of Everest? (Molecular...

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 Give the number of states (energy of the state smaller than E<0) \Phi(E) of a spinless particle with mass m in the central potential V(\vec{r})=-\frac{a}{\left|\vec{r}\right|}. Homework Equations The Attempt at a Solution Hi, the hamiltonian of this problem...

Statistical Thermodynamics - Help Wanted :( (My translation skills sucks, I hope it is understandable.) Three spins, placed at vertices of an equilateral triangle, are put in the external magnetic field with density B. Hamiltonian of the system: H = -J \sum_{<i,j>} s_{i} s_{j} - \gamma...

Hi, i'm an Applied Physics student (2nd year). Could you please tell me a book to study thermodynamics from? I've studied from Thermodynamics, Kinetic Theory, and Statistical Thermodynamics by Sears - Salinger and it is pretty good. Has anyone "tested" : 1) An Introduction to Thermal Physics by...

Hi all, I'm looking for a rigorous (in a mathematical sense) treatment of statistical thermodynamics. I'm at the tail end of a class on stat thermo that used the book by Bowley and Sanchez. This book is not what I'm looking for. Does anyone have any suggestions?

I took classical (engineering) thermodynamics a few years ago, and this semester I am taking a statistical thermodynamics class from the physics department. We are using the book "Fundamentals of statistical and thermal physics" by Reif, which seems to be a pretty good book. Unfortunately I...

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'm just finishing up a "Classical Thermodynamics" class. Here is a list of topics we covered: Chapter 1: Ideal gas, equipartition of energy, heat and work, heat capacities, rates of processes Chapter 2: Multiplicity of an Einstein solid, of an ideal gas, of interacting systems Chapter 3...

Does anyone else have a lot of trouble comprehending the derivations in statistical mechanics? To me the mathematics feels somewhat archaic. Somehow it just seems as though it'd be neater if it was dealt with using matrix or operator methods. I always have trouble with the concept of entropy...

This isn't a homework question. I'm studying this from a book (Thermal Physics by Kittel & Kroemer) currently. Up til now I've had no problem following it. There's one derivation that's got me a little stumped however. I had thought my calculus was proficient enough, but I'm just not seeing...