dt V I. OBJECTIVE OF THE EXPERIMENT

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1 I. OBJECTIVE OF THE EXPERIMENT Detere the effective throughut (ug kinetics) and the limiting ressure of a vane um and a diffusion um. tudy the temerature-ressure diagram of nitrogen, in articular the trile oint. II. PHENOMENOLOGY II.1. VACUUM TECHNOLOGY When installing a vacuum um, two fundamental arameters come into lay. The work ressure, which is not to be confused with the limiting ressure, and the time required to reach it. These two arameters deend on the um, and the vacuum chamber. In the I unit system, the unit for ressure is the Pascal 2 (1 Pa = 1 Nm ), but we often use the mbar 100 or the Torr i.e. mm de Hg Limiting ressure The limiting ressure that can be reached in a vacuum setu is given by the equilibrium between the ug throughut and the leakage and outgassing of the walls. The equiment must be ket as clean as ossible, and most imortantly remain dry. Condensable vaor leaves the system through outgassing, after heating the walls by a few hundred degrees. Nitrogen tras can be laced between the gas source and the vacuum chamber as another means of urification. Pug seed The ug seed (volumetric throughut) through a surface is defined by the volume of gas that crosses it er unit time. The volume is measured according to the ressure of the surface. The ug rate deends on the tye of the um (vane, diffusion, etc.) on the used liquid (silicone oil) and also the ressure. When designing a vacuum setu, always choose a ug grou with a seed well above that which would maintain the desired limit ressure. Pum sizing The effective throughut of a um can be detered form ug dynamics. During the ug rocess, the ressure inside a chamber of volume V evolves according to: Pa dp ( ) P P P 0 dt V Pa

2 EPFL-TRAVAUX PRATIQUE DE PHYIQUE K14-2 where P 0 is the limiting ressure of the um. In the region where the can integrate this equation, yielding: P1 P0 V 2 0 ln P P t can be suosed constant, we In this equation, t reresents the amount of time required to get from a ressure P1 to a lower ressure P 2. II.2. TATE OF MATTER Matter is made of different article: atoms, molecules, ions, etc. These articles are subject to thermal agitation, and their seed deend on temerature. These articles interact with one another, and the forces detere the macroscoic asect of matter: we call these different asect hases (solid, liquid, gaseous). We also call hase any homogeneous art of a material that has the same hysical and chemical roerties. Examles: - A homogeneous mixture of O 2 and N 2 reresents a single gaseous hase - a mixture of water and ice, i.e. the mixture of two chemically identical but hysically distinct bodies reresents two hases. The interaction forces between articles deend on the temerature, the ressure and the volume that reresent the thermodynamic variables of matter. Phase changes FUION-OLIDIFICATION Bodies of crystalline form switch from the solid hase to the liquid hase or conversely in very secific conditions. If we suly heat to the body, it s temerature rises until it starts switching to the liquid hase. We call this the fusion rocess. At that oint, the temerature remains constant and the energy sulied in the form of heat is consumed by the work necessary to beat the cohesion forces of the solid (Fig. 1). The amount of work required to melt a unit of mass of a ure body at the fusion temerature, is called latent heat. The inverse rocess is called solidification. The solidification of a liquid generally includes a volume change. For most liquids, the volume decreases when solidifying. Therefore, an increased ressure increases the fusion temerature. However, certain liquids (water, bismuth) and certain alloys exand in volume when solidifying (ice floats in water). Therefore, an increase in ressure reduces their fusion oint. Figure 1: Amount of heat required to transform 1g of ice at 10 C into vaor at 100 C.

