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Questions tagged [kinetic-theory]

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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What happens when a photon hits a particle (radiative heat transfer, photoelectric effect)?

By relating temperature to particle motion, the kinetic theory of gases gives an intuitive explanation of conductive heat transfer; faster particles collide with slower ones to transfer kinetic energy....
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Determining Gas Constant (R) from Boyles Law?

I have done an experiment (Boyles Law experiment using Boyles Law Apparatus) in order to determine the value of the gas constant R. I have also taken into account the dead space volume in my ...
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From Boltzmann transport equation to fouriers law - infinite speed of propagation of information

The macroscopic Fourier's law can be derived from the Boltzmann transport equation using the relaxation time approximation for the collision integral. This is demonstrated for an ideal gas in this ...
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Can a v(2) vibrationally active carbon dioxide molecule increase the kinetic energy of neighbouring molecules?

Water shows properties of -- for lack of a better word -- clumping from its permanent dipole (at STP), but what of a molecule with a temporary dipole moment, such as a v(2) vibrationally active carbon ...
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Reflectance of a gas in a tube

In the paper "The Positional and Angular Distribution of Molecules Flowing through Cylindrical Tube in Free Molecular Flow" is listed a relation for finding the reflectance and transition probability ...
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Why use a cube as a reference volume in the kinetic theory of gases?

In basic kinetic theory we often use cubes. For example, the derivation of the ideal gas law is done with a cubical volume. Is a cube necessary for it to work? If not, wouldn't a sphere be more ...
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Force around corner [closed]

I am having big trouble with this exercise: Exercise 6: A weight with mass 6 kg slides without friction along a circle-shaped pipe. In the end is a spring with constant k=60kN/m. The weight is ...
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Why doesn't a monoatomic particle have 6 degrees of freedom? [duplicate]

A monatomic particle can move in three directions(X,Y,Z). So the number of degrees of freedom(DOF) for translation is 3. The particle can also rotate on three axes. So the number of DOF for rotaion is ...
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Kinetic theory of gas. Pressure in a container derivation feels wrong

NOTE: Please Imagine A cube with 2 parllel faces I and II lying along the x axis. In the derivation what we are thought Change in the momentum of the molecule = Final momentum - Initial momentum =...
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Drude model electronic drift momentum rigorously derived

Specifically I'm referring to the equation below which I took from wikipedia. The derivation of this equation based on the Drude model seems to somewhat standard as all the resources I've looked at ...
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1answer
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Question derived from Bernoulli's book “ Hydrodynamica” and his contribution to atomic Theory

Here is the extract from the book Now the weight $π$ is sought which can compress the air $ECDF$ into the space $eCDJ$, the velocities of the particles in either air (the natural and the ...
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Absolute Heat With Kinetic Energy

I’ve read some of the questions posted here about absolute hot. Planck’s temperature. I understand that that temp comes from the natural units. Where my question comes into play is when thinking ...
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Boltzmann transport equation for granular gases

I am researching about granular gases and their collisions, and have come across this Boltzmann transport equation: $$\frac { \partial f ( v ) } { \partial t } = \iint d u _ { 1 } d u _ { 2 } f \left( ...
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van der Waals equation of state plot limitations

When I plot the van der Waals equation of state in terms of Pressure (bar) versus density (mol/L) for propane at 400 K, $$P=\frac{RT}{\big(V_m-b\big)}-\frac{a}{V_m^2}$$ in terms of density, $$P=\...
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Compression of gas [closed]

What happens when a gas kept in a metallic container is suddenly compressed via a piston and left for some time? Does the pressure increase or decrease?
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How was Maxwell able to derive velocity distribution? [closed]

Did he assume that their velocities follow some kind of statistical distribution and fit the parameters accordingly. Or did he mathematically prove it?
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Vrms for monotomic, diatomic, and polyatomic molecules

in my notes from class I have that Vrms= sqrt(3kT/m) for a pt molecule Vrms= sqrt(5kT/m) for a diatomic molecule and that Vrms= sqrt(6kT/m) for a triatomic-> higher order molecule but RMS Speed of ...
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Reverse engineering Newton's approximation of impact depth

I recently learned about Newton's approximation of impact depth, Depth = (Projectile Density / Target Density) * Length of the projectile. Where length and depth is measured in meters, and density is ...
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Why is the electric current is a scalar quantity? [duplicate]

Please help me because I didn't know why. If you know please help me!!
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Is there any equation to calculate water vapor condensation?

