What is Kinetic theory: Definition and 144 Discussions
The kinetic theory of gases is a simple, historically significant classical model of the thermodynamic behavior of gases, with which many principal concepts of thermodynamics were established. The model describes a gas as a large number of identical submicroscopic particles (atoms or molecules), all of which are in constant, rapid, random motion. Their size is assumed to be much smaller than the average distance between the particles. The particles undergo random elastic collisions between themselves and with the enclosing walls of the container. The basic version of the model describes the ideal gas, and considers no other interactions between the particles.
The kinetic theory of gases explains the macroscopic properties of gases, such as volume, pressure, and temperature, as well as transport properties such as viscosity, thermal conductivity and mass diffusivity. The model also accounts for related phenomena, such as Brownian motion.
I am seeing conflicting definitions of degree of freedom in my textbook. If I look at the definition given as per screenshot below then it is the number of independent terms/variables/coordinates used to define the energy of a molecule. But, if I look at the statement of Equipartition of energy...
I have been trying to make sense of the derivation of pressure under Kinetic Theory of Gases chapter, but it's not making sense to me when the impulse momentum equation is used for the collision between a gas molecule and the wall of the container.
The book says that for the elastic collision...
It is usual, in plasma physics, to combine the kinetic description for electron fluid and the hydrodynamic description for ion fluid, when studying the plasma properties or the dynamics of the electrostatic waves.
I am wondering what are the physical meaning and limits of such an approach.
Thanks.
Hi, Folks,...new around here. Please excuse my naivete, but--
I have a problem with the physics behind GHG Theory/GW. Most discussions seem to center around absorbtion/transmission spectra of gases, their correlation with temperature, ala' Black Box radiation and such, and the fact that GHG...
I've been trying for a very long time to show that the following integral:
$$ I_D=2{\displaystyle \int} \, {\displaystyle \prod_{i=1}^3} d \Pi_i \, (2\pi
)^4\delta^4(p_H-p_L-p_R) |{\cal M}({e_L}^c e_R \leftrightarrow h^*)|^2
f_{L}^0f_{R}^0(1+f_{H}^0). $$
can be reduced to one dimension:
$$
I_D...
It is a long problem, but it is simple to understand.
I am having trouble with part A. My attempt:
Pressure outside > pressure inside container. pV = constant (isothermal). At equilibrium, all gases are at atmospheric pressure. Because it is quasi-static, the pressures of both compartments are...
Consider instead a thermally insulated container of volume V with a
small hole of area A, containing a gas with molecular mass m. At time t = 0, the density is ##n_0## and temperature is ##T_0##. As gas effuses out through a small hole, both density and temperature inside the container will...
So I know Dalton's law as stated above which I think is applicable in this question. Then I know the effusion rate is ##\frac{1}{4} n \bar{v}##, and from this we can make a differential for the time evolution of the number density of the gas in the container which is:
##\frac{dn}{dt} =...
Does anybody know of a derivation of the van der Waals equation from the molecular kinetic theory of gases, but without using the tools of statistical physics (such as partition functions)?
In Kinetic theory of gases, what is the reason behind introducing a new kind of average known as root mean square velocity (##v_{rms}##)?
I read the following: The molecules in a container are in constant random motion. So when we add all the velocity vectors to find the average it cancels out...
If one considers the kinetic theory of gases, can a first order estimate of thermal transfer be performed by considering momentum exchange at the container's surface?
I understand the basics of explaining and calculating pressure with the kinetic theory of gases, but if we assume energy is...
In the derivation of finding pressure exerted by a gas using kinetic theory of gases I am not understanding why the time between two collisions is taken as the time for rate of change of momentum when a particle bounces back from the wall. please help me
I have been reading up on the kinetic theory of gases, and I'm unsure whether I have correctly understood why particle velocities become correlated after colliding. Is it because during the collision they exchange momentum and thus their velocities (and hence trajectories) are altered in a...
When deriving the kinetic theory of gases, we take the change in momentum of a particle as it hits one side of a box and divide it by the time over which the collision takes place. The time is derived by taking the total distance the particle traveled in the box (i.e. from one end, off the side...
Homework Statement
Homework EquationsThe Attempt at a Solution
How to do part biii?
I tried to find change of U and W, then use ΔU-W=Q=0.
I can find the change in U by using the fact the rms of the x-component of the velocity is doubled. Therefore, originally, if isotropic <c2> =...
Hi guys!
