Questions tagged [kinetic-theory]

Kinetic theory is part of statistical physics. DO NOT USE this tag for macroscopic kinematics; use the [kinematics] tag instead.

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Collisional cross-section from attenuation factor

I am trying to find the mean free path of silver atoms travelling through air (I am given the temperature, pressure and that they are attenuated by a factor $2.72$ in a distance of $10^{-2}$m). I know ...
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Quasi-linear theory of plasma, some queries

I was studying about quasi linear theory of plasma turbulene and stuck at some questions (derivations), I could able to derive upto Eq.14 of this paper, but not sure how proceed for deriving the ...
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Kinetic energy of evaporated gas as source of energy loss for evaporating liquid?

Currently, I am looking at a system that is composed of a metal cylinder (lets say Iron) that is being heated by a laser inside of a vacuum chamber. As the laser strikes the surface of the iron, part ...
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Significance of Stokes Hypothesis

When we derive the Navier-Stokes Equation, we come across a a common assumption made by Stokes that makes the two quantities namely Mechanical pressure and Thermodynamic pressure equal to each other. ...
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Pressure exerted by a single electron in an spherical bubble

This is from APhO 2010, Problem 3, Part (A) When an electron is planted inside liquid helium, it can repel atoms of liquid helium and form what is called an electron bubble. The bubble contains ...
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Why does rotational collision number in dilute gases such as N2 increases with temperature?

In the kinetic theory of dilute gases, the rotational collision number and rotational relaxation time are defined as follows- rotational relaxation time = time required for the establishment of ...
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Velocity distribution function and Boltzmann factor

In Blundell and Blundell's Thermal physics book there is a chapter on the explanation of the Boltzmann distribution. It is explained that for canonical ensemble with a reservoir at temperature $T$ in ...
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Ratio of mean free paths between two equal volumes at different temperature, separated by a partition with pinhole

Question: A container is divided into two equal parts I and II by a partition with a small hole of diameter $d$. The two partitions are filled with same ideal gas, but held at temperatures $T_I$​= ...
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Time Scales in the BBGKY Hierarchy

(I am following Chapter 3 of Mehran Kardar's Statistical Mechanics of Particles)When working with the BBGKY hierarchy of equations, we get the following for the two-particle probability density $f_2$: ...
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Why air particles in a longitudinal sound wave don't leave their mean position?

Air particles have random zigzag motion. However,in a longitudinal sound wave in air the particles vibrate to and fro about their mean position in the direction of propagation of sound wave(ie, the ...
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Doubt on obtaining Boltzmann Equation given in the book "Modern Cosmology" Ed 1, Dodelson, equation 3.9

My question refers to Equation (3.9) of Dodelson "Modern Cosmology" Edition 1, $$ n^{-3} \frac{d(n_1 a^3)}{dt}=n_1^0 n_2^0 <\sigma v>\{\frac{n_3 n_4}{n_3^0 n_4^0}-\frac{n_1 n_2}{n_1^0 ...
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Is Radon a gas due to its radioactivity?

I think most gases are light but Radon is really heavy. I of course know that plenty of gases are not radioactive, but could the reason that Radon is a gas be due to the radiation contributing to the ...
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Is is possible to extract an effective Hamiltonian from a Boltzmann equation (or any other kinetic theories)?

I got kind of confused when reading Xiaogang Wen's famous textbook Quantum Field Theory of Many-body Systems. In Section 5.3.3 the book claims that From a kinetic theory of Fermi liquid (a Boltzmann ...
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Resultant particle distribution function for mixing of two particle species

I would like to know if there is any way to compute the resultant particle distribution for system where two kinds of particles are mixed. For me one kind is Maxwellian and another is non-thermal ...
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At freezing/condensation point, why does the temperature remain constant? [duplicate]

I understand that at freezing and condensation points, potential energy of molecules are given off to form intermolecular bonds while the kinetic energy of the molecule stays constant. My question is, ...
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Trouble integrating Maxwell-Boltzmann velocity distribution for RMS speed

I am trying to integrate over the Maxwell-Boltzmann velocity distribution to find the $v_{\text{rms}}$. The Maxwell-Boltzmann velocity distribution is given by: $$P(v) =\sqrt{\frac{m}{2\pi kT}} e^{-mV^...
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Kinetic temperature and kinetic energies [closed]

From my understanding, kinetic temperature is related to the average translational kinetic energy of particles by $$ \frac{1}{2}m\left<v^2\right> = N k_B T $$ I have several questions regarding ...
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How can entropy be created from nothing? [duplicate]

In my textbook, it is written that entropy can be created but it can't be destroyed. But I have a doubt about this line. I don't understand where does the 'created entropy' come from? How can entropy ...
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Is this a valid interpretation of the mean relative speed/collision rate of particles in a Maxwell-Boltzmann distribution?