Basically, I can to calculate the mass of water accumulated on a surface at a given time if the surface is exposed to Room temperature keeping its temperature let say -25 C. Any help will be ...
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58 views

Kinetic Theory of Solids

Is there a clean way to examine temperature for solids and liquids in classical mechanics like the kinetic theory for gases? I'd like to get a good explanation that doesn't involve much in the way of ...
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1answer
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A hypothetical scenario regarding the pressure exerted by an ideal gas on the walls of a container using kinetic theory

This is a question I came across recently : "1 mole of an ideal gas is contained in a cubical vessel of volume V, ABCDEFGH (these are the vertices of the cube). One of the faces of the cube EFGH is ...
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Kinetic theory postulates and Van der Waals

What was the purpose to assume that gas molecules are point particles? What could be explained through this postulate? Also when we refer to kinetic theory the postulates of this theory are the ...
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Estimating the inter-molecular van der Waals' force from the boiling point of water

Background: I understand that inter-molecular van der Waals' forces are responsible for maintaining water in the liquid phase. Now, if we suppose that the net van der Waals' force on a given H2O ...
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Entropy in the Klimontovich Picture of Kinetic Theory

In the Klimontovich picture of kinetic theory, a classical $N$-body system is fully specified by the phase-space distribution $$ \rho(\vec X,t) = \sum_{i=1}^N\delta[\vec X-\vec X_i(t)] , $$ where $\...
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Rigorous derivation of the mean free path in a gas

Can anyone supply me with a derivation of the mean free path, of particles in a Maxwell Boltzmann Gas? Cited in various literature is the formula, \begin{align} \begin{split} \ell&=\frac{1}{\...
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Solution of the diffusion equation in a plasma

considering the diffusion equation taking into account diffusion and mobility of charged particules in a plasma of density $n(z)$ and potential $\phi(z)$, we have : $$ \frac{n(z)}{\tau}=\frac{\...
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What is temperature as a function of time in Fourier's Law?

Can we find temperature as a function of time using Fourier's Law of thermal conduction? For example: If we have two square parallel plates of a given length, width, and distance apart with one ...
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1answer
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Is the rate of nucleation of bubbles in beer dependent on the temperature of the liquid?

Since there's more energy in the fluid, I believe that you will have a higher nucleation rate in a hotter (assuming all other relevant variables remain unchanged), is this the case? How can I ...
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What are the specific heats of Dysprosium in its gas phase?

What are the specific heats of Dysprosium in its gas phase? The handbook of chemistry and physics [1], is a single volume of 1500 pages containing all the information an experimentalist would need ...
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1answer
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Reconciling various expressions of flux and flow in kinetic theory

There are a few expressions I have been shown to describe the flux $\vec{\Phi}_A$ of some quantity $A$ described in kinetic theory. I am having trouble understanding how they are related or if they ...
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Why gas molecules move with different speed at a given tempreture?