3 EPFL-TRAVAUX PRATIQUE DE PHYIQUE K14-3 EVAPORATION-CONDENATION If we lace a liquid in a vase, it reaches an equilibrium state. The molecules continually leave the surface to become vaor molecules. This is called evaoration. On the other hand, the vaor molecules constantly hit the surface of the liquid and enetrate it. When the amount of articles exiting the water is equal to the amount entering it, we call the vaor saturated. The ressure of the saturated vaor is called saturation ressure. It is defined by the substance and the temerature. Evaoration is a cooling rocess, since it is the more energetic molecules leave the liquid. A fast evaoration can freeze the rest of the liquid. The energy sulied to the system in the form of heat roduces, on the one had the work required to beat the intermolecular forces of art of the liquid, and on the other hand the work due to the volume increase. The latent heat of vaorization for a liquid at a given temerature is the amount of heat required to vaorize a unit mass of the liquid at that temerature and at the equilibrium ressure. The latent heat of vaorization deends on the temerature: it decreases temerature increases. At a certain critical oint (see below), the latent heat of vaorization vanishes. When heating a liquid-vaor mixture in a closed body, we can see that the liquid-vaor limit disaears at a given time. The temerature at which this henomenon aears is called the critical oint. While the gas is being heated, the density of the liquid decrease, and the density of the gas increases, until they are both equal. Above this temerature, the liquid can t exist, under any ressure. To liquefy a gas, it is necessary to increase the ressure, but simultaneously reduce the temerature. A hase sunder the critical temerature is called vaor, above, it is called gas. HUMIDITY At any given time, water is resent in the atmoshere under one or several different hases (solid, liquid, vaor). Invisible vaors are always resent in large or small quantities. The quantity of vaor required for the saturation deends on the temerature. If the air isn t saturated, we can saturate it either by adding vaor or reducing the temerature. The temerature at which the air must be cooled to roduce this saturation is called the dew oint. The condensation of water will only occur if there are imurities on which the condensation can form. These can be small salt crystals, smoke articles, etc. The absolute humidity reresents the mass of water vaor er unit volume in the air. Relative humidity is defined by the ratio of the vaor ressure to the saturating vaor ressure at that ressure (Fig. 2). It s generally exressed as a ercentage. It s one of the most imortant arameters of meteorology. When the dew oint is over the freezing oint, small water drolets form. When it is under the the freezing oint, ice crystals form instead. Frost, clouds and fog are examles of this. Physicists use the hase change to visualize certain nuclear henomena. The device that is used is called Wilson chamber, or fog chamber. A cylinder containing saturated vaors is closed by a iston or by a diahragm. When increasing the volume by ulling the iston, the gas cools, and the saturated vaors condense on the ions formed by ionizing articles. UBLIMATION ublimation is the direct transformation from the solid state to the gaseous state, without going through the liquid state. This is through which laundry that is hung to dry in the winter can freeze and still dry. olid 2 CO sublimates into gas, without humidifying the walls of its container. The smell of camhor or nahthalene at room temerature roves that they sublimate.

4 EPFL-TRAVAUX PRATIQUE DE PHYIQUE K14-4 Figure 2: AB AC Vaor ressure at temerature A aturating vaor ressure at temerature A relative humidity. A AB / AC TRIPLE POINT The three hases of a body can coexist at a temerature and ressure that are the coordinates of the trile oint on a diagram. At this oint, the three curves join (vaorization, fusion and ( T, ) sublimation). The vaorization curve can be extended under the trile oint, which indicates a suercooled state. These oints of the curve reresent metastable equilibrium states. The vaorization curve of the suercooled liquid is always above the sublimation curve. For instance, water and ice have the same vaor tension ( 4.58 Torr) at the trile oint ( TT tension is 2.15 Torr for suercooled water and 1.95 Torr for ice. C ), but at 10 C the vaor LIQUID HELIUM Figure 3: Helium at low temerature At low temerature, helium has a very secific behavior. It has no trile oint in the general sense of the term. At very low temeratures and ressures, the liquid hase is more stable than the gaseous hase. There exist two liquid hases He 1 stable at rather high temeratures, and He 2 stable at very low temeratures. There is an equilibrium curve between both liquids (Fig. 3). At the trile oint ( T 2.2 K ; 3.9 Torr) the two liquids and the vaor coexist. At the oint ' ( T 1.75 K ; 30 atm ) the two liquids and the solid coexist.

