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15 views

Why is the probability that the collision angle will be in the range of 0 to 60 degrees than in the range of 60 to 180 degrees

Pretty much the title. It is given that the probability that the collision angle will be in the range of 0 to 60 degrees than in the range of 60 to 180 degrees I don't remember seeing such statement ...
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0answers
22 views

Collision frequency of ideal gas and velocities of molecule

Is collision frequency of gas molecule $ = \frac{V_{RMS}}{\lambda}$ where $\lambda$ is mean free path. Shouldn't it be $\frac{V_{average}}{\lambda}$? (I often see that in theories books suggest that ...
1
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1answer
63 views

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 ...
3
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0answers
61 views

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 ...
0
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1answer
56 views

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 ...
2
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1answer
125 views

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
0
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0answers
30 views

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....
0
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1answer
29 views

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 ...
3
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1answer
50 views

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 ...
2
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0answers
35 views

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( ...
-3
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2answers
72 views

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?
0
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1answer
73 views

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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0answers
29 views

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 ...
1
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1answer
84 views

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-...
3
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2answers
194 views

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 ...
11
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5answers
3k views

Is Avogadro's law applicable for atoms or just for molecules?

I notice that online definitions of this experimental law always say, molecules or atoms. From the Wikipedia article on Avogadro's Law: $${\frac {V_{1}}{n_{1}}}={\frac {V_{2}}{n_{2}}}$$ The ...
1
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0answers
134 views

Feynman Lectures I 40: Is the homogeneity of the Maxwell-Boltzmann distribution a result of, or a pre-requisite for its derivation?

I refer to hand-waving a lot in this post. That is not to say that it was in appropriate. Feynman pretty much said at the outset that his treatment of thermal physics was going to be less than ...
1
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0answers
33 views

Demonstrating the average dot-product of relative incident velocity with CM velocity of colliding pairs of ideal gas atoms is zero

In The Feynman Lectures on Physics Vol. I Ch. 39: The Kinetic Theory of Gases an argument is given in 39–4 Temperature and kinetic energy, showing that the average value of the dot-product of the ...
3
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1answer
269 views

Understanding Feynman's development of the ideal gas law: Vol I 39-2 of The Feynman Lectures on Physics

In The Feynman Lectures on Physics, Volume I 39-2 The pressure of a gas, the following is presented: If $v$ is the velocity of an atom, and $v_{x}$ is the $x$-component of $v$, then $mv_{x}$ is ...
0
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1answer
117 views

Relating the maximum entropy with the pressure given in terms of volume

For a monoatomic ideal gas let the pressure of gas in a container be given as $p=p_0- \alpha V$ Where $p_0$ and $\alpha$ are constants and $V$ is the volume of gas. Then find the volume at which ...
3
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2answers
639 views

In a gravitational field, will the temperature of an ideal gas will be lower at higher altitude?

I know there are similar questions, but I have some arguments which seem to explain that temperature of an ideal gas in a gravitational field will be lower at higher altitudes. I am assuming that: 1....
1
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3answers
186 views

Relation between particle numbers and collisions between gas molecules inside a closed container

I'm not a physicist, nor studying physics, so this may be a dumb or a very hard question, I don’t know. I'm not sure if I used correct tags, feel free to correct them if you feel like it is necesary. ...
2
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0answers
202 views

How was the ideal gas equation derived?

How did people come up with the formula: $$PV = nRT = k_BT \qquad$$? I see two possible ways: 1.) We did some measurements and defined $$kB:=\frac{PV}{T},$$ remarking that $\frac{PV}{T}$ is ...
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1answer
103 views

Kinetic theory for Charles' Law: does frequency and time interval of collisions change?

So I was given this table in class about Charles' Law: The table I got from class says that the time interval and frequency of collisions increases. However, if the velocity of molecules and volume ...
2
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1answer
2k views

Derivation of the virial expansion

It is easy to derive the ideal gas law form the kinetic theory of gases, but how do you derive the other coefficients of the virial expansion? Is it even possible to get a closed-form formula for the ...
3
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3answers
1k views

Why does the specific heat of a real gas depends on temperature but not for the ideal gas?

The specific heat of a real gas, unlike an ideal gas, depends on temperature. How can we physically understand this? Thanks.
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2answers
83 views

What is an Ideal Gas?

I have read that there are no molecular interactions between the molecules of a gas, neither attractive forces nor repulsive. But how does that makes it an Ideal Gas. What are the effects of these ...
0
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1answer
195 views

Why does molecular potential energy increase with constant temperature?

