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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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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Justification of volume of exclusion sphere

How does volume of exclusion signify the excluded volume as in the green lined region between A and B molecules can move (if not the whole volume but a part of volume of neighborhood molecule can move ...
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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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2answers
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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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1answer
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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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1answer
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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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1answer
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Finding the equilibrium vapor pressure of two solutions(of different concentrations) enclosed in a vessel

The saturated vapour pressure above an aqueous solution of sugar is known to be lower than that above pure water, where it is equal to $p_{sat}$, by $\Delta p = 0.05p_{sat}c$. where c is the molar ...
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How heavier liquids settle down?

If we put water and gasoline in a bottle, and shake it, it is not necessary to wait too long to see the two liquids separated, with the water below. I can understand that the potential gravitational ...
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Would changing the geometry of the container of gas change the results of kinetic gas theory?

One of the predictions of Kinetic gas theory is that kinetic energy is a function of temperature but does this conclusion hold for geometries other than a cube? I say cube because if you see the ...
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Why is mean free path independent of mass?

In this page of Hyperphysics, I am puzzled as to why there isn't any mass dependence in the expressions for mean free path. Here are the two equations as mentioned in the website: When only one ...
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In plasma physics what does beam of particles mean

I often hear about a beam of particles on top of a background population in plasma physics. What does exactly beam mean? Is it a subset of particles that belong to a different distribution? What ...
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Relativistically correct velocity moments?

We know that the nth moment of a velocity distribution function (VDF), $f\left( \mathbf{x}, \mathbf{v}, t \right)$, is given by: $$ \langle g^{n}\left( \mathbf{x}, \mathbf{v} \right) \rangle = \int \ ...
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Does "wind speed" depend on the density of air?

Our intuitive notion of "wind speed" is that it is the speed at which air molecules are moving at point. Consider two situations where the velocity of the air molecules are the same but the ...
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What happens to a Maxwell-Boltzmann speed distribution when samples mix?

I have a few questions related to how it changes when two samples mix. How would it change if two identical samples, one with higher KEavg and one with lower KEavg are added together? would the peak ...
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If a system has energy which is inversely proportional to temperature. What can be said about this kind of system. What about its specific heat?

Can we model a canonical ensemble for this system? Please answer this question in context of statistical physics.
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1answer
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How to calculate the free mean path of electrons in the gas mixture?

How to calculate the free mean path of electrons in the gas mixture? I understand (a little bit) the mean free path concept for the atomic collisions but I am not sure what to do if I am interested in ...
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Why does it take so long for a gas to reach a thermal equilibrium?

Imagine a 1m cube of air in an insulated container, where you have heated the air in one half but not in the other. Intuitively, given molecules are moving so fast, you would expect the energetic ...
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Number of interaction of early universe

I am reading An introduction to particle dark matter by Stefano Profumo. I am struggling on a derivation. As given from the text, in the early universe $\frac{\dot{T}}{T}=-\frac{\dot{a}}{a}=-H$, ...
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Does the solar wind blow *through* the moon's atmosphere/exosphere?

The Wikipedia article on "Atmosphere of moon" says: One source of the lunar atmosphere is outgassing: the release of gases such as radon and helium resulting from radioactive decay within ...
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Why $c_p- c_v =R$ is not working in this question? [closed]

If $C_p - C_v = R$ is universally true,why in this question,it is not working? $4.0 \mathrm{g}$ of a gas occupies $22.4\mathrm{L}$ at NTP. The specific heat capacity of the gas at constant volume is ...
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Average speed and RMS speed, given speeds of objects

I am given the speeds of eight objects, and I have to find the average speed and the RMS speed of these objects. I tried taking the actual average of these speeds: $\frac{1}{8}\Sigma(v_i)$, but I get $...
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How is this relation between energy, temperature and number of microstates derived?

In "Concepts in Thermal Physics" (second edition) by Blundell and Blundell, temperature is defined using the following relation: $\frac{1}{k_BT}=\frac{\mathrm{d}\ln(\Omega)}{\mathrm{d}E}$. ...
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Intuition behind order of speeds in kinetic gas theory

In kinetic gas theory, we have the following result for the order of speeds $v_{rms}>v_{av}>v_{mp}$ i.e: the ratio of $1:1.128:1.224$ for the speeds $v_{mp}:v_{av} : v_{rms}$. Definitions (...
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How can mean free path affect the propagation of sound in a gas?

I was thinking, since mean free path is a measure of "how long" a particle has to travel to collide with another, that this surely must influence sound propagation somehow. I would say this ...
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How can kinetic theory be used to verify Dalton's law of partial pressures?

I have been told Dalton's law of partial pressures can be proved from kinetic theory. This is my reasoning for why this might be: Since in kinetic theory there are no forces of attraction between the ...
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The range of velocity in Maxwell Velocity Distribution [closed]

If we see the formula for velocity distributions in x,y, and z-direction their range of velocity goes from -infinity to +infinity but when we take the whole velocity distribution, the range goes from ...
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What is contribution of Rotational Kinetic energy in temperature of gas according to kinetic theory of gasses?

We know that, for one molecule of ideal gas, $U = \text{Kinetic energy} = \frac{f}{2}RT$ where $f$ is the number of degrees of freedom, $R$ is the gas constant and $T$ is the absolute temperature. So ...
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Difference in deriving sound waves in liquids and gases

In our fluids course we derive the small amplitude approximation of waves in both a perfect gas and liquids using the Navier Stokes Equations, Mass Conservation Equation and then: for a perfect gas, ...
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Which physical variables are considered conserved in the solar wind stream?

Can anyone tell me which physical variables are considered conserved in the solar wind stream? I am also trying to know if there is a governing equation that describes them.
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What is the actual meaning of fact used in langevin's theory that averaging and differentiation are commutative?

I am studying Langevin's theory of Brownian motion and in the derivation I came across a statement(1) that differentiation and averaging are commutative i.e $\overline{\frac{d}{dt}x^{2}}=\frac{d{\bar{...
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How accurate is it to use the kinetic gas theory equation of most probable speed on a water droplet?

Find the most probable velocity of a water droplet of diameter $ d= .10 \mu m$ suspended in air at temperature $17C$ -From JEE question bank The solution involves using the most probable speed ...

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