Kinetic theory is part of statistical physics. DO NOT USE THIS TAG for macroscopic [kinematics](http://en.wikipedia.org/wiki/Kinematics). In this case use the tag [tag:kinematics] instead.

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Multiple ways to solve Boltzmann equation [on hold]

I am studying about the Boltzmann equation and I am little confused on the different approaches on how to solve it. I know there are 2 main ways: analytical and numerical (DSMC). I also know that the ...
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Liouville's Theorem and Boltzmann equation for plasma

The Boltzmann equation for a plasma can be thought of as coming from a continuity equation in the 6 dimensional phase space of the plasma with coordinates $\left\{x,y,z,v_x,v_y,v_z \right\}$. So ...
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What is the gas entropy as a functional of a one-particle distribution function?

There are some discrepancies on how to introduce entropy in classical kinetic theory. In what follows $f(r,p,t)$ is the usual one-particle distribution function of a monatomic gas, normalised to the ...
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How can I determine the pound-force behind a punch?

I am a martial arts instructor always looking for the next best way to enhance the performance of my students. However, I'm having difficulty understanding how to determine the pound-force (ibf) of a ...
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Accessible system where specific heat and thermal conductivity vary in different ways?

I'm teaching undergrad thermo this semester and to my surprise several students are having trouble conceptualizing heat capacity and thermal conductivity as different properties; they can apply them ...
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97 views

Why don't the collisions of the particles in a gas affect its temperature?

Temperature is defined as the mean kinetic energy of the system. Now the particles are constantly colliding with each other; as a result of which kinetic energy of each particle changes. ...
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68 views

Average kinetic energy of molecules hitting a surface

I am trying to prove that the average kinetic energy of gas molecules hitting a containers surface is $2k_{B}T$ instead of the average for the entire gas, which is $\frac{3}{2}k_{B}T$, where $k_{B}$ ...
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What is isotropy actually & how does it ensure that exactly same number of molecules will move in either sides?

Kinetic theory is also an example of isotropy. It is assumed that the molecules move in random directions and as a consequence, there is an equal probability of a molecule moving in any ...
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26 views

What kind of force comes into play when two molecules of a gas collide?

As per kinetic theory there is no force of attraction or repulsion between two molecules of a gas except when they collide. So, what is that force which is realized during collision with wall or ...
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90 views

Is temperature affected by gravitational potential?

Ok, I feel a bit silly asking this. I'm asking in relation to this question here on the molecular basis of hydrostatic pressure in a gas. There's been quite a bit of discussion and one of the ...
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49 views

Doesn't the gas molecule hit the opposite wall during the time $\Delta{t} = \frac{2L}{v_x}$?

We should include only those accelerations that are caused by the piston, not those caused by the opposite side. The best way to accomplish this is to take $\Delta{t}$, exactly the time it takes ...
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assumption of molecular chaos and the Loschmidt paradox

The assumption of molecular chaos says the velocities of two colliding particles are uncorrelated and also independent of time. Boltzmann actually used this assumption in his formulation of the ...
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173 views

More detail on why pressure increases at the bottom of a column of gas

The question Why does the air pressure at the surface of the earth exactly equal the weight of the entire air column above it asks why the air pressure at any elevation is equal to the weight of the ...
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42 views

What does the temperature of the early universe tell me?

I am re-reading Weinberg's book "The First Three Minutes". In the Introduction he makes this statement: "At about one-hundreth of a second, the earliest time about which we can speak with any ...
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1answer
49 views

Measuring the viscosity of a gas

A method to measure the viscosity of a gas uses two vertical coaxial cylinders, with the gas confined between them. The inner cylinder has radius $a$, whilst the outer cylindrical shell has inner ...
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1answer
110 views

Kinetic theory derivation of viscosity of a gas

Encountering a lot of issues trying to understand this. The basic idea of the derivation I'm using is as follows (the image here may help): I'm going to write $<u_x>$ as the general horizontal ...
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1answer
58 views

