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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Error in mathematics of collision theory

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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461 views

Momentum change in collisions (Drude model)

A particle suffers elastic collisions with scattering centres with a probability of collision per unit time $\lambda$. After a collision the particle is in a direction characterized by a solid angle $\...
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3answers
50 views

Theoretical Calculation of Specific Heat of a Gas

I've read that the theoretical specific heat of a monatomic gas (like dissociated hydrogen or oxygen) is $20.8\, \mathrm{\dfrac{J}{mol\cdot K}}$ at constant pressure and $12.5\, \mathrm{\dfrac{J}{mol\...
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1answer
252 views

Flow rate of gas down a pipe at low pressures

I'm trying to understand an 'approximate derivation' of the flow rate of gas down a pipe at low pressure from my book (an example problem). It uses the result that the flux of a gas is given by $\...
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1answer
17 views

Rate of collision of gas molecules

On what factors does the rate of collisions of gas molecules with walls of a container depends? I know one would be temperature but are there any other factors like density,pressure,volume etc. I ...
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1answer
307 views

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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1answer
29 views

Will temperature, pressure and volume effect the value of universal gas constant in any way?

Effect of variables on constants: Will temperature, pressure and volume effect the value of universal gas constant in any way?
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1answer
50 views

What is the relation between the Boltzmann distribution and Boltzmann equation?

The Boltzmann equation without collision operator $\Omega$ is as follows: $$\dfrac{\partial f}{\partial t} + \mathbf v \cdot \nabla f = 0 \tag{1}$$ Where $\mathbf v$ is the velocity, and $f$ is the ...
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1answer
203 views

Is the Maxwell distribution a solution of the Boltzmann equation?

I am studying about the Boltzmann Equation for non-equilibrium rarefied gases (dilute gases to be more specific): $$\frac{\partial f}{\partial t}+\pmb{v}\cdot\nabla_{\pmb{x}}f=Q(f,f)$$ My question is ...
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1answer
26 views

Collision probability vs rate of collision

While studying the kinetic theory of matter I came across a term called collision rate ($P$) which is the number of collisions suffered by a molecule in unit time. Later it was stated that $P$ is also ...
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2answers
37 views

Compressibility factor and deviation from ideal gas behaviour

I have recently started to study the deviation of ideal gas behavior. The source from which I am reading doesn't give me an intuitive understanding of the compressibility factor. I dont understand how ...
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24 views

Video lectures for studying graduate level kinetic theory

As the title says it all, I require Video lectures for studying graduate level kinetic theory including but not limited to detailed analysis of viscosity and conductivity, diffusion and Maxwell's ...
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2answers
192 views

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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682 views

Relativity of temperature paradox

The imagined scenario: Part A: From special relativity we know that velocity is a relative physical quantity, that is, it is dependent on the frame of reference of choice. This means that kinetic ...
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1answer
52 views

Ohnesorge Number - why square root?

I understood the Weber number, but why would the Ohnesorge Number go like this: $$Oh = \frac{\text{viscous forces}}{\sqrt{\text{inertia $\cdot$ surface tension}}}$$ Why the root? There seems to be no ...
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1answer
2k views

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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0answers
67 views

How to calculate the minimum kinetic energy required by a surface molecule to escape the liquid (during evaporation)?

Evaporation occurs when surface molecules have enough Kinetic Energy to escape the surface of the liquid. Given a certain volume of liquid at a certain temperature, is it possible to determine this ...
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1answer
38 views

Viscosity and mean free path

I have troubles understanding how to derive the formula for viscosity in terms of the mean free path $$\eta\sim \rho \lambda \bar v$$ where $\bar v$ is the average molecular velocity of the gas, $\...
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1answer
45 views

If a flywheel is spinning at say 1,000 rpm, would an input of 500 rpm would actually slow it down? [closed]

When a flywheel is stationery, an input of 500 rpm would translate to less than 500 rpm in the flywheel considering entropy, but what happens if the flywheel is already running at 1000 rpm, wouldn't ...
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2answers
61 views

What VOLUME does exactly the $V$ term in ideal gas equation represent?

According to kinetic theory of gases 'the actual volume occupied by the gas molecules are negligible in comparison to the volume of the container.' I believe that this assumption is significant ...
2
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1answer
91 views

Relation between master, Fokker-Planck, Langevin, Kramers-Moyal and Boltzmann equations

I'm looking for the relation between four important equations which we study in stochastic processes in physics. These equations include Master, Fokker-Planck, Langevin, Kramers-Moyal and Boltzmann. ...
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35 views

probability of striking the circular ring by gas molecules

In kinetic theory we use probabilistic case to derive pressure, no. Of molecules having speed c to c+dc or in such cases.and to derive such equations we introduce a term called "SOLID ANGLE" I come ...
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2answers
69 views

How much faster are airmolecules going when the temperature raise from 15 to 25 degrees C?

As far as I know the temperature of the air depends on how fast the airmolecules are moving. But what is the increase of speed (in km/h) of those air molecules?
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2answers
81 views

Maxwell velocity distribution, in 1D or otherwise

I learned from my textbook that Maxwell's velocity distribution gives: $$v_{rms} =\sqrt{\frac{3kT}{m}}$$ $$v_{avg} = \sqrt{\frac{8kT}{\pi m}}$$ Presumably this is for a three dimensions. This confuses ...
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1answer
68 views

How does pressure change over time in an open box?

