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Questions tagged [kinetic-theory]

Kinetic theory is part of statistical physics. DO NOT USE THIS TAG for macroscopic kinematics. In this case, use the tag [tag:kinematics] instead.

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Is internal energy a function of pressure?

I read that internal energy is a function of temperature only and not pressure. But say, we compress a volume of gas. Won't the particles start moving more quickly? Meaning an increase in their ...
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Law of equipartition of energy, shouldn't kinetic energy per molecule by $(3/2)kT/f$

I study that according to the law of equipartition of energy the average kinetic energy associated with each degree of freedom is equal to $(1/2)kT$. But shouldn't it be $\frac{(3/2)kT}{f}$ where $f$ ...
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Time derivative of classical position and momentum averages

Consider a one-dimensional Hamiltonian system $H(q,p,t)$, and some classical phase space distribution function $\rho(q,p,t)$ satisfying Liouville's equation $$\frac{\partial \rho}{\partial t} = \{H,\...
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1answer
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Is the kinetic theory of gas relative in nature

In kinetic theory of gas the foremost assumption is that the temperature of an object is due to the kinetic energy of the atoms/molecules contained in it. But as we know that kinetic energy is a ...
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Gas Transport Problem

I have a question that I thought would be a very simple effusion calculation that sent me down a massive rabbit hole after I tried to look it up in Landau's Physical Kinetics and so now I'm coming to ...
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1answer
32 views

Why do we require Boltzmann equation to be applicable for only dilute regime?

Why do we force the assumption for Boltzmann Equation to be dilute? Is there any exact formula that defines this DILUTE? and why it has to be dilute? Does it has anything to do with mean free path? (...
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Virial theorem lmplies loss of potential energy

Learning equipartition theorem, I search related content on this web. But I stuck at some point when I look at this part: "However as we climb out of the potential well to large interatomic distances ...
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2answers
19 views

Pressure on a fluid element

We consider an element in a liquid at hydrostatic equilibrium such that continuum is maintained. Now to calculate the forces on it we consider body forces and surface force. Our system is simply a ...
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14 views

Shouldn't Z(compressibility factor) be < 1 for all real gases?

So compressibility factor(z) is defined as $$Z = \frac{V_{real}}{V_{ideal}}$$ where $ V_{real}$ is volume occupied by real gas and $V_{ideal}$ is volume occupied by ideal gas at same conditions but by ...
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36 views

Derivation of the velocity distribution function in kinetic gas theory

I'm reading a book and got stuck at how one formula during the process of deriving the velocity distribution function. $$ \Omega\left(v_{x}, v_{y}, v_{z}\right)=f\left(v_{x}\right) f\left(v_{y}\right) ...
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Is Lithium Plating possible at the cathode, too?

When talking about the Failure Mode 'Lithium Plating' in Lithium Ion batteries, in literature it is just described at the anode and I could not find answers to why it is not happening at the cathode, ...
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25 views

Kinetics of thermal fluctuations in liquid

I have an instinct that tells me that particles in water at temperature $T$ should be receiving and emitting "quanta" of energy of size $kT$ at a certain rate $r$. My question is: what is $r$? This ...
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1answer
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Particle in kinetic gas theory without collision

Hello I have a (Gedankenexperiment) question about the kinetic gas theory. As far as I understand temperature corresponds to kinetic energy. Assume now there would be one particle that does not ...
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How do we tell which part of kinetic energy gives rise to temperature?

I know that macroscopic temperature is a measure of kinetic energy of particles at very low scales (let's call it microscopic kinetic energy). But how can we derive which part of this microscopic ...
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2answers
257 views

Why isn't temperature definable for a single, classical particle? [duplicate]

I read that the relation between temperature and kinetic energy of an ideal gas is only applicable to a large number of particles so that the mean value for kinetic energy has to be considered, so the ...
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1answer
51 views

Is internal energy frame-dependent? [duplicate]

In the realm of kinetic theory of gases, the internal energy of gas is solely due to the sum of kinetic energies of all particles, since kinetic energy is frame dependent I was thinking whether a ...
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1answer
27 views

Pressure in Bernoulli principle [duplicate]

In Bernoulli principle we say that as velocity increases the pressure of fluid decreases but it contradicts kinetic theory of gas which says that as velocity increase-pressure increases. And this ...
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13 views

Reference Request: An introductory book on Kinetics, similar to Schroeder's on thermodynamics [duplicate]

I come from a statistics background and don't have much knowledge of physics. I need to gain bit of knowledge in statistical physics for one of the projects that I work on. I started looking at Reichl'...
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Why are solutions in Chapman-Enskog formalism expressed via Sonine polynomials?