In textbooks, the collision frequency $Z_{ab}$ between two species "a" and "b" is always given as something like: $$Z_{ab} = n_an_b\sigma_{ab} \Bigg(\frac{8 k T}{\pi \mu}\Bigg)^{1/...
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How to derive fluid equations for electrons from the linearised kinetic equations?

Starting from the linearised kinetic equation for electrons and ignoring perturbations of the ion distribution function completely, how can I work out the fluid equations for electrons (i.e., the ...
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Is the Navier-Stokes equation valid in $d=2$ spatial dimensions?

In this article, the authors study the time behaviour of the velocity-velocity correlation function of a particle in a gas. If the gas is immersed in $d$ spatial dimensions, they find that $$ C(t)=\...
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Description of Van Allen's Belt and Magnetic Mirrors

The "Van Allen Belt" is a region near earth that concentrates a high density of energy particles. The formation of this region originates in a phenomenon called a magnetic mirror, when ...
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Absolute zero: how close can we go?

Kinetic theory says that the minimal temperature is zero kelvin, at which every motion is stopped. However, we do know that quantum theory says that we have unavoidable quantum fluctuations, so: what ...
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A question based on paradoxical situation in Statistical Mechanics by Kerson Huang

I recently found a question in Stat Mech book by Kerson Huang (Pg No. 142) and it kind off intrigued me. The question goes as follow: Let the "uniform" ensemble of energy E be defined as the ...
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When we shrink a box containing a gas, does the increased frequency of molecule impacts on the box cause the rise of its temperature?

When we shrink a box containing a gas, does the increased frequency of molecule impacts on the box cause the rise of its temperature? I assume the kinetic energy of the molecules shouldn't change ...
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What Assumptions Govern the Applicability of the Boltzmann Distribution?

In the book "Concepts in Thermal Physics" the Boltzmann distribution is derived with the following assumptions: There are two systems, one enormous heat reservoir and one comparatively ...
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How can internal energy be $\Delta{U} = nC_{v}\Delta{T}$?

How can internal energy be $\Delta{U} = nC_{v}\Delta{T}$? Here's what my teacher did From Law of equipartion of energy Energy of one molecule having f Degree of freedom $= \frac{1}{2}KTf$ $K=\frac{R}{...
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Do drifting particles violate Alfvén's theorem?

According to this Wikipedia article, Alfvén's theorem states that "in a fluid with infinite electric conductivity, the magnetic field is frozen into the fluid and has to move along with it". ...
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Understanding mean rate of change in Brownian motion

I found a nice discussion of Brownian motion in the Feynman lectures, reproduced online here: https://www.feynmanlectures.caltech.edu/I_41.html Feynman considers a particle undergoing a Brownian ...
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Gas particle collision rate dependence on particle velocity/ Hard sphere simulation

From a basic kinetic theory perspective the A-B collision rate $\theta_{AB}$ is given as a function of the mean speed and the number density.$$\theta_{AB} \propto \bar{C}_A n_B$$ If we are considering ...
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How do you derive the Maxwell-Boltzmann distribution?

I have searched for a reasonable derivation online, but so far have been unable to find one which doesn't skip steps or presume prior knowledge. I found a derivation on this Wikipedia article which ...
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Deduction of no. of molecules crossing due to velocity gradient in mass flow

enter image description here The above two pictures show the deduction of number of molecules crossing an imaginary plane for a mass flow of air molecules. Here we have considered horizontal ...
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Doubt in derivation of pressure exerted by ideal gas

In books the derivation of pressure exerted by a gas on a closed container is derived for a cubical geometry, but since it contains number of molecules per volume (denote it by $n$) the books say it's ...
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Which average are we taking in a rigorous calculation of the mean free path in a gas?

