In physics and chemistry, effusion is the process in which a gas escapes from a container through a hole of diameter considerably smaller than the mean free path of the molecules. Such a hole is often described as a pinhole and the escape of the gas is due to the pressure difference between the container and the exterior. Under these conditions, essentially all molecules which arrive at the hole continue and pass through the hole, since collisions between molecules in the region of the hole are negligible. Conversely, when the diameter is larger than the mean free path of the gas, flow obeys the Sampson flow law.
In medical terminology, an effusion refers to accumulation of fluid in an anatomic space, usually without loculation. Specific examples include subdural, mastoid, pericardial and pleural effusions.
I could not find any derivations in the litterature, except for the expected value of the energy flux expression itself:
$$\overline{\Phi_{effusion,\epsilon}} = \overline{\dot{N_{ef}}}\overline{\epsilon_{ef}}=\frac{3Nl}{2A}\sqrt{\frac{(k_BT)^3}{2\pi m}}$$
I've started off by calculating the...
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...
I understand that diffusion is the movement of molecules from a region where concentration is high to one where it is lower.
This happens due to the molecular agitation which leads to frequent collisions and hence scattering of molecules.
But I do not know what is effusion. Any help? Thanks
Homework Statement
A thin-walled container of volume 10−3 m3 is evacuated to a pressure of 10−7 mbar. The vessel is surrounded by air at 1 bar and 290 K. If a small hole of area 10−17 m2 is made in the wall of the container, how long does it take the pressure inside to rise to 10−6 mbar...
Homework Statement
Gas escapes from a leaky cylinder so that the rate of decrease of pressure in the cylinder is proportional to P - Patm where P is the pressure in the cylinder and Patm is atmospheric pressure (1.0 atm). The initial pressure in the cylinder is 1.1 x 103 atm. If the rate of...
1. In a gas UF6 (uranium hexafluoride) are uranium atoms of both the fissionable uranium isotope 235U , and 238U. To enrich the fissile isotope can let a gas UF6 with natural isotopic composition (0.7% 235U, 99.3% 238U) undergo effusion process. The process is then repeated in many steps in the...
Homework Statement
Naturally occurring uranium contains 0.7% ##\;^{235}U## and 99.3% ##\; ^{238}U## . To enrich it one uses a method based on repeated effusion.
a) Consider a step in this process. In a container, which is divided in two parts by a porous plug, one part contains natural uranium...
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...
when the gas effuse out of an insulated container, its velocity is given by
\sqrt{\frac{2\gamma RT}{(\gamma-1)M}}
(irodov's problem 2.42)
This leads to the result that every mole of leaking gas has an energy of
\frac{\gamma RT}{(\gamma-1)}
whereas we know the energy contained in 1 mole of gas...
Homework Statement
Show that the number of molecules hitting unit area of a surface per second with speeds between v and v+dv and angle between θ and θ+dθ to the normal is
dΦ=0.5vnf(v)dvsinθcosθdθ
where f(v) is the distribution of molecular speeds and n is the number density.
Hence calculate...
If we have a hole in a container with pressure equal to the pressure outside it and the concentration of gas inside the container is more than that outside will the gas effuse out?
Homework Statement
Suppose we have a container divided into equal halves. Right half is fixed at temperature ##T##, volume ##V_2##.
Initially it has pressure ##P_0##, a hole of area ##A## is opened between them.
Part (a): Show that the pressure in the right half is:
p =...
Homework Statement
Uranium has two common isotopes with atomic masses of 238 and 235. One way to separate these isotopes is to combine the uranium with fluorine to make uranium hexafluoride gas, UF6, and then to let it effuse through a small hole. The natural abundance of the 235U isotope is...
Homework Statement
Part (a): Explain what A and f means. Describe an experiment that shows this relation is true.
Part (b):Find the temperature of vessel 1.
Part (c): Why is temperature of vessel initially the same as vessel 1? Calculate the final temperature of vessel 2. Find the time taken...
Homework Statement
Part(a): Find rate of incidence of gas molecules.
Part(b): Find v1 and v2.
Part (c): Find mean free path for faster molecules.
Part (d): Find mean free path of 10m/s molecules.
Homework Equations
The Attempt at a Solution
Part (a)
Letting ##\phi## be flux, and ##\Delta...
Homework Statement
Part(a): explain the meaning of f(v) and A.
Part(b): Gas from surrounding air effuse into a box; find the temperature in the box.
Part (c): Explain why initial temperature of gas escaping from first box into second is the same as temperature in first box.
Part...
Homework Statement
A container of volume 10−3 m3 has a pressure of 10−7 mbar.
Surrounded by air at 1 bar and 290 K, how long does it take the pressure inside to rise to 10−6 mbar when air effuses through a small hole of area 10−17 m2?
