Première loi de la thermodynamique: détermination du coefficient
Contents
1. la pression atmosph rique alors qu un signal lu de 3 48 V correspondra 58 5 PSIG Pour vos analyses vous devrez convertir le voltage en pression l aide des informations pr c dentes L unit SI de pression est le bar alors vous aurez effectuer une conversion Veuillez prendre note que le capteur de pression peut avoir un d calage offset ce qui aura pour cons quence que le voltage ne sera pas exactement de OV pression ambiante Vous devrez en tenir compte dans le traitement de vos donn es Pour fonctionner les capteurs de pression ont besoin d une source d alimentation 24VDC Vous devrez donc connecter le petit transformateur dans une des fiches d alimentation situ e sur votre espace de travail Thermocouple type T Cuivre Constantan R sum de fa on simple un thermocouple est la jonction physique entre deux m taux ou deux alliages diff rents Cette jonction g n re un potentiel appel potentiel de jonction dont la valeur d pend de la temp rature En mesurant ce potentiel par rapport une r f rence la temp rature de la jonction peut tre d termin e avec une assez bonne pr cision Le thermocouple est l un des outils de mesure de temp rature le plus utilis puisqu il est peu co teux durable et qu il est g n ralement assez sensible Dans l exp rience de d termination du coefficient Joule Thomson deux thermocouples seront mis en s rie de sorte que la diff rence de potentiel mesur e entre le2. Carte d acquisition Futek DAQ 0311A La petite carte d acquisition Futek permet de mesurer et d enregistrer un signal lectrique sur l ordinateur en fonction du temps Vous pourrez enregistrer la pression et la temp rature de votre syst me pour ensuite effectuer l analyse de vos donn es Le mod le que vous utiliserez comporte trois entr es diff rentes soit une entr e pour mesure diff rentielle et deux entr es pour des mesures par rapport la terre ground qui agit comme r f rence Vous utiliserez seulement les entr es r f renc es par rapport au ground Cette carte permet l acquisition entre 10V et 10 V avec une r solution de 16 bits Elle a donc une gamme dynamique dynamic range de 20 V r parti en 16 bits 2 6 possibilit s Sa plus petite mesure possible peut tre calcul e en divisant la gamme dynamique par le nombre de possibilit s on obtient donc 0 3 mV La gamme dynamique de cette carte peut cependant tre r duite ce qui permet d augmenter la r solution CPH316 M thodes de la chimie physique E SHERBROOKE Montage exp rimental Le montage exp rimental que vous allez utiliser est d taill dans l article qui se trouve en annexe ce document Halpern et Gozashti Lorsque vous arriverez au laboratoire le montage se trouvera en pi ce d tach es que vous devrez assembler par vous m me Les diff rentes parties pourront s assembler gr ce des connecteurs Swagelok que vous devrez serrer l aide d
3. 0 0596 0 229 s 1 10 Hyr meas 0 066 0 230 0 968 1 07 ulit 0 0624 0 2217 0 962 1 10 The JT coefficient defined as 8T dp can be expressed in terms of the T and V partial derivatives of the equation of state explicit in P see also 7 8 uyr 1 Cp T dp dT y dp dV 7 V 6 The application of equation 6 to the vdW RK and BB equations of state provides in the limit of large V the fol lowing V independent expressions for uyr Myr 1 Cp 2a RT b vdW 7 ur 1 Cp 5a 2RT b RK 8 Hsr 1 Cp 2Ao RT 4c T Bo BB 9 The values of uyr calculated from eqs 7 9 along with those measured with the apparatus described are listed in the table which also contains the literature values as well as the critical constants of the gases As can be seen the agreement is quite satisfactory and demonstrates the sensitivity and accuracy attainable with this simple apparatus Literature Cited 1 Shoemaker D P Garland C W Steinfeld J L Nibler J W Experiments in Physical Chemistry 4th ed McGraw Hill New York 1981 p 65 2 Hecht C E Zimmerman G J Chem Educ 1954 31 530 3 Levine I N Physical Chemistry 2nd ed McGraw Hill New York 1983 pp 200 206 4 Redlich O Kwong J N S Chem Rev 1949 44 233 5 Beattie J A Bridgeman O C J Amer Chem Soc 1928 50 3133 6 Catellan G W Physical Chemistry 3rd ed Addis
4. 5 324 5 372 5 420 5 469 5 517 5 566 5 615 5 663 5 712 120 130 5 712 5 761 5 810 5 859 5 908 5 957 6 007 6 056 6 105 6 155 6204 130 140 6 204 6254 6 303 6 353 6 403 6 452 6 502 6 552 6 602 6 652 6 702 140 150 6 702 6 753 6 803 6853 6 903 6 954 7 004 7 055 7 106 7 156 7 207 150 160 7 207 7 258 7 309 7 360 7 411 7 462 7 513 7 564 7 615 7 7 718 160 170 7 718 7 769 7 821 7 872 7 924 7 975 8 027 8 079 8 131 8 183 8235 170 180 8 235 8 287 8 339 8 391 8 443 8 495 8 548 8 600 8 652 8 705 8 757 180 190 8 757 8 810 8 863 8915 8 968 9 021 9 074 9 127 9 180 9 233 9 286 190 200 9 286 9 339 9 392 9 446 9 499 9 553 9 606 9 659 9 713 9 767 9 820 200 210 9 820 9 87 9 928 9 982 10 036 10 090 10 144 10 198 10 252 10 306 10 360 210 220 10 360 10414 10 469 10 523 10 578 10 632 10 687 10 741 10 796 10 851 10 905 220 230 10 905 10 960 11 015 11 070 11 125 11 180 11 235 11 290 11 345 11 401 11 456 230 240 11 456 11 511 11 566 11 622 11 677 11 733 11 788 11 844 11 900 11 956 12 011 240 250 12 011 12 067 12 123 12 17 12 235 12 291 12 347 12 403 12 459 12 515 12 572 250 260 12 572 12 628 12 684 12 741 12 797 12 854 12 910 12 967 13 024 13 080 13 137 260 270 13 137 13194 13 251 13 307 13 364 13 421 13 478 13 535 13 592 13 650 13 707 270 280 13 707 137 13 821 13 879 13 936 13 993 14 051 14 108 14 166 14 223 14 281 280 290 14 281 14339 14 396 14 454 14 512 14 570 14 628 14 686 14 7 14 802 14 860 290 300 14 860 14918 14 976 15 034 15 092 15 151 15 209 15 267 15 326 15 384 15 443 300
5. 6 232 250 240 6 105 6 114 6 122 6 130 6 138 6 146 6 153 6 160 6 167 6 17 6 181 240 230 6 007 6 018 6 028 6 039 6 049 6 059 6 068 6 078 6 087 6 096 6 105 230 220 5 889 5901 5 914 5 926 5 938 5 950 5 962 5 973 5 985 5 996 6 007 220 210 5 753 5 767 5 782 5 795 5 809 5 823 5 836 5 850 5 863 5 876 5 889 210 200 5 603 5 619 5 634 5 650 5 665 5 680 5 695 5 710 5 724 5 739 5 753 200 190 5 439 5 456 5 473 5 489 5 506 5 522 5 539 5 555 5 571 5 587 5 603 190 180 5 261 5 27 5 297 5 315 5 333 5 351 5 369 5 387 5 404 5 421 5 439 100 170 5 069 5 089 5 109 5 128 5 147 5 167 5 186 5 205 5 223 5 242 5 261 170 160 4 865 4 886 4 907 4928 4 948 4 969 4 989 5 010 5 030 5 050 5 069 160 150 4 648 4 67 4 693 4 715 4 737 4 758 4 780 4 801 4 823 4 844 4 865 150 140 4419 4442 4 466 4 489 4512 4 535 4 558 4 581 4 603 4 626 4 648 140 130 4 177 4 202 4 226 4251 4 275 4 299 4 323 4 347 4 371 4 395 4 419 130 120 3 923 3 949 3 974 4 000 4 026 4 051 4 077 4 102 4 127 4 152 4 177 120 110 3 656 3 684 3 711 3 737 3 764 3 791 3 818 3 844 3 871 3 897 3 923 110 100 3 378 3 407 3 435 3 463 3 491 3 519 3 547 3 574 3 602 3 629 3 656 100 90 3 089 3 118 3 147 3 177 3 206 3 235 3 264 3 293 3 321 3 350 3 378 90 80 2 788 2 818 2 849 2 879 2 909 2 939 2 970 2 999 3 029 3 059 3 089 80 70 2 475 2 5
