Questions tagged [kinetic-theory]

Kinetic theory is part of statistical physics. DO NOT USE this tag for macroscopic kinematics; use the [kinematics] tag instead.

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My interpretation of kinetic theory of gases predicts empirically false thermal decomposition temperature

I have an intuition that, for 50% thermal decomposition of water gas, the average collision energy must equal the $2H_2 + O_2 \iff 2H_2O$ enthalpy of reaction divided per unit molecule. I have another ...
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How can mechanical equilibrium be guaranteed in adiabatic expansion? [closed]

Assuming I have a perfectly thermally insulated metal piston in my hand. I reach for the piston, pull on it and let go again- nothing moves. What happened to the gas in my system: T down, p down, V up....
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Is the pressure-gradient force that causes hydrostatic equilibrium entropic, contact, or both?

This question considers classical fluid mechanics, particularly the kinetic theory of gasses. In the simple one-dimensional gravitational setting, a fluid is in hydrostatic equilibrium if $\frac{dP}{...
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From the non-relativistic particle distribution $f(\vec{r}, \vec{v}, t)$ to the relativistic $dN/d \gamma$

In the plasma community it is common to use the 6+1 D particle distribution function $f(\vec{r}, \vec{v}, t)$, and from this obtain the different-order momenta (density, velocity, and so on). ...
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Can Brownian particle itself theoretically exhibit thermal motion? [closed]

The reason that we observe a Brownian Motion of a particle is being commonly explained by collisions of molecules of the surrounding fluid (liquid, gas) that the Brownian particle is suspended in. ...
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Why is energy flux not equalized across an effusive hole between two gases?

Consider two gases in a thermally insulated container separated by an insulated wall with a small hole in it (smaller than the mean free path). We can claim that, in equilibrium, the net particle flux ...
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Cubic nature of van der Waals' gas equation [duplicate]

$V_m^3-\dfrac{RT+bP}{P}V_m^2+\dfrac{a}{P}V_m-\dfrac{ab}{P}=0$ So, At $T<T_c$ the above equation has three real roots say $V_1,V_2,V_3$, my doubt is what does this mean physically because for some ...
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What causes the volume of an ideal gas in a container that changes volume (like a balloon)?

As we don't consider molecular volume or any interaction between molecules in an ideal gas, what causes its volume? What is the volume given by PV=nRT? If we take a balloon as an example, what ...
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Most likely velocity vector of ideal gas?

$$\left( \text{probability of a molecule having velocity }\vec{v}\right) \propto e^{-mv^{2}/2kT}$$ So the most likely velocity vector for a molecule in an ideal gas is zero. Given what we know about ...
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How small is $dt$ in this derivation of the kinetic energy of ideal gasses?

I was reading the derivation of the average translational kinetic energy of an ideal gas in Sears and Zemansky's University Physics. This derivation uses a cylinder with height $|v_{x}|dt$ and base ...
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Is thermal vibration a property of a particle moving back and forth by itself, or of a system of particles colliding?

When we say gas has a given temperature, it means the particles vibrate, or move back and forth, in the aggregate. Is this movement back and forth only due to each particle moving linearly and then ...
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Work done in Free Expansion of ideal gases [duplicate]

My textbook says that work done by a gas is loosely defined as the product of the pressure of system and the corresponding change in volume. It also states that work done in free expansion is zero ...
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Equilibrium in blackbody radiation

I was reading this post and I think I am still confused. A blackbody $radiator$ is not in equilibrium, by definition, since it is radiating. If so, why does the blackbody spectrum accurately describe ...
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What is the formula for mean time of collision in kinetic theory of gases?

Does in the formula for mean time of collision we use $V_{rms}$ of $V_{avg}$ ? Is the average time for collision Same as mean time for collision?
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Are collisions ignored while calculating fluid pressure?

Consider a container of height $h$ filled completely with fluid of density $\rho$, Assume pressure at top is zero therefore pressure at the bottommost points will be $p_b=\rho gh$ and therefore force ...
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How can the Maxwell-Boltzmann distribution be reconciled with the Boltzmann distribution?

The Boltzmann distribution asserts that a state at a lower energy is more likely to be populated than a state at a higher energy level. However, the Maxwell-Boltzmann distribution asserts that small ...
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Why do we take root mean square velocity while finding the kinetic energy of one molecule of an ideal ga?

