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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478 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 ...
8
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1answer
2k views

Are two thin blankets significantly warmer than a single thick blanket?

Almost every source I can find online maintains that two 0.5 cm blankets are significantly warmer than a single 1cm blanket due to air trapped between the thin blankets. However, the thermal ...
6
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4answers
872 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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2answers
1k views

Why do moving particles emit thermal radiation?

While answering another question about heat in an atom, the discussion in the comments led to the question of how heat is related to thermal radiation picked up by infrared cameras. The answer is that ...
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1answer
1k views

Collision frequency at surfaces

Collision frequency for particles in gases is well known, and collision theory is used to derive chemical reaction rates in gases, (and particles in liquid solutions as well). Using the mean velocity ...
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406 views

What physical processes may underly the collisional term in the Boltzmann equation, and how do they increase entropy?

Consider particles interacting only by long-range (inverse square law) forces, either attractive or repulsive. I am comfortable with the idea that their behavior may be described by the collsionless ...
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166 views

What information is lost in the symmetrization necessary to derive the BBGKY hierarchy?

The book on Kinetic theory I'm reading derives the BBGKY hierarchy after introducing the reduced distribution functions $f_s(q^1,p_1,q^2,p_2,\dots,q^s,p_s):=\int\ \rho\ \ \mathrm d q^{s+1} \mathrm d ...
5
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2answers
100 views

Influence of choice of statistics on gas kinetics

In the derivation of distributions over energy states, a common assumption made is that under normal conditions (normal from a fluid dynamics standpoint, so > 300K typically) the energy states are ...
4
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2answers
119 views

Can the Sun's core be treated as an ideal gas?

I know that a gas behaves more like an ideal gas at higher temperature, and that is very well achieved in the Sun's core. But also low pressure is needed for a gas to behave like an ideal gas, and the ...
4
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4answers
421 views

Understanding Heat

Heat or thermal energy as understood is nothing but motion of molecules of the matter. If the molecules are tightly bound (in case of solids), it is to-and-fro molecular vibrations, otherwise it is ...
4
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4answers
207 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 ...
4
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1answer
264 views

Does the kinetic theory of gases means gases mix almost instantaneously?

This theory has bugged me ever since my first physics class on the subject. If this (http://en.wikipedia.org/wiki/Kinetic_theory) is true, it leads me to a few weird conclusions. Opening the rear ...
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52 views

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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115 views

Cauchy Problem for Boltzmann Equations

One of the first profound analysis about the solutions of the Boltzmann Equation was given by DiPerna and Lions in the late 1980s. You can find one of their main papers here: ...
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2answers
261 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.
3
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1answer
153 views

Why is the $\langle v_{x}^{2} \rangle=\frac{1}{3} \langle v^2 \rangle$?

For a randomly moving particle. Or, I suppose that 1/3 could generalise to 1/n, where n is the non rotational degrees of freedom for that particle. Related reference Kinetic Theory of Gasses.
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4answers
1k views

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 ...
3
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1answer
124 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 ...
3
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1answer
115 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 ...
3
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3answers
193 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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365 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 ...
3
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2answers
147 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 ...
3
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2answers
154 views

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 ...
3
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2answers
231 views

Probability Density Function for Dust in the Colision-less Vlasov equation

My problem is the following: I'm trying to model a dust (pressure-less relativistic gas) in the presence of electromagnetic field using colisioness vlasov-equation (relativistic version of boltzmann ...
3
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2answers
101 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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3answers
22k views

How to deduce E=(3/2)kT?

It says in my course notes that a particle has so-called "kinetic energy" $E=\frac{3}{2}kT=\frac{1}{2}mv^²$ Where does this formula come from? What is k?
2
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2answers
1k views

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: ...
2
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1answer
4k views

formula for mean free path in two dimensions

I'm running some simulations of particle collisions in two dimensions with discretised time and space. In essence, particles only collide if they occupy the same location (cell) at the same time step. ...
2
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1answer
129 views

Integral related to particle diffusion

In the context of particle diffusion, I am trying to understand the equations that describe Brownian motion as a macroscopic process. Assume $N(x,t)$ is a number concentration and $D$ is a diffusion ...
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3answers
843 views

Why is a hot air balloon “stiff”?

1) Why is a hot air balloon stiff? 2) Is the pressure inside the balloon higher than the pressure outside (atmospheric pressure)? 3) If the pressure inside is higher than the outside, how is it ...
2
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1answer
131 views

Ergodicity of the Drude model

The Drude model of electric conduction in solids deals with independent free electrons subject to random collisions with the crystal lattice (the direction where the electrons are scattered after a ...
2
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1answer
305 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} \, ...
2
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1answer
727 views

Question regarding Drift velocity in general?

The derivation of drift velocity in case of electrons is equivalent to the case of an charged ionic gas and therefore all the arguments also apply there. Now for an ideal "ionic" gas which interacts ...
2
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1answer
185 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 ...
2
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1answer
64 views

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 ...
2
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1answer
172 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 ...
2
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1answer
151 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 ...
2
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1answer
2k views

Heavy vs Light Particle Ideal Gases

Assume there are two ideal gases. The first is made of a light particle, and the second is made of a heavy particle. The two are of the same amount, in the same volume container, and at the same ...
2
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1answer
66 views

Is the diffusion coefficient for a macromolecule sensitive to mass?

Suppose I have two neutrally-buoyant macromolecules diffusing in water. They have the same radius of gyration (i.e. same root-mean-square distance from their center of mass), but one of them is ...
2
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0answers
26 views

Mean free path in spherical coordinate

I am thinking about a distribution with spatially inhomogeneous cross section in spherical coordinate. Starting with 1-dimensional case, a change of the flux passing through a slab with length $dx$ is ...
2
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0answers
98 views

How to formally write down the Boltzmann equation?

Can someone write down the Boltzmann equation, not neglecting any of the variables of the involved functions and integrals? Specifically, how to concisely capture the "primed" variables in a sensible ...
2
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0answers
165 views

Confined in a box, what is the average distance between a particle hitting a side?

This particle, alone in the box, at a constant velocity $v$, travels in straight lines until hitting a side of the hollow cube, bouncing off in a random direction independent of incident angle (I know ...
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3answers
122 views

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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1answer
45 views

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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1answer
83 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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1answer
65 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 ...
1
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1answer
220 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 ...
1
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1answer
711 views

Expression for kinetic energy of gas per molecule

The average kinetic energy (KE) per molecule of a gas is $\frac{3}{2}kT$. While finding this we do $$ \text{ Average KE} =\frac{1}{2} M \frac{1}{N}\sum v^2=\frac{3}{2}kT$$ But why do we not add ...
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2answers
407 views

naive question on Boltzmann equation and conservation laws

The Boltzmann equation in absence of external force reads: $\frac{\partial f}{\partial t} + \vec{v} \cdot \frac{\partial f}{\partial \vec{r}} = \left( \frac{\partial f}{\partial t}\right)_{coll}$ ...
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2answers
147 views

Photon gas kinetic theory

Suppose a black body as an enclosure of volume $V$ with a hole of section $A$. In the interior there is a photon gas, whose energy density $u$ is, at temperature $T$. $$ u=cT^4$$ How can I show that ...