6. DISCUSSION The Joule Thomson coefficient gives a measure of how much potential energy is con verted into kinetic energy or vice versa as molecules in a dense gas change their average separation during an adiabatic expansion As mentioned earlier the magnitude and sign of p are determined by the balance of attractive and repulsive interactions and for most gases at room temperature cooling occurs as molecules work against a net attractive force as they move apart The exceptions are the weakly interacting species He and H where yp is negative at 300 K and precooling below the inversion temperature is first necessary before cooling can occur on expansion Calculate the inversion temperature for the gases of Table 1 using Eqs 11 14 and 16 neglecting the last small pressure dependent term in 14 and compare your values with experimental ones you find in the literature Equations 14 and 16 can be most easily solved for T by iteration using for example the Solve For function of spreadsheet programs as discussed in Chapter III Joule Thomson cooling is the basis for the Linde method of gas liquefaction in which a gas is compressed allowed to cool by heat exchange and is then expanded to cool suf ficiently that the gas liquefies This effect is also important in the operation of refrigerators and heat pumps Using cylinders of high pressure gas cooling can be achieved without power input in a device without moving parts and hence t
7. R4 est de 10 kQ R3 de 1 kQ et C2 a une valeur de 0 001 UF L amplification de cette partie est de 10 et l amplification totale de ce circuit est donc d un facteur 1000 Vec Hi L alimentation des amplificateurs op rationnels doit tre accompagn e de condensateurs de d couplage Ceux ci permettent encore une fois de filtrer une partie du bruit qui pourrait affecter votre circuit Vous devrez connecter des condensateurs lectrolytiques pour relier chacune des bornes d alimentation la terre Veillez bien connecter les H condensateurs dans la bonne direction la direction ne sera pas la m me pour les deux polarit s de l alimentation N h sitez pas demander de vee CPH316 M thodes de la chimie physique S SHERBROOKE l aide votre d monstrateur au besoin La photo ci dessous est un exemple de circuit qui pourra vous aider vous orienter dans le montage de votre circuit Connecter le thermocouple ici x RA Veuillez prendre note que les amplificateurs op rationnels sont des pi ces tr s fragiles et sensibles l lectricit statique Il est toujours conseill de toucher une pi ce de m tal reli la terre par exemple un bo tier d ordinateur avant de toucher aux composantes du circuit Ceci permet d vacuer l lectricit statique qui pourrait rester dans votre corps Aussi veuillez vous assurer d avoir connect les composantes correctement avant d ajouter l alimentation du circuit
8. experiment EXPERIMENTAL The experimental apparatus shown in Fig 2 is patterned after a design given in Ref 7 The porous plug is a in OD stainless steel frit of 2 wm pore size and 4 in thick ness pressed into a 3 in Swagelok tee made of nylon for reduced thermal conductivity Exp 2 Joule Thomson Effect 103 To Bourdon gauge Gas outlet To purge valve outlet Insulation x Polyethylene tubing 3 2 micron g Teflon frit pressed rod with into fitting 0 063 hole Le Constantan N PA Thermocouples Nylon epoxied inside copper disnmocounle fittings 0 0625 stainless steel tube Gas inlet The high pressure inlet is attached to a 3 in cross to provide ports for gas introduction pressure measurement and thermocouple placement just in front of the frit The Bourdon gauge 0 10 bar should be connected via a tee to a purge valve to facilitate gas changes Before use the assembly should be tested at 10 bar for leaks Thermal insulation such as glass wool should be wrapped around the frit assembly to keep the expansion as adiabatic as possible The temperature difference AT across the frit is measured with two copper Constantan type T thermocouples with wires of 0 010
9. in diameter or less for reduced thermal conductivity The thermocouples can be sealed with epoxy into a in stainless steel sheathing tube which can be connected to the cross fitting by a 4 in to 3 in Swagelok adaptor or more simply by swaging a 2 in Teflon rod with a 0 063 in feedthrough hole for the thermocouple tube as shown in Fig 2 A convenient 6 in in OD sealed subminiature probe with an exposed thermocouple junction and external strain relief is available from Omega e g probe TM TSS 062E 6 The 6 in length is suf ficient to allow the thermocouples to be positioned adjacent to the center of the frit as shown in the figure Because the maximum temperature change will be only 0 5 to 4 K a sensitive digital voltmeter 0 1 uV null voltmeter or potentiometer is desirable for accurate measurements To obtain the temperature difference directly the two Constantan leads of the thermocouples FIGURE 2 Detail of J oule T homson cell 104 Chapter IV Gases should be clamped together and the copper leads should be attached to the measuring device t For best absolute accuracy the two thermocouples should be calibrated e g using a standard thermometer to determine their temperature coefficients Seebeck coefficient However for a copper C onstantan thermocouple varies only slightly with temperature from 39 to 43 uV KT from 0 to 50 C At 25 C a is 40 6 uV K t and the variation is small from one thermocou ple t
