The Basics of Vacuum Technology

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1 Te Basics of Vacuum Tecnology Grolik Benno, Kopp Joacim January 2, 2003 Basics Many scientific and industrial processes are so sensitive tat is is necessary to omit te disturbing influence of air. For example a particle accellerator could never reac energies of several GeV if te particles would be decellerated by colliding wit molecules of te air. Terefore vacuum tecnology is a basic tool in modern science and engineering. Te experiments described in tis report were designed to study some basic concepts of vacuum tecnology: different metods of pressure measurement, te caracteristics of a rotary slide valve vacuum pump and te influence of tubes and pipes on te overall efficiency of te system. We are not going to give a detailed explanation of te experimental assembly and te teoretical backgrounds (please refer to te description of te experiment or to appropriate literature for tese), but will be concentrating on te discussion of our results. 2 Pressure Measurement At very low pressures it is difficult to use conventional U-Tube manometers because tey would be too inaccurate. Two possible alternatives are te McLeod manometer wic performs its measurements on a compressed sample of te gas and te Pirani manometer, wic measures te eat conductivity of te gas, wic is proportional to its pressure in te orders of magnitude tat are of interest ere. Terefore, a tin tungsten wire is brougt into te recipient. Its temperature (wic is proportional to its electrical resistance) is kept constant by varying te current flux troug it. Te electrical power tat is needed for tis is a measure for te eat conductivity of te gas. 2. Calibration of a Pirani Manometer Te disadvantage of a Pirani manometer is te fact tat it needs to be calibrated before use. In our case te calibration was done wit a McLeod manometer and and ordinary U-Tube manometer. Te calibration curves are sown in figure (). Te red curve sows te electrical current troug te Pirani, te black one visualizes te electrical power calculated from te current measurements. Note te bilogaritmic scale.

2 P el [W] I [ma] p [mbar] Figure : Te calibration curve of te Pirani manometer From around 0 mbar to mbar te electrical power and (terefore te measured eat conductivity) are approximately proportional to te pressure. In tis range a straigt line can be fitted to te data points wic simplifies te conversion from electrical currents to pressure a lot in te following experiments.. For iger pressures te eat conductivity does not depend on te gas pressure so muc any more. Tis is in good agreement wit te kinetic gas teory, wic states tat eat conductivity is independant of pressure as long as te mean free pat λ of te gas particles is some orders of magnitude smaller tan te dimensions of te gas volume, wile it is proportional to pressure if λ gets greater tan tese dimensions. For very low pressures, te calibration curves in figure () get flat again. Tis is due to te non-vanising eat conductivity of te Manometer itself: In tis area te eat flux troug te metal wires of te Pirani becomes relevant. Terefore, a straigt line approximation is valid only for pressure between 0 and mbar respectively currents between 6 ma and 5 ma. For iger and lower currents te conversion needs to be done manually. 2.2 Discussion of Errors and Inaccuracies In figure (), error bars are given for bot pressure and electrical power. As you can see, te pressure measurement was quiet accurate in te low pressure area, were te McLeod could be used to perform good measurements. For ig pressures (above 0 mbar) owever, te U-Tube manometer ad to be used instead of te McLeod wic is wy te measurements are muc more inaccurate in tis area (errors of up to ±5 mbar). 2

3 Te accuracy of te current measurement is quiet good because a digital multimeter was used for it. Wat is astonising owever is te sarp bend in te curve wic appears between mbar and 0 mbar. Te reason for tis seems to be tat te digital multimeter automatically switced to a different measurement mode ere because te currents grew too big. Tis cange of te multimeters inner resistor affects our calibration curve ere. However it cannot be treated as an error because tis kind of non-linearities is wy te manometer is calibrated before use. 3 Te Pumping speed of te Rotary Slide Valve Pump 3. Experimental setup and results In order to measure te pumping speed of our vacuum pump, a piston probing unit was evacuated at a constant pressure wic was regulated at te pump inlet. A simple clock was used to measure te overall pumping time at several remaining volumes (00 ml to 0 ml) Tis measurement was performed tree times to get enoug information for a statistical analysis. Tis measurement led to an average volume trougput of dv dt = m 3 / Te pumping speed S can now be calculated by using te equation p 0 dv dt = S p () were p 0 is te atmosperic pressure of aroung 000 mbar ±20 mbar against wic te pump as to work, and p is te pressure at te inlet of te pump, wic was adjusted to 0.4 mbar ±0.025 mbar (corresponding to a current flow of 8 ma in te Pirani manometer) in our experiment. Te error of p is due to te inaccurate grapical conversion of te Pirani current into pressure by using te calibration curve recorded in te first experiment. Te pumping speed calculated wit te above formula is S = 3.57 ± 0.24 m3 Tis value is in very good agreement wit te manufacturers specification of 3.7 m 3 /. It is a little smaller, owever, because te conditions (tube sizes etc.) were probably not optimal in our experiments Statistical error analysis Some explications must be given on te error of S wic is composed of te errors of te constants p 0 and p (see above) and te statistical standard deviation of te average. Tis is te result of applying te student function to te standard deviation of te dv dt measurement results. Its numerical value is dv dt = m 3 /. By applying 3