5 EPFL-TRAVAUX PRATIQUE DE PHYIQUE K14-5 The liquid He 1 is very mobile and volatile. Its vaorization heat is only of 5 has very strange roerties: it s extremely mobile and 200 transformation of He 1 into He 2 calories. The He 2 liquid more heat conductive than coer. The occurs with ni volume change or latent heat exchange. The internal energy doesn t change. However, under constant, ressure, we observe a discontinuous secific heat. All the rocesses caused by the variation of the three thermodynamic variables, i.e. T, V and be illustrated in the three dimensional sace and its rojection on the lanes ( V, ) T VT can, (, ), (, ). V T The figure 4 reresents the (,, ) sace as well as the rojections on the aforementioned saces The curves contained in the those of the VT, T, lane corresond to the isochoric rocesses (at constant volume), lane are isochoric (at constant ressure) and those of the ( V, T, ) V, are isothermal (constant temerature). The searation surfaces in the sace are intersected by the lanes V cst, T cst, cst according to the corresonding rojection lines. The sloe d dt at any boundary between two hases equation and is connected to the latent heat L i, j : i and j is given by the Clausius-Claeyron d dt Li, j T V i, j (1) where, V V V reresents the volume difference of the considered body in both hases I and j. The latent heat i j j i L i, j is defined as the heat required to transform one unit of hase at equilibrium (i.e. slowly) and constant temerature. If V is indicated in m 3 /mole, V V V cst. i into the hase L i, jwill be in J/mole. Please note that we are working at constant volume, i.e. j i The released or absorbed heat of a body is therefore not only used for temerature variations, but also for searating article when the body transforms from one hase to another. Let s mention water, as an examle - in order to increase the temerature of 1g of ice from to 0, we need 1 calorie. - the fusion of one gram of ice requires 80 calories, though the temerature doesn t change during the whole rocess. 1 C C j

6 EPFL-TRAVAUX PRATIQUE DE PHYIQUE K14-6 Figure 4: Volume, temerature and ressure sace The three curves of sublimation, vaorization and fusion have one single intersection: the trile oint for which the three hases coexist in equilibrium (Fig. 5). The deteration of the trile oint can be achieved from the knowledge of at least two of these three curves of hase change. For most materials, the trile oint is located at low temeratures and ressures. To detere this, it is then necessary to reduce the ressure and temerature in a sealed container, which can be done simultaneously by means of a vacuum um. The fundamental question that arises is to know starting what ressure is it ossible to have temeratures lower than the trile oint. We are therefore faced with the roblem of obtaining a ressure low enough to lower the temerature below the trile oint. Figure 5: -T diagram

7 EPFL-TRAVAUX PRATIQUE DE PHYIQUE K14-7 PUMPING ON A LIQUID PHAE When immersed in a thermally isolated Dewar, a liquid kees it s own temerature T. However, if the isolation isn t erfect, there will be a heat exchange of Joules/s with the outside. If, by using a vacuum um, we reduce the ressure vaorization ressure of the liquid, we will generate an excess of vaorization, which will require a latent heat every second. The difference must come from the liquid, therefore, it is cooled, solidified, and continues to be cooled. The vacuum however, is limited to a ium ressure, that deends on the characteristics of the um. The amount of moles of vaor exchanges with is outside is equal to the number of moles of substance sublimated every second by the incog heat Q : where Q L Q '' Q ' Q '' Q' L is the sublimation heat of the solid. The ideal gas equation can be alied here, and allow us to calculate the corresonding vaor volume V RT V (3) : (2) i.e.: T R V (4) In order to calculate the solid s imal temerature T when in equilibrium with the vaor ressure, we start from the Clausius-Claeyron equation. The volume of the solid being negligible with resect to the vaor, we can relace: d L dt 2 R T V i, j with RT whence:, L is suosed indeendent of temerature. (5) After integration: L log logc (6) RT In order to detere the integration constant C, let s write equation (6) for two different equilibrium conditions, e.g. T 0 (trile oint with ressure 0 ) and T (sublimation temerature at imum ressure ): R 1 log 0 logc L T R 1 log logc L T 0 (7)

8 EPFL-TRAVAUX PRATIQUE DE PHYIQUE K14-8 ubtracting the first equation from the second yields: R 1 1 log log 0 L T T 0 which leads to: T 1 R log T L (8) III. EXPERIMENTAL ETUP III.1. VACUUM CHAMBER. The elements that make u a vacuum setu are, in addition to the ums and ressure gauges, the junction ieces, joints, valves, searating units, and tras (fig. 6). The most used materials are metal (aluum or stainless steel), glass, quartz, ceramic, rubber and lastic. valve air inut microvalve Bourdon gauge 17 vacuum chambre Pirani gauge 13 Penning gauge liquid nitrogen tra valve 10 Pressure gauge late valve 6 vanne 4 18 valve 19 valve water-cooled baffle Kammerer gauge 5 Diffusion um Pirani gauge 2 3 valve 1 gas cartridge Figure 6: Diagram of the high vacuum setu. The numbering corresond to that on location. III.2. TRIPLE POINT Figure 7 shows a diagram of the setu and Figure 8 a hoto. Vane um

