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Kinetic theory and MAXWELL-BOLTZMANN distribution - How to express a gas microscopically

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this gentleman I'd like to welcome you to our calls physical chemists along my name is Dr. Nobel and its topic is I can express a gas and numbers microscopical we assume that the
state of the guests can my mother greedy acquired by the equation of state p be unique was an RT we will now trying to explain the product is sold the guest on the basis of modern concept the conceptual
model which we discuss today is called kinetic theory of gasses yeah gas orders gripes against a macroscopic good do the relation between state variables mathematical the kinetic theory of gasses describes a gas microscopic a conceptual model previously and guess what from kind of black box to how we are able to make measurements on its band quote determined macroscopic state variables such as pressure while temperature this college it's a land of thermal conductivity and on no 1 in this set of a model which allows us to get a deeper understanding of again and which relates these macroscopic measurable quantities to microscopic quantities which measurement is not only these macroscopic quantities
are essential properties of the gas cosmological works on the number of nodes and the market goes in that analogical side particle Siegman velocity me and so on in kinetic theory of gasses in the simplest form it is assumed that a gas consists of many many math on the volume of these mass times is very much smaller than the larger occupied by the the last point have known that action digital Leslie upon because I'm constant motion collide with each other and with the container wars because very very many particles and because their velocities of energies are constantly changing and went to deal with mean that mean value are represented by a horizontal bar on this all by to square so the mean was the the bombs as the sum of all velocities of all particles divided by the number of particles capital and that has plagued the just thought the kinetic theory of gasses temperature of a gas is directly proportional to the average translational energy of the topic in fact temperature is just another term for the average inflation and in the following annotation by it was we had Boston's constant times the particle 3 gravitational degrees of freedom to move in space so this result in water have K can achieve where each Suresh the pressure p is calculated by the following formula for room right it's just pick properties 1 and square corresponds to the kinetic energy and divided by the volume so pressure is a measure of energy density at room temperature
and by the UN kelvins yeah translational energy of any guarantee of particle is 6 comma decimal tool times 10 to the minus 21st June all the ones you have to be 9 and model all the point and and all parent to gasses for example oxygen low tool and hydrogen age to understand conditions Rivera different bands the oxygen which has got a density of 1 comma decimal 3 grams per liter about things and is substantially less than just when I it the 1 0 a process for the since those gasses are saying temperature they both have the thinking and a guarantee of inflation the point 7 kilojoules per mole same temperature saying that energy big energy can be expressed those wanna have tons and tons square it just had to hold from both gasses there must be a mathematical relation between the velocities and the masses we arrive
at so-called greyhounds long which states that the mean velocities are inversely proportional to the square and you know because the mass of hydrogen is 16 times smaller than the mass of oxygen yeah it's velocity of glycogen 4 times who have 16 not only average mobility of oxygen Author she has never trilogy of 400 comma decimal 1 in the 2nd Hi this is far off the lens 7 keen on me the is the energy of gasses is
closely linked to the 2 scientists Maxwell and balls they developed this phase of the grazing which the velocity distribution in again to put it bluntly the formula shows how many particles move at a certain speed on the X. axis we plot the velocity and only by axis the block number of particles and now the the verification number of particles that means the velocity interval he is at most activation partygoers to do traveling velocity of about 400 meters the set
are also very fast particles moving at want thousands meters per 2nd or these latter higher level of energy and I'm calling for stopping so so and in the process equally there are part of that move very slowly
mathematically speaking the method was converted into the solutions of product prepared what function we square purple the exponential function It'll negative and the square owing to a the the maximum at about 400 meters per 2nd for oxygen a hydrogen the Red the maximum involvement with diffusion is much flat but also shifted to the right this about the distribution is not symmetric which shifted slightly to the right it's not the same as those found in biology there we won't use that this level of special attention 1 of the more this the news an corresponds to the maximum the method was anticipation but her sketching we can easily find the same but the
1st derivative of you we obtain the expression Beirut to Archie over time the most important of these is the area relatively about slightly right of the maximum we got equal really they party over pi times and there is
another important property is the rule to mean square grows up and this is the velocity of the particle that exhibit exactly the average energy in the 3
formulas formulas that you use gas constant all of us all the ratio k by the Othman's constant all amount of individual parts it is important to always use consistent use I as I the
particle collides with the wall and was long along if you want to calculate the number of variations of a particle the ball particles they have to deal with the concept of collision cross sections we do mathematically
defined clearly what collision consider a particle be moving from left to right with Voevodsky the around the velocity vector or particle we imagine that kind of cylinder collisions said and that as a cross section fever when collisions crossing another particle is located in the center of mass in the then this particle experience of the college there will be no localization particle a crime as a center of mass is outside on the conditions and in contrast
populated with collided B because the center of mass is located within fit in that count the number of particles from the collisions and it gets a number quantity or a collision theory now as base of face FIL and the length proportional to the ball