4 te Gaussian error propagation function ( p0 ) 2 S S = + p 0 ( ) 2 dv/dt + dv/dt ( ) 2 p (2) p one obtains S S 0.24 m 3 /. = 6.7 % wic is equivalent to te absolute value given above: S = 4 Effective pumping speed 4. Experimental setup and grapical analysis Te final part of our experiments consisted of a study of te effective pumping speed, a quantity wic depends on te efficiency of te pump, wic was discussed in te previous section, and on te conductance of tubes and pipes. Te experimental setup consisted of a brass recipient (V = 3 l) wic was connected to te pump over differently sized tubes: One wit a diameter of 25 mm wic is appropriate for our pump and two capillaries wit diameter of 2 mm respectively 3 mm. During te evacuation process pressure was measured at fixed time intervals wit te Pirani manometer. Te results are sown in figure (2). Note te semilogaritmic scale. For te 25 mm tube te measurement was performed tree times. As te results are reproducable very well, only one curve is sown in te diagram. As one migt expect, te evacuation takes significantly longer for te tin capillaries tan for te large tube. Tis experiment demonstrates tat tube size is essential to te effinciency of a vacuum system. Tis means one does not only need a powerful pump to create good vacua but also a system of tubes and pipes wit very low resistances to te gas flow. 4.2 Matematical analysis From te definition of S V dp dt = Sp (3) one can derive a formula for te pressure at a given time p(t): p(t) = p 0 exp ( SV ) t S eff = V ln p t Altoug figure (2) sows tat tis formula is only valid for low pressures (ideally, te curves sould be straigt lines because of te semilogaritmic scale), te gradient of te curve sould be equal to te exponent S/V t in equation (4). (4) (5) 4

5 p [mbar] e 6 e 5 e 4 e 3 e 2 e e 0 e - e -2 e -3 e -4 e -5 e -6 e -7 Capillary 2 mm Capillary 3 mm Tube 25 mm t [s] Figure 2: Evacuation time of a 3 l brass recipient at different tube setups Consider for example te curve for te 25 mm tube at a pressure of 0.7 mbar. Its gradient at tis point is ln p t = ln p ln p 2 t t 2 = For p, p 2, t, t 2 te values from two neigbouring measurements were used. Applying equation 5 gives S eff = 3.62 m3 Performing similar calculations for te 2 mm capillary gives te following results: S eff (5mbar) = 0.79 m3 S eff (0.3mbar) = m3 Tese values are quiet inaccurate because of te inaccurate determination of ln p/ t from only two neigbouring measurements. If te curves in figure (2) were straigt lines, one could calculate te gradient wit a regression algoritm wic would be muc more accurate. Te conductances of te capillary can be calculated teoretically as well. At 5 mbar te gas flow is viscous, so te capillary s conductance is given by te formula L = πd4 28ηl p p 2 2 (6) 5

6 were d is te diameter of te tube, η is te viscosity of air, l is te lengt of te tube (9.5 cm in our case) and p and p 2 are te pressures at bot ends of te tube. Here te pressure in te recipient is p = 5 mbar; for p 2 we took te lowest pressure tat is acievable wit our pump: p 2 = 0.00 mbar. Tis results in a conductivity of L viscous = m3. Finally, tere is te following teorem about series of conductances: S eff = S + L Here, S is te pumping speed of te vacuum pump. Using te value given by te manufacturer for S (3.7 m 3 / ) we obtained te resulting effective pumping speed: S eff (5mbar) = 0.94 m3 For very low pressures, equation (6) is no more valid and as to be replaced by πkt L = d3 8m a l were k is te Boltzmann constant, T is te absolute gas temperatur and m a is te molecular mass of te gas particles. For our 2 mm capillary, one obtains: L molecular = m3 S eff Here, S eff is approximated by L molecular because te resistance of te capillary is muc greater tan tat of te pump. Te calculated values for S eff differ greatly from te experimental results. Tis migt be due to inaccuracies in te given capillary diameter wic will affect te results greatly because d is raised to te fourt respectively tird power in equations (6) and (8). Additionally tere is a great inaccuracy in te experimental values because tey were derived from te gradient of te curves in figure (2) (see above). Finally, for S eff (5mbar) te efficiency of te pump is possibly greater tan we assumed in te teoretical calculations, because te difference between te gas pressure and te atmosperic pressure (against wic te pump as to work) is not so great. 5 Minimum pressure At te end of our experiments we wanted to know te minimum gas pressure tat was acievable wit our vacuum pump. Wit a configuration similar to te one we used to measure te effective pumping speed for te 25 mm tube we acieved a current of only 3.6 ma at te Pirani manometer. Altoug our calibration curve does not go tat far down, one can extrapolate tat gas pressure at tis point sould ave been around mbar. It was interesting to observe tat, as soon as te pump was switced off, te Pirani current immediately went up to about 4 ma, wic corresponds to a gas pressure of 0.00 mbar. Tis is because of te inevitable leakings in te system. (7) (8) 6