9 EPFL-TRAVAUX PRATIQUE DE PHYIQUE K14-9 Figure 7: Exerimental setu diagram 1: Vane um 2: Derivation valve 3: Entrance valve in the main Dewar 4: Entrance valve of the cold nitrogen 5: Main Dewar 6: Lid of the main Dewar 7: Control button of the agitator 8: Thermal robe 9: Pressure gauge 10: Dewar containing liquid nitrogen at atmosheric ressure Measurng temerature and ressure In order to detere the three curves (sublimation, fusion and vaorization), and their intersection on a ( ) diagram, we need two main conditions: T, 1) The indicated values must be instantaneous (no measurement inertia) 2) The two indications must be simultaneous (we need values of T, at the same moment) We will use an electronic ressure gauge to measure the and a latinum robe to measure the temerature. For the values of temerature to be exact, we need a good thermal contact between the robe and the measured body, which isn t the case for solid nitrogen, since it s orous. The robe has been erfected to best satisfy this condition. otting the trile oint The method consists in erforg maniulations that maintain the resence of several hases simultaneously, after a cooling rocess. By using this method, we will eventually reach the trile oint, and stay there long enough to verify that the temerature and corresonding ressure remain constant. T j j

10 EPFL-TRAVAUX PRATIQUE DE PHYIQUE K14-10 IV. REQUIRED EXPERIMENT VACUUM TECHNOLOGY 1) Measure the rimary ug kinetics when the vacuum chamber of volume V is emtied. Detere from this the effective throughut, and the limiting ressure of the vane um. The vacuum haens very quickly. You may want to film the ressure gauge, and then match the indicated ressure of a given frame to the corresonding time of the video. 2) Measure the secondary ug kinetics, using the diffusion um. Detere the ug seed, as well as the limiting ressure of the diffusion um. Procedure: The hot oil of the diffusion um must never come in contact with that atmoshere at a ressure exceeding 0 01Torr. Therefore, roceed as follows:. a) Emty out the vacuum chamber until aroximately 0.01Torr using the rotary vane um. b) Pum out the diffusion um until it reaches aroximately 0.01 Torr. c) tart the diffusion um, while making sure to kee the vane um running behind it. The vane um serves as an outgassing um for the oil. After arox. 15. The diffusion um reaches its working ressure. d) If the ressure inside the chamber is less than 0.01Torr, then we can oen the late valve, and the ressure quickly dros from 0.01Torr to 10, Torr Torr, turn on the Penning gauge, and write down the ressure as a function of time, e) tarting at until reaching the limiting ressure. Plot the corresonding curve, and detere the corresonding ug throughut. toing the diffusion um Close the late valve. Turn off the diffusion um and the Penning gauge. After MINIMUM 20 utes, close all the valves leading to the vane um, before turning it off. Turn off the Pirani gauge, and the main ower suly. Using the microvalve When the microvalve is correctly closed, the button can turn freely. NEVER FORCEFULLY TRY TO CLOE THE VALVE by screwing it assed the free rotation. TRIPLE POINT OF NITROGEN Before doing anything, make sure you have gone through all of the tis below: - Liquid nitrogen under 1 atm boils at C. Any contact will cause sever burns - Try to avoid gas exchang between the Dewar and the atmoshere, to avoid the formation of frost in the Dewar. - The otimal fill level of the main Dewar is indicated by the red line. - Avoid letting the vane um work on the atmoshere, i.e. with an oen valve. The um heats u. - When turning off the um, immediately introduce atmosheric ressure into it, by oening the valve 2 (lever ointing right) without letting oil reach the valve. - Never let the agitator run when the nitrogen is solid. - When in resence of small crystals in the liquid, reduce the seed of the agitator - When in resence of liquid only, the maximal seed of the joint should be the graduation 4 on the otentiometer