Imagine that you have a 1 cubic meter metal box with two 20 mm diameter holes. One of them is connected to an air-compressor that constantly pressurizes the inside of cube. Let's say 5 atm. The other ...
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3answers
38 views

Why only $x$-component of gas particle changes when it strikes with wall perpendicular to $x$-axis elastically?

In my book ''Ncert Class 12" It is written We begin by considering the collision of one molecule with one of the walls of the container, oriented with a unit normal vector pointing out of the ...
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1answer
23 views

How does gas friction emerge?

The fluid parcel model states that a gas can be modelled as the sum of infinitesimal small parcels. According to this model, the friction of a gas with a solid surface (e.g. the wall of a pipe) ...
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1answer
70 views

Deriving Ideal Gas law from Hamiltonian Mechanics

I just don't understand the explanation in Wikipedia. Is there a nice & elegant way of arriving at the Ideal Gas Law from Hamilton's Equations?
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2answers
82 views

Water compressibility and pressure

I am so sorry if I am missing something, but for some reason I am very confused on how water can have pressure but not be compressible. If pressure is created by individual molecules bumping into the ...
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0answers
9 views

Modeling stilts with equations

I'm trying to make a set of stilts 20 ft in the air that someone could wear to run/jog with, but I was advised that I should first start by modeling the system (user + environment + stilts) in the ...
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2answers
105 views

Boyle's Law-$ PV= nRT.$ What equation should be used to find pressure if n is not constant, like in an elastic system?

When air is added to an elastic system, like a balloon, the volume and pressure change. Would use Boyle's Law- $PV=nRT,$ but n does not remain constant in this situation. Known: $V_1$ is at ...
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0answers
20 views

Is there a temperature drop at the rotor plane of a wind turbine?

A wind turbine rotor produces power from the torque generated by the rotor blades. This torque arises from forces on blade elements which in turn are the consequence of pressure differences on each ...
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32 views

Statistical mechanics - average particle energy, average kinetic energy

I'm looking at derivations for average particle energy giving $E=kT$: http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/bolapp.html And average particle kinetic energy giving $K_E=\dfrac{3}{2}kT$: ...
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Average Rate of Evaporation of Water

Consider a container of volume $V$ and cross sectional area (exposed to another fluid, say air) $SA$. The container is at constant temperature $T$, and contains $N$ molecules of water, where $N$ is ...
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1answer
37 views

Physical reason why Prandtl number is order unity for gases?

Is there a physical reason behind the fact that for gases the thermal diffusivity is on the same order of magnitude as kinematic viscosity (and as such a Prandtl number of order unity) and if so what ...
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1answer
51 views

Conceptual problem on Maxwell's velocity distribution law

I already read about Maxwell's velocity distribution law for gas molecule. And the expression for that distribution is following dnc=4πnA^3e^(-bc^2)c^2dc Now if we assume that the molecules have no ...
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1answer
24 views

Interial Momentium Question

I had a question for my Physics 101 class and was wondering if anyone could share some insights. The question was stated as follows. A pottery wheel of radius 0.5 m and mass 15 kg rotates ...
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2answers
37 views

Why does the temperature of the gas in a container moving with constant velocity not change?

Systematic changes do not affect thermodynamic equilibrium. What does this mean? And what kind of systematic changes are allowed? The container with gas is stationary till some time then it's given ...
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2answers
309 views

Why does Triple point exist?

In thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium. Is the ...
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1answer
66 views

Is the pressure-gradient force an entropic force?

A gas flows from an area of high pressure to an area of low pressure when there are no other forces preventing it. From a macrosopic perspective you have to infer that an underlying force is ...
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38 views

Gas diffusion through a flat plate boundary layer

Set-up Suppose we have a flat plate with a flow of gas parallel to the plate. The flow creates a boundary layer on the surface of the plate. Now, the gas is carrying a reactive species, which is ...
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1answer
58 views

Difference between semi-classical Maxwell Boltzmann Statistics and Boson Statistics

Since semi-classical MB assumes the indistinguishability of particles and Boson Einstein statistics similarly treats degenerate states as indistinguishable states. What is their difference when ...
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1answer
37 views

What is the relation of particle velocity, temperature, and reaction activation energy

So, this curiosity has arisen for a fun project I thought I'd tackle, where I'm attempting create a crude simulation of an internal combustion cylinder. I wanted to explore the particle level ...
3
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2answers
63 views

Can wind be defined as momentum/mass of air molecules?

In the past I thought a breeze of wind was "made" from a large amount of air molecules going all the same direction in the same speed. But it's not like that, actually this voted answer, this site, ...
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2answers
221 views

relationship between pressure and thermal conductivity

Using a kinetic model for gases, is it possible to derive a relationship between pressure and thermal conductivity? From what I have read, I thought pressure was independent of thermal conductivity? ...
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14 views

Collision: How can I calculate the effect of an object below 1 kg on another heavier object after colliding [closed]

I have a question on collision: 1. A light object (0.75 kg) is travel in velocity V m/s. 2. This object collide into another object which is about 9.5 times of its weight. 3. So, the question is ...
4
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1answer
58 views

Van der Waals equation

In the Van der Waals equation, $$\left(p+\frac{a'}{v^2}\right)(v-b')= kT$$ The excluded volume b is not just equal to the volume occupied by the solid, finite-sized particles, but actually four ...
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1answer
37 views

Diffusion (2 species) versus advection (1 species)

Why do we see diffusion with 2 species but advection with a single species if both cases involve molecules spreading to increase entropy? To take a physical example: Let's say I have a box with two ...