10. of the experimental ratio of temperature difference to pressure difference as the pressure difference approaches zero u lim 5 Ap 0 Ap 4 Experimentally AT is found to be very nearly linear with Ap over a considerable range this isin accord with expectations based on the theory given below The denominator on the right side of Eq 4 is the heat capacity at constant pressure C The numerator is zero for an ideal gas see Eq 1 Accordingly for an ideal gas the J oule Thomson coefficient is zero and there should be no temperature difference across the porous plug For a real gas the J oule Thomson coefficient is a measure of the quantity OH dp which can be related thermodynamically to the quantity involved in the Joule experiment dE aV Using the general thermodynamic relation aH av a a ua P it can be shown that for an ideal gas satisfying the criteria already given pV const x T 7 where T is the absolute thermodynamic temperature The coefficient dH ap is therefore a measure of the deviation from the behavior predicted by Eq 7 On combining Eqs 4 and 6 we obtain _ T aV aT V C In order to predict the magnitude and behavior of the J oule Thomson coefficient for a real gas we can use the van der W aals equation of state which is 8 0 RT 9 where V is the molar volume We can rearrange this equation neglecting the very small second order term ab V2 and su
11. qui permet de d terminer sa valeur Pour conna tre la valeur de la r sistance plus rapidement vous pourrez utiliser votre multim tre Keithley qui comprend une option pour la mesurer L image ci contre vous donne un exemple de ce quoi ressemble une resistance et vous montre le symbole utilis afin de noter une r sistance sur un sch ma lectrique Il y a aussi des condensateurs de deux diff rents types A c ramique et lectrolytique Les condensateurs c ramiques droite dans la figure peuvent tre reli s dans n importe quelle direction alors que les condenateurs lectrolytiques gauche rs sont polaris s et doivent tre reli s dans la bonne direction Les condensateurs lectrolytiques ont deux extr mit s diff rentes L extr mit de couleur noir doit tre plac e vers le c t le plus n gatif du circuit alors que l extr mit de couleur m tallique doit tre reli e au c t le plus positif L extr mit noire est aussi identifi e par un anneau noir sur l enveloppe externe du condensateur Le 8 a symbole d un condensateur dans un circuit lectrique est repr sent e ci contre Finalement il y aura des amplificateurs op rationnels qui permettront d effectuer Input Output l amplification de votre signal L amplificateur Vy que vous utiliserez sera le TLO71 Il sera J repr sent par le symbole triangulaire suivant dans le circuit lectrique et ressemblera la petite puce ci cont
12. vdW equation is P RT V b a V 1 and the RK equation which is a very useful two parameter state function reads P RT V b a V V b T 2 The vdW a and b parameters expressed in terms of the critical temperature T and pressure P are a 2 8408 x 10 T P and b 0 010257T P 3 where units of dm atm and K are implied Likewise for the RK equation a 2 879 x 10 T 5 P and b 7 1097 X 10 T P The BB equation containing the five parameters a b Ao Bo and c is P RTU c VTSHV Bol b V V Ag 1 a V V 4 The BB equation can be cast into the more convenient virial form 6 P RT VT RT V By Ao RT c T RT V Byb Aoa RT Boc T RT V4 Bybe T 5 1002 Journal of Chemical Education Critical Data Heat Capacities vdW RK and BB Parameters for He N2 CO and SF 9 as well as Calculated Measured and Literature Values 10 11 for uyr He N2 SFe CO2 Ve 0 0578 0 0901 0 199 0 0940 dm mol P 2 261 33 54 37 11 72 85 atm To 5 20 126 27 318 71 304 20 K Cp 0 2052 0 2875 0 9602 0 366 dm atm mol K avdW 0 03397 1 350 7 775 3 609 b vdW 0 02359 0 03862 0 08809 0 04283 a RK 0 07851 15 38 140 7 63 78 b RK 0 01635 0 02677 0 06106 0 02969 Ao 0 0216 1 3445 a 5 0065 B 0 0140 0 05046 Si 0 07235 C 40 4 20 X 104 6 600 X 105 l vdW 0 101 0 250 0 571 0 689 Lsr RK 0 0774 0 224 0 804 0 951 Lsr BB
13. wall pressure tubing Dewar flask large ring stirrer notched cover plate for Dewar with hole for mounting gas thermometer bulb electrical heating mantle steam generator with rubber connecting tubing steam jacket two ring stands ring clamp two clamp holders one large and one medium clamp Cylinder of helium or dry nitrogen pure ice 1 kg ice grinder liquid nitrogen 1 L boiling chips stopcock grease vacuum pump or water aspirator REFERENCES 1 R J Silbey R A Alberty and M G Bawendi Physical Chemistry 4th ed pp 7 8 97 Wiley N ew Y ork 2005 2 J A Beattie and coworkers Proc Am Acad Arts Sci 74 327 1941 77 255 1949 GENERAL READING J R Leigh Temperature Measurement and Control INSPEC Edison NJ 1988 R P Benedict Fundamentals of Temperature Pressure and F low M easurements 3d ed Wiley Interscience New York 1984 J F Schooley Thermometry CRC Reprint Franklin Elkins Park PA 1986 EXPERIMENT 2 Joule Thomson Effect The Joule Thomson effect is a measure of the deviation of the behavior of a real gas from what is defined to be ideal gas behavior In this experiment a simple technique for measur ing this effect will be applied to a few common gases THEORY An ideal gas may be defined as one for which the following two conditions apply at all temperatures for a fixed quantity of the gas 1 Boyle s law is obeyed i e pV f T Exp 2 Joul
14. 07 2 539 2 570 2 602 2 633 2 664 2 695 2 726 2 757 2 788 70 60 2 152 2 185 2 218 2 250 2 283 2 315 2 348 2 380 2 412 2 444 2475 60 50 1 819 1 853 1 886 1 920 1 953 1 987 2 020 2 053 2 087 2 120 2 152 50 40 1 475 1 510 1 544 1 579 1 614 1 648 1 682 1 717 1 751 1 785 1 819 40 30 1 121 1 157 1 192 1 228 1 263 1 299 1 334 1 370 1 405 1 440 1 475 30 20 0 757 0 794 0 830 0 867 0 903 0 940 0 97 1 013 1 049 1 085 1 121 20 10 0 383 0421 0 458 0 496 0 534 0 571 0 608 0 646 0 683 0 720 0 757 10 0 000 0 039 0 077 0 116 0 154 0 193 0 231 0 269 0 307 0 345 0 383 0 0 000 039 078 117 156 195 234 273 312 351 391 0 10 391 430 470 510 549 589 629 669 709 749 789 10 20 789 30 870 11 951 992 1 032 1 073 1114 1 155 1 196 20 30 1 196 1 237 1 279 1 320 1 361 1 403 1 444 1 486 1 528 1 569 1 611 30 40 1 611 1 653 1 695 1 738 1 780 1 822 1 865 1 907 1 950 1 992 2 035 40 50 2 035 2 078 2 121 2 164 2 207 2 250 2 294 2 337 2 380 2 424 2467 50 60 2 467 2511 2 555 2 599 2 643 2 687 2 731 2 775 2 819 2 364 2 908 60 70 2 908 2 953 2 997 3 042 3 087 3 131 3 17 3 221 3 266 3 312 3 357 70 80 3 357 3 402 3 447 3 493 3 538 3 584 3 630 3 676 3 721 3 767 3813 80 90 3 813 3 859 3 906 3 952 3 998 4 044 4 091 4 137 4 184 4 231 4277 90 100 4277 4324 4 371 4418 4 465 4 512 4 559 4 607 4 654 4 701 4 749 100 110 4 749 4 796 4 844 4 891 4 939 4 987 035 083 5 131 5 179 5 227 110 120 5 227 5 275