11 EPFL-TRAVAUX PRATIQUE DE PHYIQUE K ) Pum the liquid nitrogen until reaching a artial evaoration, which will cool the rest of the liquid. After a few utes, we notice that a solid hase aears. Kee ug until reaching arox. 10 Torr. 2) Close valve (3) (lever ointing u). to ug, and write down the measurements for ( as the nitrogen gets warmer T, 3) Using these measurements, lot ( T ) at constant volume, you should get three branches (PJ, FJ, JC). We should notice four different stages during this rocess: - simultaneous increase of T and (sublimation curve) - constant T and (trile oint) - aroximate constant value of T and increase in (fusion curve) To obtain the vaorization curve, sto ug just before formation of a solid hase and trace the increase of T and. 4) Reeat stes 1 through 3 at least once. 5) olidify the nitrogen (down to arox. 10 Torr), and close the valve (3). After having filled the Dewar (10) with liquid nitrogen, let nitrogen into the system using the valve (4). What henomenon can you observe? How can you exlain this? 6) Knowing the arameter of the um, use equation (8) to calculate the imal temerature that can be reached. ), Fig. 8 : Image of the exerimental setu.

12 EPFL-TRAVAUX PRATIQUE DE PHYIQUE K14-12 ANNEX VACUUM PUMP Rotary vane ums A vane um (fig. 9) consists of a hollow cylinder (1) in which an uncentered rotor (2) containing vanes (3) is rotated. The vanes are constantly ressed against the cylinder walls, thus sucking air from one side of the um (11) and ushing it through the exhaust valve (5) on the other side. The rotor is off center, so that the volume of gas traed by two vanes is variable. This allows the air to be comressed when arriving towards valve, which ensures that there will always be enough ressure to lift it. Many arts of the system are covered in oil. The oil simultaneously acts as a lubricant and covers u the remaining gas. 1. Cylindrical ug body 2. Uncentered rotor 3. Vanes 4. Gas Ballast entry 5. Oil covered exhaust valve 6. Oil deflectors 7. Oil gauge 8. Exhaust tubing 9. Entrance tubing 10. Imurity tra 11. uction canal Figure 9: ectional view of a rotary vane um Gas Ballast The gas ballast allows for vane ums to not only um gas, but also large quantities of condensable vaor. When a vane um is used at low ressures, of the order of Torr, the comression rate 5 2 reaches 10 (i.e ). If the um absorbs vaor, it could be comressed assed its saturation ressure. For instance, if the um is at 70 C and absorbs water vaor, the vaor can only be comressed u to 250 Torr (saturation ressure of water at 70 C ). If we continue comressing the water vaor, it will condense into drolets, without increasing the ressure. The exhaust valve doesn t oen, and the water stays in the system, where it will create an emulsion with the oil, and deteriorate its lubricating roerties. The gas ballast stos water vaor from condensing (fig. 10). Before the comression starts, a well dosed amount of air is injected into the suction chamber, in order to lower the comression rate (u to 10 1 ). The vaor that get sucked into the system can now be comressed with the extra gas, and will oen the exhaust valve before condensing. When starting the ug rocess, the gas ballast must always be oen. The small layer of water that almost always covers the walls of a vacuum chamber evaorate rogressively when starting the ug. It is only once this vaor has been comletely eliated (after 1 to 2 ), that we can close the gas ballast in order to reach the desired low ressures. 10 2

