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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Explanation of this proof of distribution of molecules after collision
The below excerpt is taken from Section no.4 from "The Feynman Lectures on Physics Vol.1 Ch.39" (here is the link to the exact text). Here Sir Richard Feynman tries to explain and "...
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What is $Z$ in collision theory of chemical reactions?
According to collision theory given by Max Trautz and William Lewis the rate of chemical reaction is proportional to $Z$ (number of collision per second per unit volume of reaction mixture)
Suppose a,...
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Doubt in the derivation of pressure of an Ideal Gas Using Kinetic Theory Of Gasses
Link of the book https://www.feynmanlectures.caltech.edu/I_39.html Chapter:- Kinetic theory of gasses
We would like to find out what force on the piston results from the
fact that there are atoms in ...
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Phase space density behavior in finite volume
I am trying to develop better intuition for the single-particle phase space density $f(x,v,t)$ and I am confused by the tendency of $f(x,v,t)$ to become wiggly in velocity space. Consider the simplest ...
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Is the invariant distribution of the underdamped Langevin equation the Bolztmann distribution?
Essentially what the question asks. I've seen proofs that in the overdamped limit, Langevin dynamics relaxes distributions to the Boltzmann distribution in the $t \to \infty$ limit; but what happens ...
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Derive the drift velocity from drifting Maxwellian distribution
Having a drifting Maxwellian (Maxwell-Boltzmann) distribution:
$$f(\vec v) = n \left(\dfrac{m}{2\pi k_B T}\right)^\frac{3}{2}\exp\left({-\dfrac{m[(v_x-a)^2+v_y^2 + v_z^2]}{2k_BT}}\right)
$$
where $a$ ...
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Distinguishing between equilibrium and non-equilibrium distributions?
Suppose a physical system is described by some effective double-well potential landscape with fluctuation-driven motion along this landscape. If we watch the system for a sufficiently long time and ...
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Is nonlinearity a denser encoding of information?
At the microscopic level, an $n$-particle system in 3D can be described by the Liouville equation, which governs the evolution of the distribution function in a $6n$-dimensional phase space.
Going ...
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Boltzmann equation for Lennard-Jones particles?
In the Vlasov variant of Boltzmann equation, the Coulomb pair forces are included via the force term that appears as the prefactor of the derivative of the density with respect to velocity. In that ...
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How does the diode equation hold under forward bias?
In the derivation of the diode equation, the law of the junction is used, allowing us to find the carrier densities across the junction. As pointed out in this question, the law holds only ...
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Energy dissipation after a new chemical bond?
Consider a simple chemical reaction, such as the association of two hydrogen atoms within the gas phase to form one hydrogen molecule. It is known that this reaction is related with energy release in ...
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How long does it take to boil water?
Consider a simple experiment, such as boiling water in a pot in your kitchen, is it possible to estimate the time needed for the water to boil based on elementary properties of water ?
In the physics ...
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Is heat energy actually kinetic energy? [duplicate]
According to KMT, heat is just molecules moving/vibrating. By that definition, could heat energy be seen as kinetic energy?
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Does the kinetic energy of particles affect Sound waves?
We know that sound travels through a medium through vibrations in the form of longitudinal waves. An example of it is here:
We also know that particles of any medium vibrate when we give them more ...
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Why is Maxwell-Boltzmann velocity distribution not uniform?
Consider a particle moving in one dimension by discrete jumps with two options at a time and starting at the origin at time zero. Each time, the particle can jump by a small distance to the left or to ...
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Deriving diffusion coefficients from Newtonian mechanics of Lennard-Jones phases?
The diffusion coefficient is known in the traditional physical literature as an empirical parameter of Fick's law. Here the observation is that spatial gradients of densities are suppressed by a rate ...
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Does momentum transport occur via diffusion (or random walks)?
Consider a simple gas (or fluid) within a box at thermal equilibrium. I manage to give a kick to one particle within the gas, such that it acquires some momentum. After some time, it should be ...
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Why do good materials operate in non-equilibirium conditions?
If we look at the majority of useful or industrial materials surrounding us, like metallic alloys, glasses, ceramics, or plastics, it is often the case that these materials went through really hard ...