that is the volume read but times Sigmar we introduce claritin to let a correction effect of the relative movement of the particle and multiply it by the particle density of debt and below the this equation gives the the coalition pregnancy of the good cross sections the mechanic that the made geometrically as pi times the square he is particle diameter with the value of slot on at standard conditions well the chief form on a 2nd particle density 2 point 4 times 10 to the 25th particle per cubic meter
atomic radius of 0 comma decimal 1 7 and meters collision cross sectional new partner to the 6 and a square results in a collision with concealed followed 90 yeah each particle collider in 1 2nd the fall on 9 billion of party this brings us to
1 of the most important parameters that had theory of gasses the mean free path non pop FIL gas
particles this very fact about 400 meters per 2nd the vote was hindered the progression as polite as many of a gas particles this there axis we is so-called random walk in Libya the mean distance traveled by a particle 2 collisions it's called a mean free path lined up we got is your respondents destined that its level in 1 2nd z is the number of queries original 2nd so none of this equal to leave our all you have to be obtained this equation the kind of our equals 1 over scared to and I will be you know with the real data on the standard conditions we obtain land of Article 8 to 9 and
again particle means about 400 times as far as known I the vertical line and another part of and so changes direction and by comparison the average this since the need to guess what was in on a standard conditions is only 3 comma decimal 5 and to drawings not to scale deposited at the end of all he can be had at a P O K T by linear flop but it isn't that like me to find that the mean free path this book also to temperature and inversely proportional to pressure we others other collider systems wall who don't estimation of what we consume He's of covering the higher the gas density the more collisions will occur to see the w proportional to the particle density and what collisions will increase in the mean velocity of the gas particles where the collision cross-section the it was even a small pockets with the all
eventually we arrive at the following meeting a correction factor 1 falls in allowing for not every gas particle applied to which is a lot of the numbers of then the conditions we calculated in this way every year wall is sit by 2 point 4 times 10 to the 20 50 particles and
pressure is a consequence of these conditions consider unless the collision of gas particles of the world the x component of the positive momentum times these effects in all the collision and some negative and positive that after key the momentum transfer to and use of that results in a fall on the law you might the fall of the wall surface you tend to the mean free path of the mean
velocity of gas particle played a major role in the bathroom topology Britain's mass spectrometry to separate different islands according to the mass in the mass of the ions must not collide with other particles on the way from pions falls behind we pressure which allows for a mean free path of the iron which is greater than the dimension of the mass spectrum of your so we had to
order from here and then I think non-domestic until we get the following aspect my model mass of nitrogen further to the molar mass of oxygen aging water from you it kid period gasses also have put various methods of sorts coating that is physical vapor deposition PVD all chemical record of position she the mean free path there is an important role in conductive heat and mass transfer this if you wish the
arise from the gap gasses made of particles moving at high velocity who what all the individual particle being much more only told 1 more the game collisions of the particle so the container wall during reaction correlations between the gas particles results mean free path which for example this is the rate of mass and you the macroscopic state attention corresponds to the of and of brassily comenzó of
macroscopically corresponds to the entity that the mean velocity of typical gas at that condition the few 100 meters per 2nd and it ended with proportional to the square of the the mean free path depends on the bottom of the particle quantified by the collision cross sections sigma and the part of the density the number of what it is proportional to the gas density and the overflow thank you for watching by
Physikalische Chemie
Genaktivität
Physikalische Chemie
Chemische Forschung
Topizität
Gasphase
Single electron transfer
Herzfrequenzvariabilität
Tiermodell
Körpertemperatur
Druckausgleich
Gasphase
Gasphase
Fleischersatz
Tiermodell
Hydrierung
Topizität
Wasser
Ausgangsgestein
Stoffdichte
Druckausgleich
Gasphase
Werkzeugstahl
Altern
Essenz <Lebensmittel>
Schlag <Landwirtschaft>
Chemische Eigenschaft
Bewegung
Bukett <Wein>
Körpertemperatur
Thermoformen
Chemische Formel
Nanopartikel
Krankheit
Containment <Gentechnologie>
Chemischer Prozess
Sauerstoffverbindungen
Glykogen
Single electron transfer
Hydrierung
Phasengleichgewicht
Aktivität <Konzentration>
Chemische Formel
Nanopartikel
Ionenbeweglichkeit
Gasphase
Sauerstoffverbindungen
Hydrierung
Wasserstand
Elektronegativität
Nanopartikel
Funktionelle Gruppe
Lösung
Chemischer Prozess
Sauerstoffverbindungen
Derivatisierung
Chemische Eigenschaft
Nanopartikel
Querprofil
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Schlag <Landwirtschaft>
Längsprofil
Chemische Formel
Nanopartikel
Schlag <Landwirtschaft>
Längsprofil
Fieber
Nanopartikel
Krankheit
Base
Gasflasche
Stratotyp
Wasserfall
Schlag <Landwirtschaft>
Reaktionsmechanismus
Längsprofil
Thermoformen
Loratadin
Nanopartikel
Krankheit
Zuchtziel
Stoffdichte
Kubisches Gitter
Wasserstand
Schlag <Landwirtschaft>
Nanopartikel
Krankheit
Gasphase
Sonnenschutzmittel
Schlag <Landwirtschaft>
Längsprofil
Körpertemperatur
Nanopartikel
Krankheit
Zunderbeständigkeit
Stoffdichte
Systemische Therapie <Pharmakologie>
Massendichte
Insel
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Emissionsspektrum
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Wasser
Gasphase
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Gasphase
Schlag <Landwirtschaft>
Vakuumbeschichten
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Nanopartikel
Lactitol
Containment <Gentechnologie>
Periodate
Gap junction
Sauerstoffverbindungen
Schlag <Landwirtschaft>
Längsprofil
Nanopartikel
Krankheit
Stoffdichte
Gasphase
Massendichte

Metadaten

Formale Metadaten

Titel Kinetic theory and MAXWELL-BOLTZMANN distribution - How to express a gas microscopically
Serientitel Physical Chemistry
Autor Lauth, Günter Jakob
Mitwirkende Lauth, Anika (Medientechnik)
Lizenz CC-Namensnennung - keine kommerzielle Nutzung 3.0 Deutschland:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen und nicht-kommerziellen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/34686
Herausgeber Günter Jakob Lauth (SciFox)
Erscheinungsjahr 2013
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Chemie, Physik

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