I understand that RMS speed is usually used for a bunch of ideal gas molecules so we can get the mean of velocities but while finding the kinetic energy of a single gas molecule why do we write K.E=1/...
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Doubt regarding average kinetic energy of a molecule of an ideal gas

I understand that average kinetic energy of 1 mole means that every molecule has different kinetic energy due to different velocities so taking the avg gives us a general idea of the K.E of that gas ...
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Why does a magnet arranged in a magnetic accelerator propogate a wheel forward?

My question is related to an interesting video i saw on magnets. The link of the video is here https://youtu.be/iyv9GhaITNE , in this video at 1:52 of the video we see the wheel is moved forward but i ...
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What does the force equation of kinetic molecular theory actually mean?

Actually I was learning about kinetic molecular theory of gases. The equation of force exerted by molecules on the wall is $$F=N\frac{mv^{2}_{x}}{L}$$ Where N is the number of particles and L is the ...
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Why can we assume the contact time interval is $2L/v_x$ when a single molecule collides with a wall? [duplicate]

In my understanding of Newton's second law $$F=\frac{\Delta p}{\Delta t}$$ $\Delta t$ is the contact time interval between two objects. I am reviewing the process to derive $p=\frac{1}{3}\rho v^2_\...
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Radial dependence of temperature of solar wind?

How does the temperature of the solar wind plasma depend upon radial distance from the Sun?
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What is kinetic arrest?

I know what kinetic energy is and what chemical kinetics is, but what is kinetic arrest? Could someone please explain? There is no Wikipedia article, and googling throws up only journal articles (...
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Why is time of contact not taken in finding rate of change of momentum in derivation of kinetic gas equation?

In derivation of kinetic gas equation, the time taken for rate of change of momentum is taken as 2l/u but the force is change of momentum divided by time of contact so why are we taking time for gas ...
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Why temperature increases with increase in volume?

If We heat an ideal gas, its temperature rises and it's molecule becomes energetic hence they move more and more away from equilibrium position. But when we increse the volume of gas , why does its ...
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Derivation of dispersion relation of electromagnetic waves in a magnetized hot plasma

I look to solve analytically the Vlasov-Maxwell equations for a magnetized hot plasma $$\frac{\partial f_{s1}}{\partial t}+\vec{v}\cdot\frac{\partial f_{s1}}{\partial \vec{r}}+\frac{q_s}{m_s}\Big(\vec{...
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How can the temperature in a column of gas be uniform, if kinetic energy increases when gas molecules go down?

I cannot wrap my head around a supposed temperature gradient versus total energy gradient paradox for thermodynamic equilibrium of (open space ) gas in gravitational field. For simplicity, consider ...
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Physical interpretation of one-particle density, as expectation value of finding a particle with a specific momentum at a location at a time

I was reading Statistical Physics of Particles by Mehran Kardar. In unit 3.3 of chapter 3 named Kinetic theory of gases, the author derived the BBGKY hierarchy. Now in the derivation, the author ...
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Why are total kinetic energy and interaction energy roughly the same for a liquid?

Let's say one has a collection of point particles, each with a kinetic energy and (e.g. Coulomb) repulsion between all of them. Under certain conditions, the system will evolve to the stable state ...
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Is everything in nature a source of heat? [closed]

A source of heat is something from which heat is originated or obtained, whereas heat is the energy transferred due to temperature difference so heat is relative as the temperature difference is. Thus,...
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Collisional cross-section from attenuation factor

I am trying to find the mean free path of silver atoms travelling through air (I am given the temperature, pressure and that they are attenuated by a factor $2.72$ in a distance of $10^{-2}$m). I know ...
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Quasi-linear theory of plasma, some queries

I was studying about quasi linear theory of plasma turbulene and stuck at some questions (derivations), I could able to derive upto Eq.14 of this paper, but not sure how proceed for deriving the ...
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Kinetic energy of evaporated gas as source of energy loss for evaporating liquid?