15. 16 M thodes de la chimie physique S SHERBROOKE positive de la batterie 1 sur le rail a du breadboard la borne n gative de la batterie 1 sur le rail b la borne positive de la batterie 2 sur le rail m et la borne n gative de la batterie 2 sur le rail n Comme mentionn plus haut les rails b et m devront tre reli s ensembles on BE mp pe 7 Mme Aa 00 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 O0 00 0 0 0 O 0 0 0 O O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 O O 0 0O 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 0 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 0 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 O 0 0 0 0 Votre circuit comprendra plusieurs types de composantes lectroniques dont certaines que vous connaissez d j Tout d abord la r sistance avec un code de couleur
16. 310 15 443 15 501 15 560 15 619 15 677 15 736 15 795 15 853 15 912 15 971 16 030 310 320 16 030 16 089 16 148 16207 16 266 16 325 16 384 16 444 16 503 16 562 16 621 320 330 16621 16 681 16 740 16 800 16 859 16 919 16 978 17 038 17 097 17 157 17217 330 340 17 217 17277 17 336 17396 17 456 17 516 17 576 17 636 17 696 17 756 17816 340 350 17 816 17 877 17 937 17 997 18 057 18 118 18 178 18 238 18 299 18 359 18 420 350 360 18 420 18 480 18 541 18 602 18 662 18 723 18 784 18 845 18 905 18 966 19 027 360 370 19027 19 088 19 149 19 210 19 271 19 332 19 393 19 455 19 516 19 577 19 638 370 380 19 638 19 699 19 761 19 822 19 883 19 945 20 006 20 068 20 129 20 191 20 252 380 390 20 252 20314 20 376 20 437 20 499 20 560 20 622 20 684 20 746 20 807 20 869 390 CPH316 M thodes de la chimie physique S SHERBROOKE w jn 4 7 o pal ho pal QJ AN P a a N 4 7 oO a pal N E E lt P lt P H 4 m m 2 2 m m 98 ChapterIV Gases SAFETY ISSUES The ballast bulb must be taped to prevent flying glass fragments in the unlikely event of breakage Safety glasses should be worn for all laboratory work Gas cylinders must be chained securely to the wall or laboratory bench see pp 644 646 and Appendix C Liq uid nitrogen must be handled properly see A ppendix C APPARATUS Pressure manometer such as a Honeywell stain gauge device and digital voltme ter for readout properly taped and mounted ballast bulb heavy
17. 927 Proc Am Acad Arts Sci 63 229 1928 J O Hirschfelder C F Curtiss and R B Bird Molecular Theory of Gases and Liquids chap 3 and table I A Wiley New Y ork 1964 7 A M Halpern and S Gozashti Chem Educ 63 1001 1986 nn a EXPERIMENT 3 Heat Capacity Ratios for Gases The ratio C C of the heat capacity of a gas at constant pressure to that at constant vol ume will be determined by either the method of adiabatic expansion or the sound velocity method Several gases will be studied and the results will be interpreted in terms of the contribution made to the specific heat by various molecular degrees of freedom THEORY In considering the theoretical calculation of the heat capacities of gases we shall be concerned only with perfect gases Since Cp C R foranideal gas whereC andC are the molar quantities C n and C n our discussion can be restricted to C An improved Apparatus for the Measurement of the Joule Thomson Coefficient of Gases Arthur M Halpern and Saeed Gozashti Northeastern University Boston MA 02115 One of the common applications of real gases presented in undergraduate treatments of thermodynamics is the Joule Thomson JT effect This topic not only explicitly shows how a nonzero JT coefficient arises from an equation of state for a real gas but it also appeals to the student s physical experience with the cooling associated with most expanding gases
18. CPH316 M thodes de la chimie physique FE SHERBROOKE Premiere loi de la thermodynamique d termination du coefficient Joule Thomson pour diff rents gaz R dig par Pierre Alexandre Turgeon Introduction L nergie d un gaz parfait est ind pendante du volume et de la pression elle ne d pend que de la temp rature En cons quence la temp rature d un gaz id al soumis a une expansion adiabatique demeure inchang e dans le processus En revanche en 1854 James Prescott Joule et William Thomson aussi connu sous le nom de Lord Kelvin ont d montr que la temp rature d un gaz r el changeait dans une expansion adiabatique Ce ph nom ne connu sous le nom d effet Joule Thomson est aujourd hui largement utilis dans la liqu faction des gaz Pour comprendre cet effet il faut tenir compte du comportement non id al des gaz en introduisant des param tres comme les interactions intermol culaires et le volume des particules Cette non id alit se traduit par un coefficient Joule Thomson propre chaque gaz Vous aurez mesurer le coefficient Joule Thomson de 3 gaz diff rents soit l h lium le dioxyde de carbone et l azote Cette exp rience vise vous familiariser avec diff rentes techniques exp rimentales telles que la manipulation de gaz comprim s l acquisition de donn es par ordinateur ainsi que l utilisation de thermocouples et de capteurs de pression Le montage exp rimental que vous utiliserez devra tre assembl par
19. In addition the ability to calculate the JT coefficient uyr from an equation of state illustrates the computational nature of thermodynamics as well as the relative utility of equations of state Experimental measurements of uyr nicely fit into the lab oratory portion of physical chemistry Accordingly this ex periment is described in Shoemaker et al 1 The procedure described there however is awkward and probably lacks the sensitivity needed to observe and quantitatively to measure the effect for He A somewhat different approach was de scribed by Hecht and Zimmerman 2 but this procedure while an improvement is also unwieldy and may not work satisfactorily with He One of the drawbacks with these apparatus is the need to construct specialized and cumber some equipment In this paper we describe an apparatus that can be con structed from commercially available components and that has the sensitivity to measure uyr for He with reasonable accuracy The strategy is to use gas fittings and a porous plug made from stainless steel This material was chosen because of its lower thermal conductivity relative to brass Unlike the glass used in the JT cells previously described our stain less steel apparatus can withstand higher pressures and in the case of He this contributes to the ability to measure uyr with reasonable accuracy The two commonly used gases No and CO are easily studied with this apparatus In addition SF is use