My question is about the diffusion coefficient of the mixture of gases. Consider two gases in thermal equilibrium (Maxwell velocity distribution) having different densities n1 and n2. Let's suppose that the molecules are rigid spheres with diameters d1 and d2 and masses M and m...
Hi everyone,
I remember years ago at school memorising the derivation of the formula for pressure in the kinetic theory of gases, as explained in this Youtube video:
Thinking a little more deeply about this derivation there are two things I don't get:
1) At 0:53, the video says the molecule...
I am looking for a derivation of the following formula
$$
\eta=\lim_{\omega\rightarrow0} \frac{1}{2\omega}\int dt dx\langle[T_{xy}(t,x),T_{xy}(0,0)]\rangle,
$$
where $T_{xy}$ is a component of the stress-energy tensor. This is claimed in for instance https://arxiv.org/pdf/hep-th/0405231.pdf...
Homework Statement
A cylinder containing an ideal gas is in vertical position and has a piston of mass ##M## that is able to move up or down without friction (Fig. 13.2). If the temperature is increases,
...Fig (13.2)
(a) both ##p## and ##V## of the gas will change.
(b) only ##p## will...
In kinetic theory, the number of molecules hitting a unit area of a surface per unit time with speeds between v and v + dv and angles between \theta and \theta + d \theta is found to be a function of sin(theta) and cos(theta). There will often be a practice problem asking to show that the...
I have read Average translation kinetic energy is 1/2RT per degree of freedom and Average translation kinetic energy for an ideal gases is 3/2RT.How? Does it imply f=3 for all ideal gases?
Hi
I'm in high school but what I'm going to ask you is probably being teached in college.
General formula: p=(2/3)*(N/V)*Ek
p- pressure
N- amount of molecules
V- volume of the container
Ek - AVERAGE kinetic energy
I've been told by my physics teacher, that 2/3 constant factor in kinetic theory...
Hi,
I am looking for a video helping intuition on pressure, in the context of kinetic theory of gases.
I remember seeing a video where someone poured a bucketful of little hard balls (lead sinkers for fishing?) onto an electronic scales (a dynamometer, really) showing that this corresponds to...
Homework Statement
Consider the motion of charged particles, in one dimension only, in
the presence of an electric potential V ( x). Show, by direct substitution,
that a function of the form
f=f(1/mv^2 + qV)
is a solution of the Boltzmann equation under steady-state conditions.
Homework...
Temperature is the average of the kinetic energy of the particles, if the bunch of particle moves fast and you look at the particles in two differece frame of reference, on steady with the bunch of particles and the other not, in the last one you get an higher temperature of the bunch of...
Homework Statement
Calculate activation energy and pre exponential factor, i need help with the pre exponential factor
Homework Equations
Temperature °C
-20 = 253 k
-10= 263
0=273
10=283
20=293
Rate const. s-1
1.15
3.85
11.3
28.7
74.0
The Attempt at a Solution
i already plotted the graph on...
I am doing a course on statistical mechanics and we are using the textbook by Mehran Kardar. We are currently dealing with a chapter on kinetic theory. The problem is, I find the exercise problems to be quite tough (and many of my classmates agree with me), and there are no good solved examples...
I've recently begun studying thermal effects. I learned that thermal energy could be transferred within an object through conduction and from a distant object through radiation. (let me know if I'm wrong here) I also learned that when matter is heated, it's particles begin to vibrate, move apart...
Homework Statement
Find the temperature T that allows the rms speed of a gas to be equal to another gas with T=47°C.
The molecular mass of the first gas is 64, and the molecular mass of the second gas is 32.
Homework Equations
v_{rms}= \sqrt{\frac{3RT}{M}}
The Attempt at a Solution
The...
Homework Statement
The screen shot I have attached is the original question, I think I'm ok up until the Ne part.
My answer just seems like a ridiculous number, I haven't had much experience with this so don't really know what an 'normal' KE for 1kg of gas would be.
Homework EquationsThe...
Homework Statement
One mole of oxygen at 27°C and at one atmospheric pressure is enclosed in a vessel.
Assuming the molecules to be moving with Vrms, find the number of collisions per second which the molecules make with 1 m2 area of the vessel wall.
Homework Equations
vrms = √(3RT/M)
PV = nRT...
Homework Statement
Pressure in vacuum is 10^-3 Torr. External Pressure is 1atm and 300K. Pinhole of 10^-10cm^2 made in vacuum. Assuming all molecules striking hole pass through, how many molecules leak into vacuum in 1hour?
Answer: 10^17 molecules
Homework Equations
Flux = <v>*N/4V
Rate = Flux...