7 6 Questions 6. Definition of te ideal gas A gas is called ideal if forces between its particles and te volume of te molecules are bot neglectable. In vacuum experiments tis approximation is valid because te density of te gas is very small. 6.2 Explanation of eat conductivity Te best explanation for te eat conductivity of a gas is given by te kinetic teory: Gas particles collide wit te molecules of te ot reservoir and gain kinetic energy. Tis energy is propagated troug te gas volume by collisions of gas particles. Finally accelerated particles will collide wit te cold reservoir and give energy to it. 6.3 Vacuum flask Te eat conductivity of a gas is independant of its pressure only as long as te mean free pat is smaller tan te dimensions of te gas volume. If one evacuates te envelope of a vaccum flask pressure will be low enoug tat tis condition is no more met. Ten eat conductivity becomes proportional to gas pressure. 6.4 Heat conductivities of several materials Te following table lists te eat conductivities of some materials in WK m : Copper 4.0 Water 0.60 Air 0.02 Stone 2.30 Fat 0.8 Copper is a very good eat conductor. Terefore it sould be an excellent material for passive cooling systems as tey are used for computer CPUs etc. However it is very expensive, so it as no practical importance as a eat conductor. Water is not as good a eat conductor as copper because it is a liquid. However, in comparison to oter liquids its eat conductivity is relatively large. Tis is made use of in cooling systems for car engines. Air as a very poor eat conductivity. Tis is for example wy textile clotes can keep you warm: Te air tat is contained between tem and your body acts as an isolator. However, if air is flowing fast enoug, it can be used for cooling systems as well. For example formula car engines are cooled by air. Te eat conductance of stone is quiet good, and it as a ig eat capacity. Terefore it as been used for centuries in ovens. Te low eat conductance of fat makes it nature s first coice for warming living beings. 7

8 6.5 Blaise Pascal s broter-in-law Blaise Pascal s broter-in-law lived in Clermont-Ferrand wic is 400 m above sea level. As Pascal at no exact measurement devices for te eigt of a mountain, e migt ave estimates te eigt difference between Clermont-Ferrand and te Puy de Dôme as 000 m. Te mercury level in te U-Tube-manometer will fall around 0 cm over tis eigt difference. Pascal will ave concluded tat mercury is 0,000 times eavier tan air. 6.6 Definition of molecular flow Te range of molecular flow is te pressure range in wic te mean free pat of te gas molecules is as large as or lager tan te dimensions of te gas volume. Under tese circumstances, many queation of te kinetic teory are no more valid. 6.7 Pumping time for a mm capillary For a capillary tat as a diameter of only mm te effective pumping speed will be very low, so te pressure will fall very slowly. Te conductivity of te capillary is terefore given by equation (6), te equation for viscous gas flow. Beginning wit equation (3) one can derive: V dp dt Lp = πd4 28ηl p 2 dp = κ V dt p 0 p = κ V t p = p 0 + κ V t }{{} =:2κ p 2 p Acoording to tis formula, one can expect a pressure of 35 mbar after 0 minutes if a mm capillary is used. 6.8 Mean free pat in ultra ig vacuums In ultra ig vacuums tat is at pressures around 4 0 mbar one can expect a great mean free pat of te gas molecules. A numerical value can be derived from te kinetic gas teory, wic provides us wit te following formula: λ = 32 ρ F (9) 8

9 Here λ is te mean free pat and F = m 2 is te cross section of te air molecules. Te particle density ρ in ultra ig vacuums is given by ρ = 3p (0) m a c 2 As /2m a c 2 = 3/2k B T tis is equivalent to ρ = p k B T () At a pressure of 4 0 mbar and a temperature of 300 K te particle density is ρ = m 3. Now we cann apply equation (9) and obtain te result: λ = m 9

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