20. SIG dans vos montages puisqu ils n ont pas t con us pour soutenir de hautes pressions Avant de quitter le laboratoire assurez vous d avoir des donn es de qualit suffisante pour effectuer vos analyses En tout temps vous aurez un multim tre Keithley votre disposition Il s agit d un bon outil pour diagnostiquer des probl mes dans votre circuit lectrique Rapport de laboratoire Le rapport de laboratoire devra tre produit pendant la p riode r serv e cet effet Des directives plus sp cifiques vous seront donn es en temps et lieu CPH316 M thodes de la chimie physique F1 SHERBROOKE Liste de documents compl mentaires Experiments in Physical Chemistry 8 Edition by Carl W Garland Joseph W Nibler and David P Shoemaker McGraw Hill NEW YORK 2009 EXPERIENCE 2 An improved apparatus for the measurement of the Joule Thomson coefficient of gases A M Halpern and S Gozashti Journal of Chemical Education 1986 63 11 1001 Physical Chemistry 6 Edition by Ira N Levine McGraw Hill NEW YORK 2009 Manuel d utilisation pour carte d acquisition FUTEK DAQ 0311A UNIVERSIT DE SHERBROOKE Voltage mV en fonction de la temp rature pour les thermocouples de type T CPH316 M thodes de la chimie physique C 0 1 2 3 4 5 6 7 8 9 10 c 260 6 232 6 236 6 239 6 242 6 245 6 248 6 251 6 253 6 255 6 256 6 258 260 250 6 181 6 187 6 193 6 198 6 204 6 209 6 214 6 219 6 224 6 228
21. atus The potential developed by the ther mocouples was directly read by a Hewlett Packard model 419A null voltmeter Alternatively another readout device having an appropriately high input resistance can be used A calibration of 39 uV C confirmed by the freezing point of benzene was used in these experiments The measurements for He were carried out between pres sures of 90 and 30 psi Stable voltages were established after about 15 30 s Readings were taken in increments of 10 psi For the other gases where the JT effect is larger the highest pressure used could be reduced The entire experiment in volving the measurement of the four gases can be carried out in less than 3 h The JT coefficients were determined by a linear regres sion of the data see Fig 2 assuming a low pressure value of 1 atm The highest pressure used is low enough to justify the assumption of P independent JT coefficients These were compared with uyr as calculated from three equations of state van der Waals vdW Redlich Kwong RK 3 4 and Beattie Bridgeman BB 5 6 The results are shown in the table The first two involve two parameters which can be obtained from critical data while the latter incorporates five empirical parameters Volume 63 Number 11 November 1986 1001 200 160 120 Av 80 40 AP Ps Figure 2 Plots of AV versus AP for the gases studied He No SFe and CO The ambient temperature is 298 K The well known
22. bstituting p RT for 1 V in a first order term to obtain fe ap RT pv RT bp 2 R T p RP Thus Exp 2 Joule Thomson Effect Combination of these two equations yields V b la 10 Th T RT which on substitution into Eq 8 gives the expression _ la RT b van der Waals 11 This expression does not contain p or V explicitly and the molar heat capacity Ci may be considered essentially independent of these variables The temperature dependence of C p is small and accordingly that of u is also small enough to be neglected over the AT obtain able with a Ap of about 1 5 bar namely about 4 K or less for the gases considered here Accordingly we may expect that u will be approximately independent of Ap over a wide range as stated previously For most gases under ordinary conditions 2a RT gt b the attractive forces pre dominate over the repulsive forces in determining the nonideal behavior and the Joule Thomson coefficient is therefore positive gas cools on expansion At a sufficiently high temperature the inequality is reversed and the gas warms on expansion The temperature at which the Joule Thomson coefficient changes sign is called the inversion temperature T For a van der Waals gas la 1 Bb 12 This temperature is usually several hundred degrees above room temperature How ever hydrogen and helium are exceptional in having inversion temperatures that are well below roo
23. d it is a good choice for this experiment because it is presumably nontoxic nonreactive and relatively inexpen sive Moreover there is considerable interest in this material as a dielectric and possible refrigerant and as a model for multiple infrared photon absorption The students can thus made aware of this information A diagram of this apparatus is shown in Figure 1 The heart of the high pressure part of the JT cell is a 3 in union cross Swagelok SS 600 4 adapted on three sides to l4 in SS 200 R 6 The gas inlet is coupled via a h in Teflon tube and the pressure is read via a 0 100 psi gauge also connected by 4 in Teflon tubing used to reduce heat trans 10 pressure 9OU9E zoss wool insulation from gos supply Figure 1 Cut away diagram of the apparatus The stainless steel fittings and other components are described in the text fer to from the JT cell A copper constantan thermocouple sealed with an epoxy adhesive passes through a in tube and is positioned in the center of the interior of the cross This thermocouple is constructed from narrow gauge leads 0 010 in also to reduce heat transfer Omega Engineering Inc The expansion plug 2 um used was a 3 in stainless steel HPLC bed support 43 38BS Rainin Inst Co The frit is contained in a in union SS 600 6 the latter is connected to the cross via a 3 in close couple The low pressure thermocouple is fed through a 17 stainless steel syri
24. e Thomson Effect 99 and 2 the internal energy E is independent of volume ccordingly E is independent of pressure as well and in the absence of other pertinent variables such as applied fields E of an ideal gas is therefore a function of the temperature alone E g T It is apparent that the enthalpy H of an ideal gas is also a function of temperature alone H E pV h T Accordingly we can write for a definite quantity of an ideal gas at all temperatures es 4 cy s 1 aV ap aV ap The absence of any dependence of the internal energy of a gas on volume was sug gested by the early experiments of Gay L ussac and J oule They found that when a quantity of gas in a container initially at a given temperature was allowed to expand into another previously evacuated container without work or heat flow to or from the surroundings AE 0 the final temperature after the two containers came into equilibrium with each other was the same as the initial temperature However that kind of experiment known as the J oule experiment is of limited sensitivity because the heat capacity of the containers is large in comparison with that of the gases studied Subsequently J oule and Thomson showed in a different kind of experiment that real gases do undergo small temperature changes upon free expansion This experiment utilized continuous gas flow through a porous plug under adiabatic conditions Because of the continu