Currently, I am looking at a system that is composed of a metal cylinder (lets say Iron) that is being heated by a laser inside of a vacuum chamber. As the laser strikes the surface of the iron, part ...
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3 votes
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Significance of Stokes Hypothesis

When we derive the Navier-Stokes Equation, we come across a a common assumption made by Stokes that makes the two quantities namely Mechanical pressure and Thermodynamic pressure equal to each other. ...
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Pressure exerted by a single electron in an spherical bubble

This is from APhO 2010, Problem 3, Part (A) When an electron is planted inside liquid helium, it can repel atoms of liquid helium and form what is called an electron bubble. The bubble contains ...
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Why does rotational collision number in dilute gases such as N2 increases with temperature?

In the kinetic theory of dilute gases, the rotational collision number and rotational relaxation time are defined as follows- rotational relaxation time = time required for the establishment of ...
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Velocity distribution function and Boltzmann factor

In Blundell and Blundell's Thermal physics book there is a chapter on the explanation of the Boltzmann distribution. It is explained that for canonical ensemble with a reservoir at temperature $T$ in ...
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Ratio of mean free paths between two equal volumes at different temperature, separated by a partition with pinhole

Question: A container is divided into two equal parts I and II by a partition with a small hole of diameter $d$. The two partitions are filled with same ideal gas, but held at temperatures $T_I$​= ...
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Time Scales in the BBGKY Hierarchy

(I am following Chapter 3 of Mehran Kardar's Statistical Mechanics of Particles)When working with the BBGKY hierarchy of equations, we get the following for the two-particle probability density $f_2$: ...
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Why air particles in a longitudinal sound wave don't leave their mean position?

Air particles have random zigzag motion. However,in a longitudinal sound wave in air the particles vibrate to and fro about their mean position in the direction of propagation of sound wave(ie, the ...
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Doubt on obtaining Boltzmann Equation given in the book "Modern Cosmology" Ed 1, Dodelson, equation 3.9

My question refers to Equation (3.9) of Dodelson "Modern Cosmology" Edition 1, $$ n^{-3} \frac{d(n_1 a^3)}{dt}=n_1^0 n_2^0 <\sigma v>\{\frac{n_3 n_4}{n_3^0 n_4^0}-\frac{n_1 n_2}{n_1^0 ...
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Is Radon a gas due to its radioactivity?

I think most gases are light but Radon is really heavy. I of course know that plenty of gases are not radioactive, but could the reason that Radon is a gas be due to the radiation contributing to the ...
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Is is possible to extract an effective Hamiltonian from a Boltzmann equation (or any other kinetic theories)?

I got kind of confused when reading Xiaogang Wen's famous textbook Quantum Field Theory of Many-body Systems. In Section 5.3.3 the book claims that From a kinetic theory of Fermi liquid (a Boltzmann ...
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Resultant particle distribution function for mixing of two particle species

I would like to know if there is any way to compute the resultant particle distribution for system where two kinds of particles are mixed. For me one kind is Maxwellian and another is non-thermal ...
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At freezing/condensation point, why does the temperature remain constant? [duplicate]

I understand that at freezing and condensation points, potential energy of molecules are given off to form intermolecular bonds while the kinetic energy of the molecule stays constant. My question is, ...
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Trouble integrating Maxwell-Boltzmann velocity distribution for RMS speed

I am trying to integrate over the Maxwell-Boltzmann velocity distribution to find the $v_{\text{rms}}$. The Maxwell-Boltzmann velocity distribution is given by: $$P(v) =\sqrt{\frac{m}{2\pi kT}} e^{-mV^...
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Kinetic temperature and kinetic energies [closed]

From my understanding, kinetic temperature is related to the average translational kinetic energy of particles by $$ \frac{1}{2}m\left<v^2\right> = N k_B T $$ I have several questions regarding ...
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How can entropy be created from nothing? [duplicate]

In my textbook, it is written that entropy can be created but it can't be destroyed. But I have a doubt about this line. I don't understand where does the 'created entropy' come from? How can entropy ...
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Is this a valid interpretation of the mean relative speed/collision rate of particles in a Maxwell-Boltzmann distribution?

In textbooks, the collision frequency $Z_{ab}$ between two species "a" and "b" is always given as something like: $$Z_{ab} = n_an_b\sigma_{ab} \Bigg(\frac{8 k T}{\pi \mu}\Bigg)^{1/...
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How to derive fluid equations for electrons from the linearised kinetic equations?

Starting from the linearised kinetic equation for electrons and ignoring perturbations of the ion distribution function completely, how can I work out the fluid equations for electrons (i.e., the ...
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