Homework Statement
Assuming uniform distribution. What must be the size of a cubical element of volume in the container so that the number of particles in each volume element may vary by 0.1% when the gas is as standard conditions. Probable deviation is given by N^(1/2) where N is the number of...
Homework Statement
A closed vessel contains liquid water at equilibrium with its vapor at 100C and 1 atm. 1 gram of water vapor occupies 1670cm^3. Hvap = 2250Jg^-1. How many molecules are there per cm^3 of vapor?How many vapor molecules strike each cm^2 of liquid surface per second?
Homework...
Hello all,
i have been asked a question about a lump of iron being warmed, and to calculate the difference between enthalpy and internal energy. I did some algebra and found that the change in the product pV , in the case of a liquid would suffice. But, since the volume doesn't change (Assumed...
This came up whilst helping my kid with her GCSE physics so ought to be pretty straightforward. Here goes:
At his level the kinetic theory of matter is taught in a simple way and one "key point" which is stated time and time again is "the particles in a gas have more energy than the particles...
I am trying to explain the convection heat transfer and the mass transfer related (buoyancy of the heated part of the gas) using only kinetic theory of gases , I mean using only collisions between molecules of the gas. The environment is the usual one : a hot wall in contact with a gas...
In ideal gas model, temperature is the measure of average kinetic energy of the gas molecules. If by some means the gas particles are accelerated to a very high speed in one direction, KE certainly increased, can we say the gas becomes hotter? Do we need to distinguish the random vibration KE...
F = Δp/Δt
http://www.sumoware.com/images/temp/xzhhjttxobbodxgr.png [Broken]
(Sorry for bad sketch.. hehe)
In the kinetic-molecular theory of gas, the Δp is -2mv (since it's supposed to be elastic collision)
But, why the Δt is 2L/V ??
I think it must be a very small time (since the impact is...
Hi, I am struggling with a particular point on the derivation of the kinetic theory of gases. Between 5mins and 6mins 30seconds of the video below they discuss how to get a value for the average of the squared velocities of the molecules in the gas. The bit I don't get is why they divide by 'N'...
Homework Statement
"Show that particles hitting a plane boundary have traveled a distance 2λ/3 perpendicular to the plane since their last collision, on average."Homework Equations
(Root mean path squared) <x> = 2^(.5)λ
λ = ( 2^(.5) * n * sigma )^(-1)
ANSWER:
The Attempt at a Solution...
Homework Statement
Consider two chambers of equal volume separated by an insulating wall and containing an ideal gas, maintained at temperatures T1 = 225K and T2 = 400K. Initially the two chambers are connected by a long tube whose diameter is much larger than the mean free path in either...
Homework Statement
Helium gas with T1 = 500K and P1 = 0.02MPa in a rigid container with volume V = 1 cm^3.
Then Helium goes through a process where atoms with kinetic energies greater than kB*T1, where kB is Boltzmann constant, are instantaneously removed from the container.
Atoms remaining...
Homework Statement
imagine a planet with half the mass and half the radius of Earth ..with temperature reaching 800K
k=1.38×10-23
mass of O₂ = 5.3×10-26
does the planet have O₂ or not?
Homework Equations
½mv² = ½kT or ½mv² = kT or ½mv²= 3/2 kT
either only vertical or anything other than...
Hello everyone, i was looking for suggestions on the beat book in the topic of kinetic theory, i need a book with deep explanation and covers everything from A to Z. I would appreciate it if someone could post a link for their suggestion on amazon or something. thanks in Advance.
Homework Statement
A molecule has a velocity v and speed v. I've worked out (and understand) that the number of molecules in a gas with speeds between v and v+dv and moving at angles between Ө and Ө+dӨ to any chosen axis is: (1/2)nf(v)dvsin(Ө)dӨ The internet verifies this. f(v) is the speed...
One of the assumptions of Kinetic Theory states that:
A gas is a substance composed of many particles flying about randomly, colliding with one another and with the walls of the container.
My instructor mention that we might be required to Know, state, and apply this theory to one of newtoms...
In a recent class, my instructor covered the Kinetic Theory of gases. My question is in regard to the theory which states
1) The size of the individual molecues in a gas are so small that their volumes can be considered negligible.
The instructor then mentioned that the paticles in the gas can...
Homework Statement
(Pathria 6.11) Considering the loss of translational energy suffered by the molecules of a gas on reflection from a receding wall, derive, for a quasi-static adiabatic expansion of an ideal nonrelativistic gas, the well-known relation ##PV^{\gamma} = \text{const.}## where...