25. e regulator pressure by about 0 5 bar and again take readings every 30 s until a constant value is obtained Continue this procedure down to a final pressure of 0 5 bar Note that this is the excess pressure over the discharge pressure into the room assumed to be at 1 bar Change the gas supply to N and again purge the copper coil and pressure gauge with the purge valve open Close this valve and bring the pressure slowly to 10 bar a higher value than for CO since the cooling is less A fter the temperature has stabilized repeat the sequence of measurements as for CO but at 1 bar intervals Finally repeat the N proce dure using He gas In this case the temperature change will be much smaller and positive i e the gas heats on expansion because it is above the so called J oule Thomson inversion point the temperature at which the coefficient u is zero After completion of the experi ment make sure that all cylinder valves are closed CALCULATIONS For each gas studied do a linear regression to fit AV or AT versus Ap so as to obtain the slope along with its standard error On asingle graph show for each of the three gases the best fit straight line along with the experimental data points From the slopes evaluate the J oule Thomson coefficient w in units of K bar Compare your results with literature values given in Ref 7 Calculate u for these gases at 25 C from the van der tAs an alternative to a thermocouple one can use
26. er W aals equation The most general of the equations of state is the virial equation which is also the most fundamental since it has a direct theoretical connection to the intermolecular poten tial function The virial equation of state expresses the deviation from ideality as a series expansion in density and in terms of molar volume can be written PV 214 Ba T BD RT V g The virial coefficients B and B depend only on temperature and are determined by two and three body interactions between molecules respectively For pressures below about 10 bar the B term is very small and can be neglected Solving Eq 15 for and aV aT lp in a manner similar to that for the van der Waals case above gives T 9B2 8T Bz 15 16 Cp From statistical mechanics B T is given by BA T We 1 YK med 17 0 and 0B dT can be obtained by differentiation U r is the potential energy as a function of the separation of the molecules taken to be spherical and is important because it can be used to predict many of the transport and collisional properties of a molecule One com mon choice for U r is the so called Lennard ones 6 12 potential which has the form 12 vn al 2 2 oa where s is the well depth corresponding to the minimum in the potential and o is the sepa ration corresponding to U r 0 see Fig 47 1 Values for these parameters are included in Table 1 for the gases of interest in this
27. he Joule Thomson process has been used in cooling of small infrared and optical detectors on space probes Discuss some of the design factors that might be important in achieving maximum cooling efficiency in the latter kind of a device For the more difficult Joule experiment we can write 2 _ E V _ T ap oT y p a WV dE aT y C This quantity is called the Joule coefficient It is the limit of AT AV corrected for the heat capacity of the containers as AV approaches zero With the van der Waals equation of state we obtain n 4 C The corrected temperature change when the two contain 19 ers are of equal volume is found by integration to be AT a 2VC where V is the initial molar volume and C is the molar constant volume heat capacity It is instructive to calculate this AT for a gas such as CO In addition the student may consider the relative heat capacities of 10 L of the gas at a pressure of 1 bar and that of the quantity of copper required to construct two spheres of this volume with walls say 1 mm thick and then cal culate the AT expected to be observed with such an experimental arrangement SAFETY ISSUES Gas cylinders must be chained securely to the wall or laboratory bench see pp 644 646 and Appendix C 105 106 Chapter IV Gases APPARATUS Insulated J oule Thomson cell similar to that of Fig 2 suitable stainless steel frits can be obtained from chromatographic parts s
28. m temperatures This results from the very small attractive forces in these gases see Table 1 for values of the van der Waals constant a TABLE 1 Values of constants in equations of state and the Lennard Jones potential He H N CO van der Waals a 0 03457 0 2476 1 408 3 640 b 0 02370 0 02661 0 03913 0 04267 Beattie Bridgeman Ag 0 0219 0 2001 1 3623 5 0728 a 0 05984 0 00506 0 02617 0 07132 Bo 0 01400 0 02096 0 05046 0 10476 b 0 0 0 04359 0 00691 0 07235 107 0 0040 0 0504 4 20 66 00 Lennard Jonesf e k K 6 03 29 2 95 0 189 o nm 0 263 0 287 0 370 0 449 Units assumed are V in dm mol L mol p in bar 10 Pa T in K R 0 083145 bar dm K mol 101 102 Chapter IV Gases Other semiempirical equations of state can be used to predict Joule Thomson coef ficients Perhaps the best of these is the B eattie B ridgeman equation which can be writ ten for 1 mol as RT 1 e 7 ja 13 v where A A 1 a B Bol b and e c T2 In this equation of state there are five constants which are characteristic of the particular gas Ay Bo a b and c In terms of these constants and the pressure and temperature the J oule T homson coefficient is given by 1 2A Ac 2B b 3Aa 5BQC B 2 d H C RT T E RT i p 14 This equation predicts a small dependence on pressure not shown by Eq 11 which is based on the van d
