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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How to derive entropy transport equation from heat equation?

Suppose I have heat equation: $$ \rho (\partial_{t} + (u \cdot \nabla)) T = -\nabla \cdot \mathbf R, $$ where $\mathbf R$ - some vector and $T$ - temperature. How to get the equation for entropy $S$ ...
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If one were to have boots made of Vibranium, could one jump from any height? [on hold]

Vibranium is a fictional metal from the Marvel universe, with interesting properties, it "possesses the ability to absorb all vibrations in the vicinity as well as kinetic energy directed at it." It ...
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204 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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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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Error in mathematics of collision theory

I'm making lecture notes, and I felt that it would be important to explain some of the math behind collision theory. I come up with a problem, however. Here, I'm trying to show that the collision of ...
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69 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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59 views

Is Kinetic Theory part of Statistical Mechanics?

Some years ago from now I've seem some basic details about what was then called "kinetic theory of gases" where the study of property of gases was made by statistical considerations about the momentum ...
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38 views

Why Benard cells are usually hexagonal?

Solution of equations of convection (hydrodynamics equations in Boussinesq approximation) involves existence of convective cells, so-called Benard cells. They are represented by superposition of ...
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Partial pressures - beyond the concept of point masses

Imagine that I have 100 atoms of oxygen and 100 atoms of lead put together in a container. By kinetic theory of gases, they should be considered as point masses thus the partial pressure of oxygen ...
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69 views

Drifting Maxwellian distribution for energy

Assume I have a drifting Maxwellian distribution with velocity $\vec{a}$, say, in the x-direction, so something like $$ f(\vec{v}) = n\left(\frac{m}{2\pi ...
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364 views

Momentum change in collisions (Drude model)

A particle suffers elastic collisions with scattering centers with a probability of collision per unit time $\lambda$. After a collision the particle is in a direction caracterized by a solid angle ...
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37 views

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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59 views

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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On non-local physics in cosmology by prof. B.V. Alekseev

Recently I've encountered work by prof. B.V. Alekseev, in which he claims that some physical problems can be easily solved if we consider non-local interactions in kinetic theory (interactions of ...
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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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165 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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98 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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2answers
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How can I explicit the energy dependence of the Maxwell-Boltzmann distribution?

I'm having a bit of a problem figuring out the energy dependent Maxwell-Boltzmann distribution. According to my book (Ashcroft & Mermin) they write the velocity dependent distribution as: ...
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Accuracy of the Boltzmann equation

I have had this question for some time now. Hopefully someone can answer it. I know that the Boltzmann equation is widely regarded as a cornerstone of statistical mechanics and many applications have ...
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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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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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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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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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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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69 views

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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50 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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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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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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124 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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155 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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308 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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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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1answer
70 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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38 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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333 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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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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34 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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1answer
36 views

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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271 views

How to derive the two-term approximation for the Boltzmann equation?

Starting with the Boltzmann equation in terms of $f(t,\vec v,\vec x)$ or $f(t,\vec v)$ http://en.wikipedia.org/wiki/Boltzmann_equation $$\left(\frac{\partial}{\partial t} + \vec{v} \, ...
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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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55 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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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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1answer
56 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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47 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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1answer
55 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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35 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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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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286 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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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 ...