Before I posit my question, I would like to thank anyone willing to have a crack at it. I'm currently writing an assignment concerning the Chapman-Enskog method of expanding the probability density ...
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4answers
89 views

What happens to the pressure and the temperature of a gas compressed adiabatically?

The set-up is basic. There is a piston that goes down, reducing the volume. The process is adiabatic, so the acquired energy is kept inside the gas. The ideal gas law states that as the volume ...
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Sound and thin gas films: does the speed of sound become multi-valued?

The basic formula for the speed of sound in a gas $c=\sqrt{\left(\frac{\partial p}{\partial \rho}\right)_s}$ assumes that it is uniform, and thus that sound waves travel through the gas at one speed. ...
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1answer
55 views

Kinetic Energy while melting

I have a question and its really bothering me. When a substance in its solid state is heated, then while it melts, the temperature does not increase. I used to assume that this is because the energy ...
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41 views

Justification behind using probability density in kinetic gas theory

Let's consider an ideal gas, of some huge number of particles. The Maxwell-Boltzmann distribution describes the probability of measuring a particle speed in a range of speeds, through integration. ...
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15 views

How to include the possiblity of Umklapp Scattering into transport calculations

I'm trying to calculate transport properties of a certain model with a Hamiltonian that has electron-electron interactions. I know that, in order to use the Boltzmann equation \begin{equation} 0=\...
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28 views

Criteria for electrostatic approximation in microscopic/kinetic plasmas

I started pondering about the electrostatic approximation in relation to plasmas, where a particle's motion $\mathbf x(t)$ is governed by the Lorentz force: $$ m\ddot{\mathbf x}=q(\mathbf E+\dot{\...
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Pressure-velocity dispersion relation $p=\rho(r)\sigma^2$

The relation is $p=\rho(r)\sigma^2$. Where $\rho(r) $ is density distribution and $\sigma$ is velocity dispersion(RMSE/root mean square error value). This relation is given for a isotropic velocity ...
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51 views

Escape Velocity and its effect on the atmosphere

I’ve been doing some world building and wound up with a bit of a physics puzzle that’s stumped me. So rather than a long winded explanation I’ll simply state the primary parameters. Under otherwise “...
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0answers
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Confusion between molecular weight and molecular mass

Why is molecular weight not molecular mass × g? Because, mass and weight are different. Weight is the force with which you are being pulled, so molecular weight should not mean molecular mass, but why ...
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1answer
23 views

Usefulness of high molecular speeds in nuclear fusion reactions

How do molecules having speeds many times greater than mean speed help in making nuclear fusion reactions in a laboratory?
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198 views

How to write down the collision integral for any interaction in the Boltzmann equation?

I'm studying the Boltzmann equation \begin{equation} \Big[\frac{\partial}{\partial t}+\vec{v}\cdot\nabla_{r}+\frac{1}{m}\vec{f}\cdot\nabla_{v}\Big]f(v,r,t)=\frac{df}{dt}\Bigg|_{coll} \end{equation} ...
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1answer
39 views

Temperature anisotropy in plasmas

If a species of a plasma is described by a distribution function $f(\mathbf{r},\mathbf{v},t)$, is it possible to have different temperature (thermal energy) values for different directions (x, y and z)...
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1answer
21 views

What does averaging over time means in literature?

Disclaimer: This question is cross posted in here because the answer might be field dependent. Let $h: [0, L]\times \mathbb{Z}^1 \to \mathbb{Z}^1$ be a function, called the height function, and lets ...
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Why is the probability that the collision angle will be in the range of 0 to 60 degrees than in the range of 60 to 180 degrees

Pretty much the title. It is given that the probability that the collision angle will be in the range of 0 to 60 degrees than in the range of 60 to 180 degrees I don't remember seeing such statement ...
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1answer
49 views

Validity of kinetic theory

I am reading this paper, which uses (chiral) kinetic theory. The authors write: The Boltzmann method is valid only in the semiclassical limit, where $\omega_B \tau \ll 1$, $\omega_B \ll \mu$ and $\...
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3answers
74 views

From kinetic theory - why does heat rise?