29. nge needle the sharp end removed as a guide and held rigid by a 3 36 in reducing union ss 600 6 1 with Teflon ferrules The gas outlet is provided by several holes drilled through a short length 2 in of 34 in tubing placed between the frit containing union and the reducing union To damp out fluctuations in the temperature difference read by the thermocouples the low pressure thermocouple was fastened to asmall brass cup attached to the end of the guide using a minute amount of epoxy adhesive heavily impregnated with brass filings to improve the thermal conductivity The cup was prepared by simply filing down the lock end of the syringe To provide additional insulation a short length of Tygon tubing is inserted into the high pressure side of the frit Holes are provided for the thermocouple and pressure gauge Finally to keep the entire apparatus as adiabatic as possible it was wrapped in several layers of glass wool The two thermocouples were found to be very well matched so that when connected in series to indicate the temperature difference between them an immeasurably small potential was observed when they were isothermally equilibrated As an indication of the thermal balance be tween the thermocouples the voltage of the equilibrated static apparatus was usually found to be less than 1 uv Best results were obtained under this condition which could be brought about by a very slow trickle of gas He or N through the appar
30. o another For small temperature differences a linear relation AV aAT a dT dP Ap is a good approximation for the thermocouple potential difference between the two junctions t Thus to the accuracy needed for this experiment the slope of a plot of AV versus Ap can be combined with an assumed value of a 40 6 uV K to yield dT dp and hence p Procedure Setup the apparatus shown in Fig 2 The gas supply should be a cylin der or supply line equipped with a pressure regulator and a control valve The supply pres sure should be constant during the measurements B ecause a significant temperature change occurs as gases go from high to low pressure through the pressure regulator itself the gas should be passed through about 50 ft of 4 in coiled copper tubing contained in a water bath at 25 1 C A in to in adaptor can be used for a short insulated polyethylene tubing connection to the expansion apparatus Before initiating gas flow record the bath temperature and determine any offset voltage between the two thermocouples Start the measurements with CO with the pressure regulator set to minimum pressure Open the control valve and purge the copper line and pressure gauge of air or any other gases with the purge valve open Then close the purge valve and slowly increase the pres sure to 4 bar After this pressure is reached record the thermocouple reading every 30 s until the values become constant typically a few minutes L ower th
31. on Wesley Reading MA 1983 p 47 7 Rybolt T R J Chem Educ 1981 58 621 8 Noggle J T Physical Chemistry Little Brown Boston 1985 pp 105 110 9 Lange s Handbook of Chemistry 13th ed Dean J A ed McGraw Hill New York 1985 pp 9 180 9 4 10 Chemical Engineers Handbook 5th ed Perry R H Chilton C H Eds McGraw Hill New York 1973 p 3 102 11 Bier K Maurer G Sand H Ber Bunsenges Phys Chem 1980 84 430
32. ous flow the solid parts of the apparatus come into thermal equilibrium with the flowing gas and their heat capacities impose a much less serious limitation than in the case of the J oule experiment Let it be imagined that gas is flowing slowly from left to right through the porous plug in Fig 1 To the left of the plug the temperature and pressure of the gas are T and p and to the right of the plug they are T and p The volume of a definite quantity of gas say 1 mol is V on the left and V on the right and the internal energy is E and E respectively When 1 mol of gas flows through the plug the work done on the system by the surroundings is w PV P2V2 Since the process is adiabatic the change in internal energy is AE E E q w w Combining these two equations we obtain Ei pla Ez PA or H H2 2 Thus this process takes place at constant enthalpy FIGURE 1 Schematic diagram of the Joule Thomson experiment The stippled area represents a porous plug 100 Chapter IV Gases For a process involving arbitrary infinitesimal changes in pressure and temperature the change in enthalpy is oH oH H dp dT w 3 F a In the present experiment dH is zero and dT and dp cannot be arbitrary but are related by aT H p r 4 j z i aH aT 4 The quantity u defined by this equation is known as the J oule Thomson coefficient It rep resents the limiting value
33. re La connectivit de CPH316 M thodes de la chimie physique F1 SHERBROOKE l amplificateur op rationnel est repr sent e pour les connecteurs de 1 oFFser M1 fl e e JNC 8 dans la r alit vous n aurez besoin que des connecteurs 2 3 4 6 N 2 70 Vcc et 7 Les amplificateurs op rationnels ont besoin d tre aliment s IN U3 ep out Vcc et Vcc pour fonctionner Remarquez la pr sence du point Vcc U4 5p oFFseT nz noir ou du demi cercle en haut de la puce Ce symbole se retrouvera sur l amplificateur et vous permettra de l orienter correctement Voici donc le circuit que vous aurez reproduire pour l amplification de votre signal le circuit d taill est disponible en annexe C1 C2 EANN MA R2 R4 R3 AWA R1 V R4 lt I V Vous remarquerez la pr sence d un potentiom tre en bas droite du circuit Celui c1 vous permettra de compenser le d calage offset du signal en ramenant pr s de 0 le voltage de base du syst me Le circuit peut tre divis en deux sections La section de gauche amplifie d abord le signal par un facteur de R2 R1 Dans votre cas R2 a une valeur de 100 KQ et R1 de 1 KQ Les condensateurs C1 servent filtrer une partie du bruit lectrique qui pourrait affecter votre circuit Ils ont une capacit de 0 01uF L amplification de la premi re partie est donc d un facteur 100 Pour la deuxi me partie l amplification est d termin e par le facteur R4 R3 Dans ce cas
