Fundamentals of Vacuum Technology (1248463), страница 5
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Ifone takes into account, however, that at the same gas density (seeEquation 1.2) more particles of a lighter gas (large n, small m) will bepresent than for the heavier gas (small n, large m), the results becomemore understandable since only the particle number density n isdeterminant for the pressure level, assuming equal temperature (seeEquation 1.1).Quantity of gas (pV value), (mbar ⋅ l)The quantity of a gas can be indicated by way of its mass or its weight inthe units of measure normally used for mass or weight. In practice,however, the product of p á V is often more interesting in vacuumtechnology than the mass or weight of a quantity of gas. The valueembraces an energy dimension and is specified in millibar á liters (mbar á l)(Equation 1.7).
Where the nature of the gas and its temperature are known,it is possible to use Equation 1.7b to calculate the mass m for the quantityof gas on the basis of the product of p á V:p ·V = m · R · TM(1.7)10HomeVacuum physicsm=p· V ·MR ·T(1.7b)qpV = p á S(1.10a)where S is the pumping speed of the pump at intake pressure of p.Although it is not absolutely correct, reference is often made in practice tothe Òquantity of gasÓ p á V for a certain gas. This specification is incomplete;the temperature of the gas T, usually room temperature (293 K), is normallyimplicitly assumed to be known.Example: The mass of 100 mbar á l of nitrogen (N2) at room temperature(approx. 300 K) is:−m==100 mbar · ` · 28 g · mol 1=−−83 mbar · ` · mol 1 · K 1 · 300 KConductance C (l á sÐ1)The pV flow through any desired piping element, i.e.
pipe or hose, valves,nozzles, openings in a wall between two vessels, etc., is indicated withAnalogous to this, at T = 300 K:1 mbar á l O2 = 1.28 á 10-3 g O270 mbar á l Ar = 1.31 á 10-1 g ArqpV = C(p1 Ð p2) = Æp á CThe quantity of gas flowing through a piping element during a unit of time Ðin accordance with the two concepts for gas quantity described above Ð canbe indicated in either of two ways, these being:Mass flow qm (kg/h, g/s),this is the quantity of a gas which flows through a piping element, referenced totimeor aspV flow qpV (mbar á l á sÐ1).pV flow is the product of the pressure and volume of a quantity of gasflowing through a piping element, divided by time, i.e.:páVd (p á V)qpV = = tdtpV flow is a measure of the mass flow of the gas; the temperature to beindicated here.Pump throughput qpVThe pumping capacity (throughput) for a pump is equal either to the massflow through the pump intake port:mqm = tThe concept of pump throughput is of major significance in practice andshould not be confused with the pumping speed! The pump throughput isthe quantity of gas moved by the pump over a unit of time, expressed inmbar ≠ l/s; the pumping speed is the Òtransportation capacityÓ which thepump makes available within a specific unit of time, measured in m3/hor l/s.The throughput value is important in determining the size of the backingpump in relationship to the size of a high vacuum pump with which it isconnected in series in order to ensure that the backing pump will be able toÒtake offÓ the gas moved by the high vacuum pump (see Section 2.32).2800g = 0.113 g300 · 83mqm = −−−t(The throughput of a pump is often indicated with Q, as well.)(1.9)or to the pV flow through the pumpÕs intake port:páVqpV = tIt is normally specified in mbar á l á sÐ1.
Here p is the pressure on the intakeside of the pump. If p and V are constant at the intake side of the pump, thethroughput of this pump can be expressed with the simple equation(1.11)Here Æp = (p1 Ð p2) is the differential between the pressures at the inlet andoutlet ends of the piping element. The proportionality factor C is designatedas the conductance value or simply ÒconductanceÓ. It is affected by thegeometry of the piping element and can even be calculated for somesimpler configurations (see Section 1.5).In the high and ultrahigh vacuum ranges, C is a constant which isindependent of pressure; in the rough and medium-high regimes it is, bycontrast, dependent on pressure.
As a consequence, the calculation of Cfor the piping elements must be carried out separately for the individualpressure ranges (see Section 1.5 for more detailed information).From the definition of the volumetric flow it is also possible to state that:The conductance value C is the flow volume through a piping element. Theequation (1.11) could be thought of as ÒOhmÕs law for vacuum technologyÓ,in which qpV corresponds to current, Æp the voltage and C the electricalconductance value. Analogous to OhmÕs law in the science of electricity, theresistance to flow1R = −−−Chas been introduced as the reciprocal value to the conductance value. Theequation (1.11) can then be re-written as:1qpV = ÑÑ á ÆpR(1.12)The following applies directly for connection in series:R· = R1 + R2 + R3 .
. .(1.13)When connected in parallel, the following applies:1111------ = −−− + −−− + −−− + ⋅ ⋅ ⋅ ⋅R·R1R2R3(1.13a)11HomeVacuum physicsLeak rate qL (mbar á l á sÐ1)According to the definition formulated above it is easy to understand thatthe size of a gas leak, i.e. movement through undesired passages or ÒpipeÓelements, will also be given in mbar á l á sÐ1. A leak rate is often measuredor indicated with atmospheric pressure prevailing on the one side of thebarrier and a vacuum at the other side (p < 1 mbar). If helium (which maybe used as a tracer gas, for example) is passed through the leak underexactly these conditions, then one refers to Òstandard helium conditionsÓ.--CZ = ----λwhereandOutgassing (mbar á l)The term outgassing refers to the liberation of gases and vapors from thewalls of a vacuum chamber or other components on the inside of a vacuumsystem.
