# Linked Questions

29 questions linked to/from Visualising gas temperature and gas pressure
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### Relativity of temperature paradox

The imagined scenario: Part A: From special relativity we know that velocity is a relative physical quantity, that is, it is dependent on the frame of reference of choice. This means that kinetic ...
3answers
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### What is the correct relativistic distribution function?

General Statement and Questions I am trying to figure out the proper way to model a velocity/momentum distribution function that is correct in the relativistic limit. I would like to determine/know ...
3answers
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### Why are ions and electrons at different temperatures in a plasma?

In plasmas, the collision rate among ions or electrons is much larger than the collision rate between ions and electrons. Why is that so?
2answers
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### Why in plasma physics usually is given the refractive index of electrons but not for ions?

What is the refraction index of ions in plasma ? And why people do not discuss it in books ? Is it that it is not important for plasma phenomena ?
2answers
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### Maxwell velocity distribution, in 1D or otherwise

I learned from my textbook that Maxwell's velocity distribution gives: $$v_{rms} =\sqrt{\frac{3kT}{m}}$$ $$v_{avg} = \sqrt{\frac{8kT}{\pi m}}$$ Presumably this is for a three dimensions. This confuses ...
1answer
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### Differences between thermal and non-thermal plasmas

I have a doubt about plasmas which may as well be trivial or very stupid, but I couldn't get a clear and straightforward answer anywhere I looked, and I can't get the grasp of it since I wasn't given ...
2answers
607 views

### What defines a cold plasma?

Been looking for this very simple answer for a while now, and google returns a face cream with the words cold plasma in it. Very frustrated. Just wondering, what constitutes a cold plasma in the ...
1answer
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### Why is the average thermal velocity 0?

Thermal velocity is the velocity of the free electron due to their random motion. So how is the average value 0?
1answer
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### Navier-Stokes Energy Equation

I've been assigned (for homework in a mathematical modelling course) the task of deriving the Navier-Stokes energy equation in one space dimension: Consider a fluid flowing through a cylindrical ...
0answers
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### Limitations of the ideal gas law: When does it fail?

Motivation I ask this question precisely because I am looking for a fundamental, quantitative explanation of the limitations of the ideal gas law and when it should not be used. Note, I have found ...
1answer
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### Maxwell-Boltzmann distribution for transport equations

I have to calculate the transport coefficients for the Maxwell-Boltzmann distribution. But I'm not sure what distribution I have to use. As far as I know it should not be the MB distribution for $v$-...
1answer
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### How to get the moments of the Boltzmann equation?

I'm currently reading through a hydrodynamics lecture course and I'm confused at some of the key integrals that are derived. These integrals aid in deriving the moments of the Boltzmann equation. ...
1answer
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### Difficulty in understanding Maxwell Boltzmann distribution in case on ions in a field

I learned that the velocity of molecules obey Maxwell Boltzmann (MB) distribution at a Temperature T. If I have ions of mass 'M' accelerated to 2eV in a specific region. As the ions are not "...
1answer
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### Refractive index of plasma dependance on temperature

How does the refractive index of plasma changes with temperature? Temperature is not high enough for new ionization. Would it be like in gas p/T dependence ? http://farside.ph.utexas.edu/teaching/em/...
0answers
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### Statistical mechanics - average particle energy, average kinetic energy

I'm looking at derivations for average particle energy giving $E=kT$: http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/bolapp.html And average particle kinetic energy giving $K_E=\dfrac{3}{2}kT$: ...
1answer
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### Conceptual problem on Maxwell's velocity distribution law

I already read about Maxwell's velocity distribution law for gas molecule. And the expression for that distribution is following dnc=4πnA^3e^(-bc^2)c^2dc Now if we assume that the molecules have no ...
2answers
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### Velocity from the cumulative distribution function of the Boltzmann distribution [duplicate]

I want to get a Boltzmann distribution of the $v_x$, $v_y$ and $v_z$ velocity components (please, notice that the distribution is one-dimensional). To do so, I need the cumulative distribution ...
1answer
447 views

### What causes polarization current density in plasma?

Plasma current density is defined as $\textbf{j}=-\mathrm{e}n_e\textbf{u}_e$ where $\mathrm{e}$ is electron charge, $n_e$ is electron concentration and $\textbf{u}_e$ is electron velocity. What ...
1answer
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### What's the loss of information in taking the moments of the Vlasov equation for the Particle-In-Cell method

I know that when deriving the hydrodynamic equations from Boltzmann's equation we take the first three moments along momentum space to get the conservations laws. Taking infinitely many moments would ...
1answer
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### Can't prove that Fast Magnetosonic Wave's proper speed is given by the following formula

So, suppose a magnetosonic disturbance, it is proven that (You can also see it in Richard Fitzpatrick's Plasma Physics online text), that the Fast Magnetosonic Wave is equal to \begin{equation} \dfrac{...
2answers
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### How many temperatures has a plasma?

In nonthermal plasma, not all particles move in the same way. The electrons are different from other particles. Both can be described as having a temperature separately. But that would mean, one piece ...
0answers
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### Feynman Lectures I 40: Is the homogeneity of the Maxwell-Boltzmann distribution a result of, or a pre-requisite for its derivation?

I refer to hand-waving a lot in this post. That is not to say that it was in appropriate. Feynman pretty much said at the outset that his treatment of thermal physics was going to be less than ...
0answers
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### How to calculate the RMS speed of plasma?

I know the RMS (root mean square) speed of gas is calculated with $v = \sqrt{\frac{3RT}M}$, and plasma is very similar to gas, so is there a difference? If so, how do you calculate it?
1answer
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### Can a compressible fluid flowing , change its speed in the absence of a pressure gradient?

I've heard that in a high velocity nozzle, any random 'fluid particle' experiences an increase in kinetic energy at the cost of internal energy and pressure energy.And I do understand that for any ...
1answer
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### anistropic or asymetric particles distribution

As a preamble, I have several questions and I know that is preferable to ask one question per post, but they are really linked together. This is why I chose to ask them together. I am considering a ...
1answer
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### 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)...
1answer
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### Jeans equation for a spherical equilibrium

I am currently studying the Jeans equation for a system in spherical equilibrium. Since the distribution function $f(x,v)$ can be written in depency of energy and angular momentum $f(E, L)$ it seems ...
0answers
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### When can we say $x$ and $p$ are “independent variable”, in order to find the Vlasov equation?

I have a question about "independent variable" in physics, and especially variable in Lagrangian or Density Function. I read several questions about it in this forum and although I have the feeling I ...
1answer
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### Do plasmas really not experience a $\nabla \vec B$ drift even though the individual particles do?

I'm currently working through Chen's Introduction to Plasma Physics and Controlled Fusion, and I just got to the chapter on the fluid theory of plasmas. Chen claims that the $\nabla\vec B$ drift does ...