I know the explanation from fluid elements and densities however I don't find it satisfying. Is there an explanation from kinetic theory?
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1answer
184 views

Landau's approach to collisions in plasma

I can't understand some steps in obtaining the collision term in the Boltzmann equation for plasma. For the first time it was made by L.D. Landau in his article "The kinetic equation in the case of ...
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23 views

Collision frequency of ideal gas and velocities of molecule

Is collision frequency of gas molecule $ = \frac{V_{RMS}}{\lambda}$ where $\lambda$ is mean free path. Shouldn't it be $\frac{V_{average}}{\lambda}$? (I often see that in theories books suggest that ...
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1answer
85 views

Need verification for the entropy equation in statistical thermodynamics

The relationship between entropy $S$, the total number of particles $N$, the available energy levels $E_j$ and a yet to be defined parameter $\beta$ is: $$S(\beta)=k_B \cdot N \cdot \ln\bigg(\sum_{j=1}...
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2answers
67 views

Using Boltzmann distribution, what is the ratio of probabilities of two states?

I got the probability of state $i$ (in terms of Boltzmann distribution) as $$p_{i}=\frac{1}{Z_{i}}e^{-\epsilon _{i}/{kT}},$$ where $Z_{i}$ is the canonical partition function: $$Z_{i}=\sum_{i}e^{-\...
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1answer
52 views

Validity of Maxwellian distribution for interacting particles?

I have read in a few (relatively credible) sources (e.g. Cambridge Tripos exam) that the Maxwell-Boltzmann speed distribution can be valid for interacting particles, but I have not been able to find a ...
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1answer
49 views

Clausius paper “ On the motive power of heat & on the laws which can be deduced from it for the theory of heat”

My question is simple. Clausius expesses his fundamental proposition as follows: "In all cases in which work is produced by the agency of heat, a quantity of heat is consumed which is proportional to ...
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0answers
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Is the Vlasov equation a good kinetic equation for solids or even liquids?

Suppose we know the intermolecular potential $V(r-r')$ acting between the positions $r,r'$. Then we have the kinetic equation for a one-particle Distribution function $f(r,p,t)$ given by: $\frac{\...
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1answer
88 views

Regarding the Boltzmann entropy formula, is the Boltzmann constant really arbitrary?

In the top answer to this question (Is the Boltzmann constant really that important?) I read that the Boltzmann constant is just a dummy factor which converts energy to temperature. But that allows ...
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1answer
75 views

Kinetic Molecular theory ideal gases, deriving the equation $PV = \frac{1}{3}mN C^2$

The problem I have with this proof is how to acquire the fraction $\frac{1}{3}$. In theory we were taught by taking into consideration a rectangular vessel which obviously has three paths which a ...
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68 views

Ideal gas equation vs Kinetic theory equation

From the ideal gas equation: $PV = NkT$, since Pressure times Volume = Energy, my understanding is that the total (internal) energy of $N$ molecules of a gas $= NkT$. However from the kinetic theory ...
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1answer
59 views

What is the PDF of relative collision speeds in an ideal gas?

In the Kinetic theory of gases, the speeds of particles follow a Maxwell-Boltzmann distribution. However, what if one is interested in the distribution of relative collision speeds, aggregated over ...
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1answer
482 views

Derive the kinetic gas equation [closed]

I need a proof of high school level I have confusion in taking probabilities in all directions not yet concluded this, and I need a proof using momentum i.e I need a high school level proof
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55 views

Feynman's argument that at thermal equilibrium average kinetic energy of two gases are same

I had a hard time following Feynman's argument that when two different gases are present in the same box their average kinetic energy is the same at equilibrium. To quote from his book: ....Next, ...
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1answer
21 views

Why does setting kinetic energy equal not work in inelastic collision?

From my understanding, in an inelastic collision there is no loss of kinetic energy. So if we take the following problem: A 7700kg car is traveling 18 m/s and strikes a second car. The two stick ...
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1answer
70 views

Mixing 2 non-reacting gas of different temperature

Can we theoritically calculate the final temperature of 2 non-chemically reacting gases(say A and B) by modelling their collision as elastic collision and finding the net root mean square velocity. I ...