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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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Need verification for the entropy equation in statistical thermodynamics

The relationship between entropy $S$, the total number of particles $N$, the available energy levels $E_j$ and a yet to be defined parameter $\beta$ is: $$S(\beta)=k_B \cdot N \cdot \ln\bigg(\sum_{j=1}...
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Using Boltzmann distribution, what is the ratio of probabilities of two states?

I got the probability of state $i$ (in terms of Boltzmann distribution) as $$p_{i}=\frac{1}{Z_{i}}e^{-\epsilon _{i}/{kT}},$$ where $Z_{i}$ is the canonical partition function: $$Z_{i}=\sum_{i}e^{-\...
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Validity of Maxwellian distribution for interacting particles?

I have read in a few (relatively credible) sources (e.g. Cambridge Tripos exam) that the Maxwell-Boltzmann speed distribution can be valid for interacting particles, but I have not been able to find a ...
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Clausius paper “ On the motive power of heat & on the laws which can be deduced from it for the theory of heat”

My question is simple. Clausius expesses his fundamental proposition as follows: "In all cases in which work is produced by the agency of heat, a quantity of heat is consumed which is proportional to ...
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Is the Vlasov equation a good kinetic equation for solids or even liquids?

Suppose we know the intermolecular potential $V(r-r')$ acting between the positions $r,r'$. Then we have the kinetic equation for a one-particle Distribution function $f(r,p,t)$ given by: $\frac{\...
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Regarding the Boltzmann entropy formula, is the Boltzmann constant really arbitrary?

In the top answer to this question (Is the Boltzmann constant really that important?) I read that the Boltzmann constant is just a dummy factor which converts energy to temperature. But that allows ...
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Kinetic Molecular theory ideal gases, deriving the equation $PV = \frac{1}{3}mN C^2$

The problem I have with this proof is how to acquire the fraction $\frac{1}{3}$. In theory we were taught by taking into consideration a rectangular vessel which obviously has three paths which a ...
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Ideal gas equation vs Kinetic theory equation

From the ideal gas equation: $PV = NkT$, since Pressure times Volume = Energy, my understanding is that the total (internal) energy of $N$ molecules of a gas $= NkT$. However from the kinetic theory ...
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What is the PDF of relative collision speeds in an ideal gas?

In the Kinetic theory of gases, the speeds of particles follow a Maxwell-Boltzmann distribution. However, what if one is interested in the distribution of relative collision speeds, aggregated over ...
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Derive the kinetic gas equation [closed]

I need a proof of high school level I have confusion in taking probabilities in all directions not yet concluded this, and I need a proof using momentum i.e I need a high school level proof
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Feynman's argument that at thermal equilibrium average kinetic energy of two gases are same

I had a hard time following Feynman's argument that when two different gases are present in the same box their average kinetic energy is the same at equilibrium. To quote from his book: ....Next, ...
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Why does setting kinetic energy equal not work in inelastic collision?

From my understanding, in an inelastic collision there is no loss of kinetic energy. So if we take the following problem: A 7700kg car is traveling 18 m/s and strikes a second car. The two stick ...
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Mixing 2 non-reacting gas of different temperature

Can we theoritically calculate the final temperature of 2 non-chemically reacting gases(say A and B) by modelling their collision as elastic collision and finding the net root mean square velocity. I ...
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Real world applications of triple point?

What are the real world applications of triple of water? And is it worth researching what factors could effect it?
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Clausius's Carnot Cycle Equation Derivation

In his paper clausius describes a Carnot cycle and he continue arguing like below: In order to make an analytical application of the method...we will assume that all the changes which the gas ...
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Where does the kinetic energy of an object annihilated in a matter antimatter reaction go?

A bullet is moving at $0.99 c$. Now we annihilate it by having it collide with an equal mass of antimatter. (assume instant and perfect reaction) This will turn both bullet and antimatter into photons....
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Accurate derivation of electron-phonon scattering contribution to metal resistivity

My lecture derived the expression for this contribtuin using the collision integral approach but I missed lot of details. He considers the lowest order correction to distribution function $f=f_0+\...
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Does bulk translational motion factor into average kinetic energy as it relates to temperature [duplicate]

For an ideal gas, we can relate temperature to the average kinetic energy of the gas molecules. What if we view a container of this gas from a reference frame that is translating at constant speed ...
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Why we fill dU/dT value in Cv(specific heat at constant volume) only and why not in Cp?

According to equipartition of energy, the energy ossociated with each degree of freedom is $\frac{K_{b}T}{2}$ for one molecule . For 'x' molecule which has degree of freedom f it's energy is given by ...
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Can kinetic energy broken down into its components ? Even if it is scalar?

I'm confused while reading about degrees of freedom. According to what I read the number of degrees of freedom (DOF) of a monoatomic gas is 3 at low temperature. My question is: is that 1) because the ...
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What is the minimum amount of matter do I need to call it “bulk” matter?

I had been reading about bulk properties, but was confused what should the minimum amount of matter be for these properties to hold. For eg: Intensive thermodynamic variables will not remain ...
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Kinetic Energy - dependence of mass

There are 2 equations to kinetic energy: $\frac{1}{2} mv^2$ and $\frac{3}{2} kT$. By the first equation kinetic energy depends on mass, while by the second one it doesn't. How comes? So does it ...
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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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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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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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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 ...