This quantity of gas is also characterized by the product of p á V,where V is the volume of the vessel into which the gases are liberated, andby p, or better Æp, the increase in pressure resulting from the introductionof gases into this volume.Outgassing rate (mbar á l á sÐ1)This is the outgassing through a period of time, expressed in mbar á l á sÐ1.Outgassing rate (mbar á l á sÐ1 á cmÐ2)(referenced to surface area)In order to estimate the amount of gas which will have to be extracted,knowledge of the size of the interior surface area, its material and thesurface characteristics, their outgassing rate referenced to the surface areaand their progress through time are important.Mean free path of the molecules λ (cm) and collision rate z (s-1)The concept that a gas comprises a large number of distinct particlesbetween which Ð aside from the collisions Ð there are no effective forces,has led to a number of theoretical considerations which we summarizetoday under the designation Òkinetic theory of gasesÓ.One of the first and at the same time most beneficial results of this theorywas the calculation of gas pressure p as a function of gas density and themean square of velocity c2 for the individual gas molecules in the mass ofmolecules mT:__ 1__1p = --- ρ ⋅ c2 = ---- ⋅ n ⋅ mT ⋅ c233(1.14)where__káTc2 = 3 ⋅ -----mT(1.15)The gas molecules fly about and among each other, at every possiblevelocity, and bombard both the vessel walls and collide (elastically) witheach other.
This motion of the gas molecules is described numerically withthe assistance of the kinetic theory of gases. A moleculeÕs average numberof collisions over a given period of time, the so-called collision index z, andthe mean path distance which each gas molecule covers between twocollisions with other molecules, the so-called mean free path length λ, aredescribed as shown below as a function of the mean molecule velocity -cthe molecule diameter 2r and the particle number density molecules n Ð asa very good approximation:c=λ=(1.16)8· k ·T=π · mT1π · 2 · n · (2r)28· R ·Tπ ·M(1.17)(1.18)Thus the mean free path length λ for the particle number density n is, inaccordance with equation (1.1), inversely proportional to pressure p.
Thusthe following relationship holds, at constant temperature T, for every gasλ ⋅ p = const(1.19)Used to calculate the mean free path length λ for any arbitrary pressures andvarious gases are Table III and Fig. 9.1 in Chapter 9. The equations in gaskinetics which are most important for vacuum technology are alsosummarized (Table IV) in chapter 9.Impingement rate zA (cmÐ2 ⋅ sÐ1) andmonolayer formation time τ (s)A technique frequently used to characterize the pressure state in the highvacuum regime is the calculation of the time required to form amonomolecular or monoatomic layer on a gas-free surface, on theassumption that every molecule will stick to the surface. This monolayerformation time is closely related with the so-called impingement rate zA.
Witha gas at rest the impingement rate will indicate the number of moleculeswhich collide with the surface inside the vacuum vessel per unit of time andsurface area:zA =n· c4(1.20)If a is the number of spaces, per unit of surface area, which can accept aspecific gas, then the monolayer formation time isτ=a 4 ·a=zA n · c(1.21)Collision frequency zv (cmÐ3 á sÐ1)This is the product of the collision rate z and the half of the particle numberdensity n, since the collision of two molecules is to be counted as only onecollision:zV = n ·z2(1.21a)12HomeVacuum physics1.2Atmospheric airPrior to evacuation, every vacuum system on earth contains air and it willalways be surrounded by air during operation. This makes it necessary tobe familiar with the physical and chemical properties of atmospheric air.The atmosphere is made up of a number of gases and, near the earthÕssurface, water vapor as well.
The pressure exerted by atmospheric air isreferenced to sea level. Average atmospheric pressure is 1013 mbar(equivalent to the ÒatmosphereÓ, a unit of measure used earlier). Table VIIIin Chapter 9 shows the composition of the standard atmosphere at relativehumidity of 50 % and temperature of 20 ¡C. In terms of vacuum technologythe following points should be noted in regard to the composition of the air:a) The water vapor contained in the air, varying according to the humiditylevel, plays an important part when evacuating a vacuum plant (seeSection 2.2.3).b) The considerable amount of the inert gas argon should be taken intoaccount in evacuation procedures using sorption pumps (see Section2.1.8).c) In spite of the very low content of helium in the atmosphere, only about5 ppm (parts per million), this inert gas makes itself particularly obviousin ultrahigh vacuum systems which are sealed with Viton or whichincorporate glass or quartz components.
Helium is able to permeatethese substances to a measurable extent.The pressure of atmospheric air falls with rising altitude above the earthÕssurface (see Fig. 9.3 in Chapter 9). High vacuum prevails at an altitude ofabout 100 km and ultrahigh vacuum above 400 km. The composition of theair also changes with the distance to the surface of the earth (see Fig. 9.4in Chapter 9).Gay-LussacÕs Law (CharlesÕ Law)V = V0 (1 + β · t )for p = constant (isobar)AmontonÕs Lawp = p0 (1 + γ · t )for V = constant (isochor)DaltonÕs Law∑ pi = p totaliPoissonÕs Lawp ⋅ Vκ = const(adiabatic)AvogadroÕs Lawm1 m 2:= M1 : M 2V1 V2Ideal gas Lawp ·V =m· R · T = ν · R ·TMAlso: Equation of state for ideal gases (from the continuum theory)van der WaalsÕ Equation(p +1.3a) · ( Vm − b) = R · TVm2Gas laws and models1.3.1 Continuum theoryModel concept: Gas is ÒpourableÓ (fluid) and flows in a way similar to aliquid.
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