You heat up a liquid at its boiling point, and the temperature remains constant until all the liquid has turned into vapour. Since the temperature stays constant kinetic energy stays constant too, but ...
2
votes
1answer
682 views

How can I demonstrate the internal energy of diatomic gas?

I want to demonstrate the formula to find the internal energy of an ideal gas. The formula is $$U = \frac{5}{2}nRT.$$ I first tried to use the formula $U = E_c + E_p$ (Internal energy of an ideal ...
9
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2answers
1k views

Does the term “diatomic ideal gas” make any sense?

As per the kinetic theory of ideal gases, ideal gases are considered to behave as point particles that occupy negligible volume, and exert no intermolecular attractions. At the same time, diatomic ...
0
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1answer
2k views

Collisions of gas molecules with walls of a container [closed]

I am to calculate the rate of collision of gas molecules with the walls of a container with dimensions $3m\times4m\times2m$ at room temperature (20°C) and pressure 1atm. For reasons of simplicity I ...
3
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0answers
330 views

Effusion Flux according to Kinetic Theory

We know from Kinetic Theory that, for a dilute monoatomic gas, particle average velocity perpendicular to a wall of the container is given by: $$ \begin{align} \langle v \rangle _s &= \frac{\...
2
votes
2answers
612 views

When gas from a cooking gas cylinder is used, the pressure does not fall appreciably until the last few minutes. Why?

When gas from a cooking gas cylinder is used, the pressure does not fall appreciably until the last few minutes. Why? This was a question in one of my reference books and I couldn't answer it. ...
1
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2answers
1k views

What is the speed a gas expands into a vacuum?

A gas in a Joule free expansion expands into an evacuated chamber. It does this with a certain speed. Since gas molecules move into the vacuum, that speed must be dependent on the molecules' mean ...
0
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0answers
41 views

What is the microscopic equation to calculate sound speed in an ideal gas? [duplicate]

The common equations to calculate the sound speed in an ideal gas use macroscopic quantities, e.g.: $$c = \sqrt{\frac{\gamma RT}{M}}$$ What I am interested in is an equation that determines the ...
1
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0answers
57 views

What is the kinetic energy of a number of discrete particles and question related to Thermodynamics [duplicate]

If I have a Number of gas molecules in a container each having some velocity $v(i)$, what would be the $K.E$ of the gas? Will it be the sum of kinetic energies of the individual particles or will it ...
1
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1answer
499 views

Derivation of Specific Heat of an Ideal Monatomic Gas at a Fixed Volume from Maxwell-Boltzmann Distribution

How do I derive the specific heat of an ideal monatomic gas from the Maxwell-Boltzmann distribution? I think I understand the derivation based on degrees of freedom, but I'm supposed to be able to ...
2
votes
2answers
520 views

Is mean kinetic energy related to temperature of a system of interacting classical particles?

I'm trying to intuitively understand what temperature is for a system of classical particles. The usual definitions via Gibbs measure or entropy appear very unintuitive me. But, as for ideal gas ...
0
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1answer
390 views

Relationship between energy and temperature in ideal gas

I have encountered this old question and since I was bored I figured I use statisical mechanics to derive the relationship $E=\frac{3}{2}kT$ for a single particle in an ideal gas without using outside ...
1
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2answers
79 views

Pressure of a Gas and average velocities in each direction

I am learning to derive the equation of pressure of the gas which is given at the bottom of following photo. Just want the explanation of the statement "Because there are many molecules and because ...
2
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0answers
1k views

Limitations of the ideal gas law: When does it fail?

Motivation I ask this question precisely because I am looking for a fundamental, quantitative explanation of the limitations of the ideal gas law and when it should not be used. Note, I have found ...
0
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1answer
2k 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 ...
3
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0answers
507 views

How Quickly Do Gases Mix?

When I pick up my scuba tanks from the dive shop, I measure the nitrogen and oxygen levels in it. I check that they are close to what I specified and calculate the maximum depth it's safe to go to to ...
1
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2answers
513 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 ...
1
vote
1answer
332 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 ...
0
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2answers
165 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 ...
0
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1answer
518 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 ...
-1
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1answer
703 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?
2
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1answer
73 views

Kinetic theory of physics [closed]

$$E = (3/2) kT$$ For average kinetic energy of a molecule gas.The constant $k$ does not depend on the type of molecule. Can this result be true for both hydrogen and chlorine?
0
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1answer
146 views

Liquid phase is a highly compressed gaseous phase

$\mathbf{Q:}$ While teaching "Real Gases", my professor remarked last day that "Liquid phase is a highly compressed gaseous phase." But he did not explain the reason behind it and left it as food for ...