34. s deux jonctions sera directement proportionnelle la diff rence de temp rature des deux jonctions Le fait de faire une mesure diff rentielle deux thermocouples nous permet d viter l utilisation d une r f rence externe Les thermocouples de type T cuivre constantan ont une r ponse d environ 39 uV K Une charte d taill e du voltage en fonction de la temp rature est incluse a la fin de ce document Comme le signal est relativement faible il faudra l amplifier l aide d un circuit lectrique qui est d taill ci dessous Circuit d amplification thermocouple Comme mentionn pr c demment le signal g n r par le thermocouple est tr s faible 39 uV K soit 4x10 V K Pour amener ce signal un niveau acceptable il vous faudra construire un circuit d amplification Le circuit sera construit sur un breadboard une petite plaque qui permet de connecter les composantes sans les souder La figure la page suivante repr sente les connections l int rieur du breadboard Le rail a servira l alimentation positive alors que le rail n servira l alimenation n gative Les rails b et m seront reli s a la terre ground et vous devrez vous m me les relier ensembles Les composantes seront dispos es sur les rails interm diaires de c a I L alimentation du circuit sera fournie l aide de deux batteries de 9V que vous devrez connecter en s rie Une fois votre circuit compl t vous devrez connecter la borne 2 CPH3
35. two sensitive thermistor probes and an appropriate resistance bridge circuit see Chapters XVI and XVII A calibration to convert the bridge measurement to AT is required in this case tin practice one often finds that AV7 aAT Vc where 5V is a small offset voltage 1 3 uV observed when both the reference and the measuring junction are at the same temperature This nonthermodynamic result can occur if the thermocouple wire has regions of compositional variation or strain e g from kinking that are subject to a temperature gradient SV can be ignored in this experiment since it affects only the intercept of the plot of AV lt versus Ap and not the slope Exp 2 Joule Thomson Effect Waals and Beattie Bridgeman constants given in Table 1 Ci values for He N and CO at 25 C are 20 79 29 12 and 37 11 J K mol respectively Plot the Lennard Jones potentials for each of the gases studied Obtain u from Eqs 16 18 by numerical integration and compare the values from this two parameter potential with those from the van der Waals and Beattie Bridgeman equations of state Optional A simple square well potential model can also be used to crudely represent the interaction of two molecules In place of Eq 18 use the square well potential and param eters of Ref 6 to calculate u Contrast with the results from the Lennard Jones potential and comment on the sensitivity of the calculations to the form of the potential
36. u jeu de cl s wrench qui vous sera fourni Il est inutile de serrer trop fort les connecteurs Pour mettre le fritt d acier inoxydable en place il est sugg r de le placer entre deux joints toriques o rings Ceci vitera des fuites de gaz sur les c t s du frit Veuillez prendre des pr cautions avec les thermocouples puisque leur extr mit est fragile D roulement de l exp rience Vous devrez d terminer le coefficient Joule Thomson de 3 diff rents gaz h lium dioxyde de carbone et azote Pour y arriver vous devrez vous m me trouver une fa on de proc der inspirez vous des articles en annexe L acquisition des donn es se fera enti rement avec la carte d acquisition Futek ainsi que le logiciel d accompagnement FTezDAQ Le logiciel est relativement simple d utilisation et vous trouverez plus de d tails dans le manuel d utilisation disponible sur Internet et au laboratoire Rappelez vous d enregistrer les donn es entre chaque acquisition sinon elles s effaceront automatiquement Le logiciel enregistrera les donn es sous forme d un fichier texte qui contient le voltage des diff rents canaux en fonction du temps Ces donn es pourront ensuite tre import es dans Excel afin d effectuer le traitement et les analyses La manipulation de gaz comprim s n cessite certaines pr cautions assurez vous de consulter votre d monstrateur afin de vous y prendre correctement Veillez ne pas d passer une pression de 100 P
37. uppliers e g Upchurch Scientific part C 414 metal or nylon tees crosses and reducers available from Swagelok and other manufacturers 3 in Teflon rod type T insulated copper Constantan thermocouples with 0 010 in diameter wires voltmeter with 0 1 V resolution e g Keithley 196 null voltmeter e g Hewlett Packard 419A or K eithley 155 or sensitive potentiometer e g Keithley K 3 Cylinders of CO N and He with regulators and control valves 50 ft of 4 in copper coil Z in and in polyethylene tubing 0 to 10 bar Bourdon gauge 25 C water bath REFERENCES 1 J P Joule and W Thomson Lord Kelvin Phil Trans 143 357 1853 144 321 1854 Reprinted in Harper s Scientific Memoirs The Free Expansion of Gases Harper New Y ork 1898 2 R J Silbey R A Alberty and M G Bawendi Physical Chemistry 4th ed p 127 Wiley New Y ork 2005 3 Landolt B rnstein Physikalisch chimische Tabellen 5th ed p 254 Springer Berlin 1923 Reprinted by Edwards Ann Arbor MI 1943 This is the source of van der W aals constants cited in the CRC Handbook of Chemistry and Physics 4 J A Beattie and W H Stockmayer The Thermodynamics and Statistical M echanics of Real Gases in H S Taylor and S Glasstone eds A Treatise on Physical Chemistry Vol II pp 187ff esp pp 206 234 Van Nostrand Princeton NJ 1951 J A Beattie and O C Bridgeman J Am Chem Soc 49 1665 1
38. votre quipe avant de pouvoir effectuer les mesures L ensemble de la th orie reli e l exp rience de d termination du coefficient Joule Thomson se trouve dans les documents compl mentaires cit s la fin de ce protocole principalement dans l ouvrage de Garland Nibler et Shoemaker Pour cette raison elle ne sera pas expos e plus en d tail dans le pr sent document Appareillage Pour r aliser vos mesures vous aurez a votre disposition un capteur de pression lectronique des thermocouples une carte d acquisition ainsi qu un amplificateur de voltage Ces appareils sont peut tre nouveaux pour vous c est pourquoi ils seront bri vement d crits dans le protocole Capteurs de pression WIKA A 10 Les capteurs de pression WIKA fonctionnent grace l effet pi zor sistif Vous tes peut tre familiers avec l effet piezo lectrique gr ce auquel une pression appliqu e sur un cristal g n re une diff rence de potentiel Dans le cas de l effet pi zor sistif la pression appliqu e sur un semi conducteur m ne plut t un changement dans la r sistance Les capteurs sont CPH316 M thodes de la chimie physique F1 SHERBROOKE con us pour donner un signal de sortie allant de 0 10V en fonction de la pression appliqu e Ceux qui seront mis votre disposition auront une plage de r ponse lin aire allant de 0 160 PSIG PSIG PSI par rapport la pression atmosph rique Par exemple un signal lu de 0 V correspondra
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