13 EPFL-TRAVAUX PRATIQUE DE PHYIQUE K14-13 Figure 10 : Pug cycle with and without gas ballast Fluid ums Fluid ums are all based on the same rincile: the gas to be evacuated is transorted from a low ressure region to a higher ressure region using a high ressure jet of steam (oil, mercury, water, ). The steam never leaves the um, since it is condensed as soon as is hits the cooled walls of the um. Gaede was the first to notice that a relatively low gas ressure could be sucked into a jet of steam at a much higher ressure, so that the gas molecules were transorted from a low ressure area to a higher ressure area. This seegly aradoxical henomenon is due to the fact that the steam is first comletely gas-free, so that the gases diffuse from an area where there is a gas of high artial ressure (container) to an area where the artial ressure of the gas is lower (the steam). You can consider the steam as a semi-ermeable membrane (similar to the osmosis henomenon), through which the gas can diffuse to enter but not to leave, the artial ressure of the gas is therefore much higher on one side of the jet than on the other. Diffusion ums ( 3 10 Torr) Diffusion ums (fig. 11) are made of a ug body (1), in which the bottom can be heated, and the sides cooled, and an internal body with several stories (generally three) (2). The motor fluid ket in the heating tank (5), is heated and vaorized electrically. The vaor rises in the column (4) and leaves through the nozzle (3) at a suersonic seed. The fluid then condenses on the water cooled walls, and dris back into the heating tank. The umed gas is absorbed by the oil, and leaves through the exhaust tube. For oil diffusion ums, it is necessary to outgas and fractionate the oil before letting it back into the heating tank (5).

14 EPFL-TRAVAUX PRATIQUE DE PHYIQUE K14-14 Figure 11: Diffusion um diagram.(1) Pug body, (2) Internal body, (3) Nozzles, (4) team rising tube, (5) Heating tank. Outgassing: The condensed motor fluid dris along the walls is brought under the heat tank, at a temerature of aroximately 130 C, at which oint the more volatile molecules are absorbed by the rimary um. The less volatile molecules however, remain in the fluid. Fractionating oil: After being outgassed, the motor fluid is made u of elements varying in weight. The fractionating equiment makes sure the elements easiest to evaorate are brought to the first nozzle, close to the rimary vacuum, and the elements hardest to evaorate are brought to the third nozzle, close to the molecular vacuum. toing oil molecules: Most of the time, we lace a cold tra between the diffusion um and the vacuum chamber, to sto the oil molecules from leaving the um. PREURE GAUGE: MEAURING PREURE Torr, over 16 decimal To this day, the region of measurable ressures ranges from 760 Torr to oints. In order to measure ressures in such a large region, we use instruments called ressure gauges. ince no hysical object is caable of measuring ressures over this whole range, we resorted to designing a whole family of ressure gauges that are used for measuring ressures in different ranges, each of which sreads over a few decimal oints. Mechanical ressure gauges: the mechanical energy is either sulied by the gas whose ressure we wish to detere (e.g. membrane gauge, U-ressure gauge) or by and external source of work (comression gauges, e.g. Kammerer gauge). Electrical ressure gauges: The electrical energy is either transformed into heat, on which we then base our measure (e.g. thermal conductivity gauge, Pirani gauge) or used to ionize the gas (e.g. ionization gauge, Penning Gauge)

15 EPFL-TRAVAUX PRATIQUE DE PHYIQUE K14-15 Bourdon gauge The ressure gauge is mainly made of a curved tube, closed off at one end, whose other end is connected chamber whose ressure we would like to detere (fig. 12). Patm As the ressure P reduces with resect to the atmosheric ressure, the radius of the tube decreases (easy to rove). P atm This motion is then amlified and calibrated by connecting the tube to a needle. ince the tube deforms elastically, the scale is linear. The measured ressure varies with the atmosheric ressure, but does not deend on the tye of gas contained in the chamber. P Pirani gauge Figure 12: Bourdon gauge This gauge uses the thermal exchange between a hot wire and the gas (fig. 13). The heat exchange deends on the ressure, but also on the tye of gas. The temerature of the wire is detered according to its resistance. The wire is connected to a comensating voltage via a Wheatstone bridge. This is a simle and solid gauge when the required recision isn t too high. The main disadvantages of the Pirani gauge are that it must be recalibrated for each gas, and is only useful for a limited range of ressure ( Torr). R Penning gauge Figure 13 : Pirani gauge This gauge uses the ionization of the gas between two electrode (fig. 14) to detere the ressure. The current that travels through the discharge gauge varies as a function of the ressure. In this gauge, the ath of the electrons is increased using a ermanent magnetic field, which extends the range of measureable ressure The usable ressure range of the G aimant aimant anode cathode Penning gauge is Torr. These instruments are robust, insensitive to air and vibrations, but is retty imrecise when the cathode is cold. The recision doesn t exceed 20 %. This gauge needs to be recalibrated for each gas. Figure 14 : Penning gauge