As per my understanding we know that molecules of an ideal gas are identical in all aspects (size, shape, mass). Since collisions are elastic in nature, they don't lose their kinetic energy. That ...
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Air temperature equilibrium

Suppose an ideal airtight room, filled with air, no changes in volume, amount of air or energy. On the one hand, "hot air rises" (less dense, flotation, convection...) ((there's gravity, we are on ...
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Boltzmann equation derivation for $H=v\sigma \cdot p$ hamiltonian

I am trying to write the Boltzmann equation for $$H=v_{F}\vec{\sigma}\cdot(\vec{p}-e\vec{A}).$$ This is a free charged particles gas. The velocity for this hamiltonian is $$\vec{v}=v_{F} \vec{\sigma}.$...
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Angle of particles hitting a wall - Kinetic theory of gases

In Blundel's "Concepts of thermal physics" it says that the number of particles hitting a wall with speeds between $v$ and $v+dv$ and angle between $\theta$ and $\theta +d\theta$ to the normal of the ...
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Difficulty in calculating effusion rate using the kinetic theory of gases and statistical mechanics

I have tried multiple sources and methods, but my attempts at a proof of the number of particles leaving a gas using statistical mechanics keep finding the same wrong result. I have tried to read ...
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Confusion while deriving kinetic-molecular theory of gases

How many of the molecules will collide within a given area A of the wall normal to the x-direction in some fixed time interval Δt ? On average half the molecules have a positive x-...
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Reconciling two views of Matthiessen's rule for electron mobility

My understanding of Matthiessen's rule is that when electron conduction in a solid is inhibited by more than one mechanism, that the overall resistivity $\rho$ is formed as if these resistance source ...
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Help me in understanding the general principles behind evaporation and condensation of a liquid

I will place my two questions infront of you guys. Let's consider the liquid is water. 1) " How and why exactly does water vapor in air condense at the surface of water? Is vapor in air condensing at ...
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What underlying physical quantity do we measure when measuring the temperature of gases?

When we measure the temperature of, say air, or any other gas, what physical quantity do we measure? Is it the kinetic energy of molecules? Is this affected by pressure and density? And if so, how?
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How can I Derive the Equation for Coefficient of Linear Thermal Expansion?

I know the relationship between change in temperature and change in length. When the ambient temperature around any substance is increased, its length increases. This is due to molecules gaining more ...
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Time symmetry of Boltzmann kinetic equation and H-theorem for calculating time-evolution of entropy

I know the Boltzmann kinetic equation is invariant under T transformation ($t \rightarrow -t$). Also, I could derive the entropy's time evolution from H-theorem as: $$\frac{\partial S}{\partial t} = -...
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Difference between pressure and temperature

If I am given the average kinetic energy of the molecules of a gas or a liquid, how can I tell if the fluid will burn me/crush me/both if I immerse my hand in it? Equivalently, what is the difference ...
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How far does a teflon ball roll on a very even surface? [closed]

As teflon has a minimal frictional coefficient of about 0.04, how far does a ball made of teflon roll on a even surface in comparison to another ball (made of wood or iron, for example), when pushed ...
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2 Extra Degree of Freedom in Linear Triatomic Molecules?

Ok, there is a bit problem in understanding Degree of Freedom of Linear Molecules specially of Triatomic Linear Molecules. See, the DOF in general is given as $f=3N-k$. Here, N=Number of atoms in a ...
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Derive total energy balance equation from Chapman-Enskog analysis of lattice Boltzmann equation

I'm interested to derive the total energy balance from Chapman-Enskog analysis of lattice Boltzmann equation (LBE). I know, I should go to the second moment of LBE (zeroth moment gives mass ...
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Why does frequency of collision increase as volume decreases?

Today I was presented with the following scenario: A syringe with one end sealed and with a frictionless piston is dipped into cold water. What is the change in frequency of collision(ie, more or ...
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What is kinetic theory?

What is kinetic theory? I am taking a course on fluid dynamics right now, and I have been wondering about one thing for some time now. We have three ways to look at a gas ($N$ particles): 1) ...
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anistropic or asymetric particles distribution

As a preamble, I have several questions and I know that is preferable to ask one question per post, but they are really linked together. This is why I chose to ask them together. I am considering a ...
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1answer
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Temperature relaxation from kinetic equation

Suppose we have the kinetic equation $$ \frac{\partial f}{\partial t}=-\frac{f-f_0}\tau $$ for the electron distribution function in momentum space $f(\mathbf{k},t)$. Here $\tau$ is the relaxation ...