Kinetic theory is part of statistical physics. DO NOT USE THIS TAG for macroscopic kinematics. In this case, use the tag [tag:kinematics] instead.

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Physical reason why Prandtl number is order unity for gases?

Is there a physical reason behind the fact that for gases the thermal diffusivity is on the same order of magnitude as kinematic viscosity (and as such a Prandtl number of order unity) and if so what ...
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51 views

Is the pressure-gradient force an entropic force?

A gas flows from an area of high pressure to an area of low pressure when there are no other forces preventing it. From a macrosopic perspective you have to infer that an underlying force is ...
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51 views

Difference between semi-classical Maxwell Boltzmann Statistics and Boson Statistics

Since semi-classical MB assumes the indistinguishability of particles and Boson Einstein statistics similarly treats degenerate states as indistinguishable states. What is their difference when ...
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What is the relation of particle velocity, temperature, and reaction activation energy

So, this curiosity has arisen for a fun project I thought I'd tackle, where I'm attempting create a crude simulation of an internal combustion cylinder. I wanted to explore the particle level ...
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37 views

Dependence of average speed of molecules of gaseous mixture

We know that the average speed of gases in a single gas chamber is given by $\sqrt{8RT/\pi M}$ where R is universal gas constant,T is temperature,M is molar mass of gas. But what if we mix two gases ...
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52 views

Kinetic Energy of a system of ideal gas

For a nuclear fusion reaction in which goes as follows: $${}^2_1H + {}^1_1p \to {} ^3_2He + \gamma$$ If we assume that the mixture of deuterium nuclei and protons behave as an ideal gas, then can ...
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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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67 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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20 views

How does gas friction emerge?

The fluid parcel model states that a gas can be modelled as the sum of infinitesimal small parcels. According to this model, the friction of a gas with a solid surface (e.g. the wall of a pipe) ...
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52 views

isothermal compression of water and definition of temperature

During isothermal compression of water vapour (below critical temperature), the pressure increases initially, and then remains constant up to certain point, and then steeply increases with small ...
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27 views

Dilemma on work done by gas in isothermal contraction

Consider an ideal gas inside a cylinder undergoing reversible isothermal contraction. Now if we consider the forces acting on the gas inside the cylinder the force acting is $P_{ext}\cdot A$, however ...
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227 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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48 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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59 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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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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134 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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70 views

Diamonds are not forever?

It is frequently stated that although graphite is the more stable allotrope of carbon at STP, the activation energy of the diamond-to-graphite transformation is so high that our diamonds will never ...
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Equation of Motion from Vlasov Equation

From the Vlasov equation $$\frac{\partial f}{\partial t} + \vec{v} \cdot \nabla f + \vec{a} \cdot \frac{\partial f}{\partial \vec{p}} = 0$$ we can obtain the momentum transport equation by ...
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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 ...
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109 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 ...
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195 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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31 views

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 $K_E=\dfrac{3}{2}kT$: ...
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30 views

probability of striking the circular ring by gas molecules

In kinetic theory we use probabilistic case to derive pressure, no. Of molecules having speed c to c+dc or in such cases.and to derive such equations we introduce a term called "SOLID ANGLE" I come ...
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33 views

Gas diffusion through a flat plate boundary layer

Set-up Suppose we have a flat plate with a flow of gas parallel to the plate. The flow creates a boundary layer on the surface of the plate. Now, the gas is carrying a reactive species, which is ...
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Mean free path in 2d?

Let us say we have a collection of $n$ stationary balls per square meter each of diameter $d$ and we roll an identical ball between them. Then what is the free mean path of this ball? My ...
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Comparing relative velocities and kinetic energy

If object one is moving $0\frac{m}{s}$ relative to the Earth and object two is moving $1\frac{m}{s}$ and they both have $1kg$ of mass, then object one has no kinetic translational energy (relative to ...
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29 views

Boltzman equation for a collisionless medium?

In the derivation of the Boltzmann equation (link to Wikipedia) for a collisionless gas it is assumed that: $$f(\vec r+\frac{\vec p}{m} \Delta t, \vec P + \vec F \Delta t, t + \delta t)=f(\vec r, ...
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Is there a theoretical maximum speed for wind?

What we call wind is actually molecules moving into an area of lower particle density due to their thermal motion. A lower particle density offers less collisions (resistance), so more molecules move ...
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Confusion about radioactivity

The following question is from General Problems on Physics by I.E Irodov 6.220. Find the decay constant and the mean lifetime of $^{55}\operatorname{Co}$ radionuclide if its activity is known to ...
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109 views

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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58 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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65 views

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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77 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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190 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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Height of a piston in a heated cylinder containing H2O

I'm a first time user and I hope I won't be too enigmatic asking the following question: I have a cylinder (radius= $6$ $\text{cm}$) with a frictionless piston on top of it and inside $30$ $g$ of ...
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274 views

Simple: What do these ballistic impact numbers represent?

I bought physics for game programmers, found here, today to study ballistic impact, but I'm confused as to where a few numbers are coming from. I'm basically looking to understand what the values ...
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Modeling stilts with equations

I'm trying to make a set of stilts 20 ft in the air that someone could wear to run/jog with, but I was advised that I should first start by modeling the system (user + environment + stilts) in the ...
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19 views

Is there a temperature drop at the rotor plane of a wind turbine?

A wind turbine rotor produces power from the torque generated by the rotor blades. This torque arises from forces on blade elements which in turn are the consequence of pressure differences on each ...
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Average Rate of Evaporation of Water

Consider a container of volume $V$ and cross sectional area (exposed to another fluid, say air) $SA$. The container is at constant temperature $T$, and contains $N$ molecules of water, where $N$ is ...
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17 views

What is the velocity of a given ion in aqeous solution?

I have seen many calculations of the velocity of X element in air at a given temperature. It has a nice closed equation: v(O2) = √ (3kT/m) However I am unsure where to look for the velocity of ions ...
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Diffusion coefficent for a mixtures gases?

In the Pauli Lectures on physics volume 3 it is stated that for gas mixtures the diffusion coefficient is given by: $$D=a'' \frac{1}{n} (n_1 \bar u_1 l_1 + n_2 \bar u_2 l_2)$$ Where $n=n_1+n_2$. How ...
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63 views

How much do we know about the characteristic time for electron-ion recombination for a dense plasma?

As mentioned, how much do we know about the characteristic time for electron-ion recombination for a dense (noble gas) plasma (i.e. density of electrons at $\approx 10^{21} \textrm{cm}^{-3}$) at ...
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39 views

Gaussian acceleration of magnetic/nonmagnetic balls

https://youtu.be/CoHGGZfERE0?t=19s In this video, 19 seconds in, a nonmagnetic ball (henceforth just called a ball) is launched slowly at a static magnetic ball butted up against another static ball. ...
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123 views

pascals law of liquids in terms of kinetic theory of molecules

Suppose a cylindrical container of base area A filled with water is carrying a piston on top. If the piston applies no force on the liquid, assume the pressure is P for a point located on the boundary ...
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264 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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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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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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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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485 views

How does the volume change affect an adiabatic process?

A gas consisting of rigid diatomic molecules was initially under standard conditions. Then the gas was compressed adiabatically, 5 times the original volume. Find the mean KE of rotating molecules ...