Flow rate of gas down a pipe at low pressures

I'm trying to understand an 'approximate derivation' of the flow rate of gas down a pipe at low pressure from my book (an example problem). It uses the result that the flux of a gas is given by ...
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22 views

Dependence of kinetic friction on relative velocity

While I was reading my book I came across a line that tells that there is slight dependence of kinetic friction on velocity of relative motion of the bodies. Can anyone tell me how is this so?
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Applying Statistical Mechanics to Formulate Corrosion (Rusting)

I wanted to try and take my current knowledge of statistical mechanics (first quarter undergraduate course completed, beginning researcher in far from equilibrium statistical mechanics, basic ...
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116 views

Conservation of kinetic energy in collision

Why is kinetic energy conserved in collision between glass balls while it is not conserved in collision between a ball and floor?
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57 views

How can kinetic energy be conserved in an elastic collision

How can kinetic energy be conserved in an elastic collision as collision is said to occur between two bodies if they physically collide against each other or if the path of one of then is affected by ...
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36 views

Randomness of submolecular phenomena

Why do models of submolecular phenomena involving randomness work? Do these phenomena appear random to other submolecular particles? For example, people can use Einstein-Smoluchowski to characterize ...
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31 views

Extreme temperatures, relativity and kinetic theory

According to kinetic theory, average kinetic energy is proportional to temperature. Supposing $k_BT/2$ per particle, can we use relativity and kinetic theory to calculate, e.g., the temperature and ...
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1answer
33 views

Kinetic theory of photon gasses

I have recently attempted to derive a fully functional non-handwavy derivation of the photon gas energy density without having to interpret some mass term such as $mc^2$ as the "photon energy". My ...
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2answers
136 views

$E=kT$ or $\frac32kT$?

Basically, which is the correct formula for thermal energy, and is this the same as kinetic energy? My notes are pretty conflicting on this topic, and I'm getting pretty confused.
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Is it possible to describe the geometric mean of the Maxwell-Boltzmann distribution?

This may be a more appropriate question for the Mathematics stack exchange, if so forgive its extraneousness. We know the expected value of the distribution, analogous to the weighted arithmetic mean ...
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49 views

Evaporation of water at room temperature

Could anybody refer me to some literature (textbooks or research, although preferably textbooks!) dedicated to explaining quantitatively the phenomenon of evaporation of fluids? I understand that it's ...
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278 views

Difference between heat and work

According to the Kinetic Theory of Matter, temperature is nothing but a measure of the kinetic energy of matter. My textbook says that the change in internal energy of a system is the heat gained plus ...
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How does one determine the breakdown voltage of a solid-in-liquid suspension?

So I'm doing a project in which we are supposed to collect micro-scale conducting metal particles from a suspension of it in water (which is deionized). Suppose that I am charging the particles ...
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54 views

Difficulty with Feynman's chapter on kinetic theory of gases

I have been reading Chapter 39 of the Feynman Lectures in Physics. In this section he argues that collision between gas molecules will mix up their directions of motion such that ultimately any ...
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45 views

Recombination time for ionized atoms in a low pressure gas?

I am looking into some new physics and had the following question come up: You have a neutral gas of let's say, CO atoms at 1 nanoTorr. An electron(s) comes passing through the gas ionizing only 1% ...
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54 views

How can momentum changes from individual collisions be considered as a whole?

I have a question about deriving the equation of kinetic theory of ideal gas $$PV=\frac{1}{3} Nmc_r^2$$ where $N$ is number of atoms, $c_r$ is root mean square of atom speed and $m$ is mass of one ...
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33 views

Ideal gas and inelastic collisions

Why is it necessary that all inter-molecular collisions in an ideal gas be elastic? My understanding is that a gas behaves ideally so long as the potential energy arising from inter-molecular ...
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68 views

Effusion of particles from one box to another - pressure calculation

Suppose we have a container divided into equal halves. Right half is fixed at temperature $T$, volume $\frac{V}{2}$. Initially it has pressure $P_0$, a hole of area $A$ is opened between them. I ...
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310 views