Homework Equations
The Attempt at a Solution
Flux ø =...
Question:
In the following link I'm concerned with only pages 1 and 2. I'm wondering if there is a typo or an error of some kind. I feel like there is some inconsistency to what the author refers to as \upsilon, \theta, and \phi. The only angle shown in the diagram is \upsilon, which is the...
Homework Statement
A gas with equal number densities of uranium hexafluoride (UF6) molecules containing two isotopes of uranium, atomic masses 235amu and 238amu, is passed through a porous membrane containing very small holes. Use Graham's Law of Effusion to calculate:
How many successive...
Homework Statement
There are two problems:
The first problem is to calculate the slope of a phase-equilibrium line of a substance given its properties (Helium, Water, etc.) as the temperature approaches a certain value (in this case, T approaches zero).
The second problem is the effusion of...
In my class rate of effusion was told to be directly proportional to the mean speed of gas molecules which is intuitive and i understand. RMS speed of molecules is √3RT/M
So rate of effusion is inversely proportional to sqaure root of molar mass
But i don't understand how rate of effusion is...
Homework Statement
A gas effuses into a vacuum through a small hole of area A. The particles are then collimated by passing through a very small circular hole of radius a, in a screen a distance d from the first hole. Show that the rate at which particles emerge from the second hole is...
Homework Statement
A vessel contains gas at temp T (monatomic). Maxwellian distribution of speeds.
Molecules diffuse via small hole into vacuum. Box opened for short time and catches some molecules. Calc. final temp of gas in box.
Homework Equations
The Attempt at a Solution...
Homework Statement
Maxwellian gas effuses through a small hole to form a beam. After a certain distance from the hole, the beam hits a screen. Let v1 be the most probable speed of atoms that during a fixed time interval, hit the screen. Let v2 be the most probable speed of atoms situated at...
Homework Statement
Effusion is the slow leakage of atoms through a small hole in a container. We'll consider a box at pressure P, with volume V and temperature T. The hole will have the area A, and is in one of the six walls of the container.
a) At what rate do atoms (assume mass M) pass...
Homework Statement
If you poke a hole in a container full of gas: the gas will start leaking out. In this problem, you will make a rough estimate of the rate at which gas escapes through a hole: effusion. (This assumes the hole is sufficiently small).
Consider such a hole of area "A". The...
Homework Statement
So this isn't just one problem but it is a question as to why it is done one way for two instances and then the opposite way for a third problem. Here it goes.
1) An unknown gas effuses at a rate that is .462 times that of nitrogen gas (at the same temperature)...
The Problem
A sample of N2 gas is contaminated with a gas. It is found that that contaminant effuses at 0.25 times the rate of N2. What is the contaminating gas?
Choices are: He, Cl2, H2, Kr, Rn
Homework Equations
Rate x/Rate N2 = (square root of:) Mass N2/Mass x
Where Rate x...
Homework Statement
Part a: A thin walled vessel of volume V, kept at constant temperature T, contains a gas which slowly leaks through a small hole of area A. The outside pressure is negligible (assume zero), so no leakage back into the vessel is possible. Find an expression for the pressure...
Homework Statement
Suppose we make a circular hole 2 millimeter in diameter in a balloon. Calculate the initial rate at which oxygen escapes through the hole (at 0° C), in number of oxygen atoms leaving the balloon per second.
Homework Equations
1/4 n*A*v
The Attempt at a Solution...
Homework Statement
One percent of a measured amount of chlorine gas escapes through a tiny hole in 33 sec. One percent of a unknown gas escapes under the same conditions in 75.2 sec. Calculate the molar mass of the unknown gas in g/mol.
I can't seem to figure out how to do this so if some...
Homework Statement
If you poke a hole in a container full of gas, the gass will start leaking out. In this problem, you weill make a rough estimate of the rate at which gas escapes through a hole.
If we now take away this small part of the wall of the container, the molecules that would have...
hi guys ,
i did this chemistry question and me and my friends got very different answers.. so i want to know wats the right answer...
a professor fills a balloon with equal molar amounts of hydrogen and oxygen . the demo for that day gets postponed to the next day and over the night 45%...
I'm working on a question where gas is leaking out of a container from a small pinhole. I have a differential equation dN/dt = (Constants)*N. I solved this to get an exponential. The exponent is that group of constants, which are A/2V*(kT/m)^1/2. Shouldn't the exponent have something to do...
i know that the molecules in the "freedom" form that have charges equal 0. but i wonder why the molecules still moving to create the diffusion and the effusion?
some one please explain to me. thanks:!)
effusion rates...please help!
Could someone please explain to me how to do this question...
The rate of effusion of a particular gas was measured to be 24.0 mL/min. Under the same conditions the rate of effusion of pure methane gas, (CH4) is 47.8 mL/min. What is the molar mass of the unknown gas?