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Interpretation of the Boltzmann distribution and link with Maxwell-Boltzmann distribution [duplicate]
I'm having trouble interpreting the boltzmann distribution and making the link with the Maxwell-Botlzmann distribution. I have found several discussions dealing with this problem :
The shape of the ...
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Mean free path of molecules
So in the book concepts in thermal physics(by Stephan and Katherine Blundell) the expression of mean scattering time is derived as shown(please refer the book for more). If we replace vdt in the ...
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Ratio of population in two energy levels using Maxwell-Boltzmann distribution
To calculate the ratio of population in two energy levels using the Maxwell-Boltzmann distribution, you need to compare the probabilities of the two energy levels. The ratio of populations can be ...
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Confused about ideal gases, and internal energy
There are some assumptions we make about ideal gases, one of them on the lack of intermolecular attractive forces. Why ideal gases can have interatomic forces of attraction but not intermolecular ...
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Number of degrees of freedom for a gaseous mixture
I came across the formula to find the number of degrees of freedom in a gaseous mixture which is as follows:
$$f_\mathrm{mix}
=\frac{\sum n_if_i}{\sum n_i}$$
Now it has been mentioned in this lecture ...
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In non-metals, does low specific heat capacity correlates with good thermal conductivity and vice versa?
As i understand, when heat transfers by conduction, there are two main mechanisms that can take place: either by the vibrations of the lattice (mostly non-metals) or with the movement of free ...
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Planck constant in Eyring theory of rate processes and viscosity
In my research I came across an old and probably rather obscure theory, namely Eyring's theory of rate processes [1,2]. This theory is the bedrock of an important model used to explain wetting ...
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How to modify kinetic gas theory to work for macroscopic particles? (2D)
For the first time I framed a question on my own when I was recently playing carrom pool with my cousin and a striking thought ran across my mind!
I was thinking if a square frame is fixed rigidly on ...
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Kinetic equation material derivative
I am reading through Raizer's Gas Discharge Physics textbook, and I cannot figure out a bit of the math he used to get from one stage to the next. The subject is the how the distribution function ...
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On the Brownian motion and Law of Large numbers
According to the Law of Large Numbers, if I throw a million coins, I expect to observe half of them face head, and the other half tail.
Why doesn’t this apply to (1-dimensional) Brownian motion? A ...
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I'm struggling with a collisionless plasma textbook problem. Calculating the longitudinal dielectric function from the distribution
The problem is:
Given the distribution of the electrons
$$
f_0(\mathbf{p}) = \frac{1}{\pi^2}\frac{mun_e}{(p^2 + m^2u^2)^2}
$$
find longitudinal dielectric function and the dispersion equation for ...
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Can't we draw an indicator diagram for a fast adiabatic process?
We know that an indicator diagram can be drawn for an quasi static process only. An fast process in which there is no sufficient time for the exchange of heat can consider to be adiabatic. Can i draw ...
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How can temperature be absolute if kinetic energy is relative? [duplicate]
Kinetic energy is relative and depends upon the observer because velocity depends upon the frame of reference. However, we have an absolute temperature scale. How is this possible if temperature is ...
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Expression for $C_p$ using differential expression for Helmholtz free energy
This is a question from Heat and Thermodynamics by Zemansky and Dittman:
"From the differential equation for the thermodynamic potential A(T, V), derive
expressions for pressure P, entropy S, ...
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Will the ideal gas equation change if we consider non equillibrium condition and then use kinetic approach and thermodynamic approach? [closed]
My teacher said that in equilibrium no matter what approach we use we arrive to same result i.e. in this case ideal gas equation. So if we were to use the two approaches (thermodynamics and kinetic ...
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Does the temperature of a non-ideal gas only depend on the translational kinetic energy of the particles?
I know this is true for ideal gases, but is it true for non-ideal gases?
I can imagine for example a case of perfectly plastic collisions between atoms which could transfer all the translational ...
