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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Finding the approximate distance between molecules in a gas

I have a problem to understand why the below derivation can be used to find the distance between molecules: This example is an approximation. We are supposed to find the average distance between the ...
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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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Integral over a surface in kinetic theory [closed]

I am working with some kinetic theory. I have the distribution function $\Psi (\vec{r},\vec{p},t)$, Where $\vec{r}$ is the radius vector, $\vec{p}$ is the unit vector of orientation, and $t$ is the ...
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Why is there no change in speed of a charged particle in a uniform perpendicular magnetic field?

When the initial velocity is perpendicular to the magnetic field, the force acting on the charged particle F = qvBsin(theta) ...
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How are smoke cells an example of Brownian motion?

I don't get how smoke cells are an example of Brownian motion.
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How to explain the Venturi effect with Kinetic Theory?

From a macroscopic perspective a fluid flowing through a pipe gets accelerated when the pipe's cross section gets narrower. According to $F= ma$ a force must be present to do this. This force is ...
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358 views

Why do we ignore rotational energy in monatomic gases? [duplicate]

I understand that the average energy of each degree of freedom in a thermodynamic system is $\frac12kT$. And so, for an ideal monatomic gas, there are three degrees of freedom associated with the ...
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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 ...
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30 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 ...
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63 views

Why does the temperature of a gas inside a moving container not increase with velocity?

A rectangular (simplified) container with rigid surfaces, has a certain mass of ideal gas within it, and it accelerates in free space, undergoing rectilinear motion. There are no dissipative ...
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31 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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momentum and Kinetic Energy [closed]

Make some general statements about momentum and kinetic energy conservation. So, I is this correct? Two objects of varying mass have the same momentum. The least massive of the two objects will have ...
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Calculating average quantities in kinetic theory

Consider a volume $V$ with $5$ particles each of mass $m$ at positions $\mathbf{q}_i=(x_i,y_i,z_i) \in V$ and with velocities $\mathbf{v}_i=(u_i,v_i,w_i)$. The speeds of the particles are between $0$ ...
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How can I compute the average number of collisions of a particle in a spherical container? [closed]

I have to compute the average number of collisions per unit time of a particle in a spherical container. These collisions are diffuse, i.e., after colliding, the particle bounces off the inner walls ...
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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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51 views

Why covering our nose with a cloth or nose mask reduces stale smell?

Whenever there is a stale smell in air, we tend to use a cloth(maybe a handkerchief) instantly to get away with it. Why does a cloth or a mask reduce the intensity of a stale smell? Are the "smell" ...
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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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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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73 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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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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113 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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154 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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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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281 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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72 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 ...
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110 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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130 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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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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126 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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52 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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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 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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58 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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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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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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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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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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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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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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58 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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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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286 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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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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491 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 ...