Kinetic proof of law of mass action

Suppose we have a chemical reaction of the form $$n_1 A_1 + \cdots + n_r A_r \leftrightarrow m_1 B_1 + \cdots + m_s B_s$$ where $A_i$ and $B_i$ are molecules, and the $n_i$ and $m_i$ are the integer ...
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240 views

Speed distribution in 1 dimension

In 3D, the maxwell velocity distribution is: $$f = \left(\frac{\alpha}{\pi} \right)^{\frac{3}{2}} e^{-\alpha v^2} d^3 \vec v$$ To get the speed distribution in 3D, we simply expand $d^3\vec v = 4\pi ...
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Gillespie's stochastic framework valid for particles in aqueous solution?

Gillespie proposed a stochastic framework for simulating chemical reactions which is predicated on non-reactive elastic collisions serving to 'uniformize' particle position so that the assumption of ...
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725 views

Do particle velocities in liquid follow the Maxwell-Boltzmann velocity distribution?

The Maxwell-Boltzmann velocity distribution arises from non-reactive elastic collisions of particles and is usually discussed in the context of the kinetic theory (for gases). There are various ...
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Degrees of freedom of particles in Lattice Boltzmann method

Is it true that in Lattice Boltzmann method particles have only one degree of freedom even in 3D case? Can someone explain that fact or provide a link? Thanks!
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1answer
159 views

Taylor expansion in Lattice Boltzmann Method derivation

Currently I'm trying to understand Lattice Boltzmann Method for solving CFD problems. In its derivation BGK approximation is used to get rid of complicated collision integral. But when they come to ...
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447 views

If temperature is average KE per particle, and heat is total KE of all the particles, how can molar heat capacity vary?

If temperature is defined as the average kinetic energy per particle, and heat energy is defined as the total kinetic energy of all the particles (or more strictly, heat transferred is the total ...
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1answer
37 views

Kinetic energy of a gas molecule

I am working through the derivation of the equation $$pV=\frac13mNC_{rms}^2,$$ but relating to this formula my textbook states that the kinetic energy of an average molecule of gas is given by ...
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59 views

Relative change in drift velocity

Consider an ensemble of electrons which all experienced a collision at time $t=0$. Let $n(t)$ denote the number of electrons in this ensemble. Assume that the number of electrons $\mathrm{d}n$ from ...
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113 views

Is there a known equation for evolution of classical particle probability density?

Suppose we have some very imprecise knowledge of classical particle's coordinates and momentum: what we can only tell is the probability density to find it in some point of phase space. This is ...
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2answers
114 views

Three-body correlation function in kinetic theory

In Kinetic Theory, one studies the evolution of a system of $N$ particles interacting with each other. We use the notation $\boldsymbol{w}_{i}$ to describe the coordinates in phase-space of each ...
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1answer
137 views

Calculating elastic energy constant [closed]

I ran into a kinetic physics problem: "A spring is hanging on the ceiling. Let's place an object 'M' at the end of the spring. Yet hold 'M' so the spring doesn't stretch. The distance between the ...
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How to approach this kind of task about kinetic energy? [closed]

The bullet with mass $$m_{ball}=0.2 kg$$ travels with speed $$v=2 \frac{m}{s}$$ and hits Plasticine sphere with mass $$m_{sphere}=2.5 kg$$ and get stuck. I need to find the amount of heat ejected. How ...
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47 views

How close together must air molecules be to bounce off one another?

When, say $\text{N}_2$, is in the wild, it regularly collides with other $\text{N}_2$. I assume these collisions happen as, having become sufficiently close, the atomic electrons are repelled from ...
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77 views

Yearly onshore wind turbine energy production [closed]

I am trying to work out the yearly energy production of an onshore Siemens SWT-3.0-101, hub height 94m, total height 144,5. Here is the power curve at each wind speed level worked out through a ...
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187 views

Molar heat capacity of gas defined by relation $p=kV$

we have this problem where relation between Pressure($p$) , Volume($V$) is defined by relation $$p=kV$$ where $k$ is a constant and we have to find the molar heat capacity of the gas. Note:Ideal gas ...