# Tagged Questions

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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### How does potential energy relate to kinetic energy on a rollercoaster?

This is appearantly how the potential and kinetic energy are in the different positions of the rollercoaster, if I am not mistaking. However I don't understand why the total energy is energy and ...
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### Why does warm water sink?

It is well known that water at 4C is denser than water at 0C. This is the usual explanation for why a body of water freezes from the surface (also it's because ice is even less dense, but that's ...
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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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### In kinetic theory when can we ignore forces?

Let us say I have a body of gas for which there is an external force $F$ (which could be say gravity) acting on the particles. What conditions should $F$ satisfy before I can assume that the effect of ...
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### When a gas is compressed by a piston, where is the heat added to the gas?

Suppose an ideal gas is being compressed by a piston inside a cylinder in an adiabatic compression process. Does the gas closest to the piston heat up first as the gas molecules collide with the ...
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### 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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### Why take RMS velocity?

Why do we consider RMS speed of gases in various calculations? For example, I have to find the time for two successive collisions to occur for a hydrogen molecule.I get the answer if i calculate using ...
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### Liquid phase is a highly compressed gaseous phase

$\mathbf{Q:}$ While teaching "Real Gases", my professor remarked last day that "Liquid phase is a highly compressed gaseous phase." But he did not explain the reason behind it and left it as food for ...
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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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### 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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### Derivation of viscosity using basic kinetic theory?

This question has been asked in part before in the question Kinetic theory derivation of viscosity of a gas although the given accepted answer does not give the required detail for the part of the ...
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### alternative derivation of Einstein relation

Is there a derivation of the Einsteinâ€“Smoluchowski relation without the assumption of the Boltzmann distribution? Every time I see a derivation, it always assumes the Boltzmann distribution, such as ...
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### Heat capacity of solids

In the Einstein/Debye models, the specific heat capacity goes as T^3 at low temperatures and approaches the Dulong-Petit law at higher temperatures. I undestand that some molecular motions (rotation, ...
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### Specific heat capacity and temperature, 0 K?

I've found similar threads like this, but with no clear answer. I understand that the specific heat capacity of a substance increases with temperature, because the vibrational nodes and rotational ...
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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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### Can Kinetic Theory obtain fluids behavior?

My understanding is that it can't. But when presenting it here I received comments that contradict this. So, as suggested, I am asking the question to be able to receive concrete approaches on this ...
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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? [duplicate]

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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### 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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### 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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### 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 forces. ...
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### 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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### 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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### 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 [on hold]

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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### 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 ...
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 k_{B}T}\right)^{3/2}e^{-\frac{m[(v_{x}-a)^{2}+...