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What is the underlying concept in case of finding pressure inside a balloon kept at some height in atmosphere? [closed]
If we have a balloon containing air at sea level. Is the value of absolute pressure inside the balloon decided by the temperature of the enclosed air or by the height of atmospheric column above it ...
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Why must average velocity of a gas be 1/6 times escape velocity of planet for it to escape [closed]
I read this in my class textbook, and learnt the reason of absence of Hydrogen from atmosphere and Maxwell distribution curve from Physics stack exchange. But I am unsure of why should the average ...
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What happens if you have a gear ratio that’s infinitely high? [duplicate]
What happens as the gear of a gearbox expands to infinity on either side?
If you had a material that could withstand the force and friction, could the last gear spin infinitely fast? What if it’s ...
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Confusion about Feynman lectures on physics Vol I, Chapter 39-4
In Vol I, Chap.39-4 (temperature and kinetic energy),Feynman proved that, two gases in containers separated by a movable piston(which can probably be considered adiabatic)end up with an equilibrium ...
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Mercury In a J tube
This is a doubt on question 5.3 from the 5th chapter of the book Heat and Thermodynamics by Zemansky and Dittman. The problem statement is as follows:
Mercury is poured into the open end of a j-shaped ...
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Why is the sphere of influence of the molecule in mean free path a cylinder?
In my book for deriving mean free path a cylinder is taken to act as a sphere of influence of molecules with which it could bump into other molecules and its radius = diameter of the molecule we are ...
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Pressure Tensor in Two-Fluid Equations
I am reading through Fundamentals of Plasma Physics by Bellan and came across this definition of the pressure tensor:
I am wondering how the off-diagonal terms vanish in the case of an isotropic ...
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Type of thermodynamic process
This is a doubt on question 5.13 from the 5th Chapter of the book Heat and Thermodynamics by Zemansky and Dittman. The question says we have a cylinder with a movable piston, on either side of which ...
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How could I experimentally determine that conservation of kinetic energy holds true for elastic collision?
Given a physics lab with various measurement apparatus and bouncy balls, and the ability to do mathematics, how could I experimentally determine that conservation of kinetic energy holds true for ...
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Is really change in temperature inversely proportional to primary kinetic energy of ideal gas molecules?
I was trying to derive Charles law. While deriving I got two results and one of these was unexpected. Those are,
$$\Delta t \propto \Delta E_k$$
Where, $\Delta t$ is change in temperature and $\Delta ...
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Why in Stern-Gerlach experiment atoms emitted in the beam have kinetic energy $2kT$?
The book I am following to study Stern-Gerlach experiment has written -
... from kinetic theory, the velocity $v_x$ of an atom of mass $M$ is evaluated by setting \begin{equation} \frac{1}{2}Mv_x^2=...
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Maxwell-Boltzmann distribution most probable speed [duplicate]
In my thermodynamics lecture we deduced the Maxwell-Boltzmann distribution,
$$
f_{MB}(\vec{p}) = n\left(\frac{1}{2\pi m k_bT} \right)^\frac{3}{2}\exp \left[-\frac{(\vec{p} -\vec{p}_0)^2}{2 m k_b T}\...
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Relaxation of the Boltzmann transport equation
My professor in kinetic gas theory said that when considering the Boltzmann Transport Equation (BCE)
$$
\partial_tf + \frac{\vec{p}}{m}\cdot\nabla_{\vec{q}}f + \vec{F}\cdot\nabla_{\vec{p}}f = (\...
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What does the Helmholtz Free Energy in thermodynamics signify? What is its physical significance? [duplicate]
When we say internal energy, we're talking about the total kinetic energy of the particles in the system (ideal gas). So, when they say internal energy increased I imagine the particles moving faster (...
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In kinetic theory of gases, in finding connection between pressure and molecular kin. energy, why $N/2$ & not $N/6$ molecules are assumed to hit wall?
In my book While driving a relation between pressure and average kinetic energy of a single molecule [i.e. $P = (Nmv^2)/2$ ], an ideal gas of $N$ molecules is assumed to be enclosed in a cubical box ...
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Other gas models
Are there any other models to explain the behaviour of gases other than the kinetic theory of gas?
Or this is the only theory we have till now to explain the gases.