This is a question at one level beyond the standard introductions to kinetic theory. I want to know which average we are taking when we talk about a mean free path in a gas. I recently read Steve T. ...
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Dirac delta-function integral in Kerson-Huang

I found a portion in Kerson Huang $\textbf{Statistical~Mechanics}$ book, in Page No. $\textbf{61}$ where they have performed an integral over a delta function and got the last equation (given at the ...
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Why is there a factor of $\pi$ in the average velocity of gas?

Consider the most probable and RMS speeds for a kinetic gas: $$ v_{mps} = \sqrt{\frac{2RT}{M}}$$ $$ v_{rms} = \sqrt{ \frac{3RT}{M}}$$ Now consider the average speed: $$ v_{avg} = \sqrt{\frac{8RT}{\pi ...
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Plasma modes analysis with Laplace and Fourier methods

I've seen that in order to investigate plasma's modes it's possible to linearize the system and then Fourier transform it (for longitudinal modes with kinetic description the Laplace transform in time ...
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One large energy barrier vs. two small energy barriers

I am studying the reaction pathway of oxygen evolution reaction (OER) on a PtNi alloy catalyst using density functional theory (DFT). What I found is that, for different intermediates, the most ...
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Is there a pressure gradient in a stationary gas with a temperature gradient?

Consider a gas with ideal equation of state $P = n k_{\rm B} T$, in a fixed rectangular container with two opposite walls maintained at different temperatures, under conditions where there are no ...
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Pressure exerted by an ideal gas according to kinetic theory of gases

In my textbook and Wikipedia, I have observed that force exerted on a wall of the container by one molecule is taken into account. Such that $F=\frac{mu} {\Delta t}$ where ${\Delta t}=\frac{2l}{u}$. ...
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Can gas in a room rotate a fan with asymmetrical spokes?

I was asked this question in an interview. The figure in first part of the question was drawn as shown. The question was to draw the angular position of the point marked on the rim with time. It ...
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Plasma long range em interaction

I've seen that charged particles in plasma are shielded at a distance of a Debye length, so how is it possible that charges in plasma interact on a long range distance too? It seems impossible to me ...
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Component of the velocity gradient part of Vlasov equation in cylindrical coordinate

I am stuck with a problem in expanding the velocity gradient part of the Vlasov equation in cylindrical basis. It is also applicable to the spatial gradient part as well. For example here I consider ...
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Pressure exerted by gas on the wall of a container

The pressure exerted by gas on the wall of container is given by $P= (1/3)*ρ*v²$, $v$ is r.m.s velocity, $ρ$ is density of the gas while deriving this, there is an assumption made that the components ...
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How to reduce an integral in phase space to an one-dimensional form?

I've been trying for a very long time to show that the following integral: $$I_D=2{\displaystyle \int} \, {\displaystyle \prod_{i=1}^3} d \Pi_i \, (2\pi )^4\delta^4(p_H-p_L-p_R) |{\cal M}({e_L}^c e_R ...
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Why is thermal conductivity of a gas higher than one would think from diffusion coefficient

When we study kinetic theory of gases we find relationships between the processes of diffusion, heat conduction and viscosity, and collisions in the gas. In particular the diffusion coefficient is ...
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The model of a free particle in a box as an approximation for the translational motion of a particle in a gas

According to the book Introduction to Physical Gas Dynamics (starting from page 120), the translational motion of a particle in a gas in thermal equilibrium may be approximated by a free particle in a ...
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Getting different results from modelling the system in probability distribution and physical intuition in statistical mechanics

There is a problem given as - N molecules of an ideal gas are in a container of volume $V_o$. If a molecule has a same probability of being at any point in the container. The variance of number of ...
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Collision Operators

Broadly speaking, what is a collision operator? Generally, the term operator refers to a mapping from function(s) to a real number/function. What function(s) are being mapped, and to what physically ...
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Plate traveling at constant speed in rarefied gas

I'm trying to understand this article. A plate moving inside a rarefied gas, with speed comparable to the speed of the gas particles. Drag force is modeled as the difference of pressure on both sides ...

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