Gas Thermometry Using Pressures Greater Than 1 Atmosphere William M. Moore Department of Chemistry and Biochemistry, Utah State University. Logan. UT 84322
Gas thermometry is an excellent experiment in concept which shows the ideal gas temperature scale and demonstrates quantitati\.ely thr P T hehavi;,r of real ga4es. The experiment as it is usually. performed ( 1 - 3 ) shows the ideal gas tempera. ture srale nirely using helium, hut it dues nor show any k e n surable deviation for real Eases such as carhm dioxide or nitrogen. The difficulty is that with a glass container and mercury manometer the pressures must be kept to one atmosphere at the highest bath temperature. In quantitative terms this means that the instrumental corrections are of the same order of maenitude as the non-idealitv corrections. We have kept the gas thermometer concept ( I ) instead of resorting t o the gas burets which use elaborate and delicate glassware, and corresponding large amounts of mercury (4-5). The apparatus as shown in the figure consists of a stainless steel cylinder and a pressure transducer. The system is simple, easy to assemble and ruezed, -- hut it is not inexpensive. However, with the current cost of mercury, the pressure transducer and its associated carrier demodulator electronics costs about the same as one charge of mercury for a gas buret or constant volume manometer (- $1000). The equation to relate pressure and temperature using the two term virial equation of state and instrumental corrections is given in eqn. Lwhere Pi and T ; correspond to the reference condition and V is the molar volume. The reference point is T - Ti B(T;)- B ( T ) PT, (1) ~=[1+(;)(~)+3oiT-~;)+
-
]*
the ice point of water a t Ti = 273.15 K. The dead volume ratio ( v l V ) is a measure of the volume of the thermometer which must be out of the temperature bath and a t room temperature (T,). This ratio can he much less for a pressure transducer than a mercury manometer. For a typical glass gas thermometer ( u l V ) is 0.01, and for the steel gas thermometer shown in the figure ( u l V ) is 0.005. The linear coefficient of exnansion. a.is much ereater for stainless steel than Pvrexm glass and the correctionterm given is for a cylindrical chamber assumine that ol remains temoerature indeoendent. Finallv. .. the second virial coefficients h ( ~ are)eithgr found frum the literatureor cal~:ulatedfrom the Ilri(larman-l3eattirr u u ~ t i n n of state, where Bo, A,,, and c are constants for each gas (6).
Equation 1 should contain higher order terms in ( u l V ) ,and B ( T ) n ,which can he neglected under the conditions shown in the table. The table summarizes the difficulties in making P T measurements in a glass gas thermometer. For real gas such as carbon dioxide or nitrogen, the instrument corrections are com~arableto the second virial correction, since a Dressure than 1 atm is not possible. At 373 R using carbon to follow the dioxide aas thermometer, ean. 1 would appear .. ideal gas law, w h i l ~a1 77 using nitrogrn gas, thc net correction would still he less than experimentnl error. IJsing a steel gas thermometer and a pressure transducer with a 100
a
Stainless steel Gas Thermometer.The comoonents Mnsist of: (1)DP15 Variable reluctance differentialp m v e bansducer. Validyne Engr. Corp.. Norbridge. CA. (2) Whitnep 150 cc Stainless steel sample cylinder, (3)WhitneF SS-IRF2 Stainless steel shut-offvalve. (4) Swageloke 58-200-3 Stainless steel union tee. (5)~ajon"SS2-TA-1-2w (-4) Tube to NPT adapter, (6) Approximately 10 in. of 118 in. Stainless steel tubing. Products in (2j ( 5 ) are wadenames of Crawford Fitting Co.. Solon. OH
psia diaphragm, net corrections of 2 to 3 percent can be ohtained for COz and nitrogen which greatly exceed experimental error. Calibration of the differential pressure transducer is straightforward. One chamber is left a t ambient pressure and the barometric oressure is used as a reference ~ o i nfor t 0.00 V output. The gas thermometer is then evaciated and the span adjust is set to give suitable values. Full scale for 100 psi would be 10 V or 1.490 Vlatm. The linearity of the pressure transducer is f0.5%. and this can be checked easilv with helium as the working gas. Over a two-vear trial period, with students in the phvsical chemistry laboratory, it has been shown that temperature results can be obtained that have a precision error less than the net correction term by a factor 013 or more. The student average, with the helium gas thermometer, for a liquid nitrogen bath temperature was 75.2 f 1.2 K (b.p. 75.4 K @ 632 Volume 59
Number 8
August 1982
681
Gas Thermometer Corrections
Insbumen1 Factar
Non-ldeali factor Total hectlcm
Bath Temp. Steam at 373 K
Ghas
(i
= 0.01)
S t 4 (+= 0.OO5)
+ 0.0043
+ 0.0053
- 0.0036
-0.0085
- 0.0104
+ 0.0108
Liquid
Nlnogen at 77 K
,
= P(373 atmK)
torr). The nitrogen gas thermometer, which was filledtoambient pressure a t the liquid nitrogen bath temperature, gave a temperature of 75.0 f 1.2 K with a net correction term of 23% as shown in the table. The steam temnerature was determined to be 368 f 1 K (b.p. 368 K @ 63itorr) for helium a t 4 atm. nitroeen a t 4atm. and carbon dioxide a t 7 atm. The net corr&tionterm for cdzwas 1.5-2%. Our laboratory is a t an elevation of 4700 feet. Careful measurement of the liquid nitrogen bath on a given dav eave a temDerature value of 75.6 f 0.3 K for the helium &%en gas the>mometer. Without the corrections the helium gas thermometer gave an ideal gas temperature of 76.3 K, and the nitrogen gas thermometer gave an ideal temperature of 73.9 K. This is one of the first experiments performed in the physical chemistry laboratory, and it emphasizes the precision with which data must he obtained, and the many types of correction necessary in treating experimental data. The principal sources of error in the experiment are (1) insufficient time allowed for tem~eratureeouilibrium to occur in well stirred temperature baths; (2) a poss;ble valve leak, and (3) instrumental drift. The Dressure transducer must be calibrated after the measurements as well as before. These dif-
682
Journal of Chemical Education
P(273 K)
P(373 K) = 7 atm
= 481m
-
-0.0261
+ 0.0433
-
Thermomehic
Glass (1 atm)
Steel
'202
+ 0.0007
-0.0208
N2
+ 0.0023
Oas
0.0329
ferential pressure transducers have replaced mercury manometers in many applications in our physical chemistry laboratory including gas phase kinetics, homogeneous gas equilibrium, and gas adsorption isotherms. A more detailed explanation of the experimental procedure is available from the author. Acknowledgment E. A. McCullough, Jr. and I have had m a w discussions on how to impress upon students the concept o?non-ideality in gases experimentally. He has provided me with encouragement and criticism for which I thank him. Literature Clted (1) ShaemaLer , D. P., Garland, C. W.. and Stoinfeld, J. I., "Experiments in Physical Chemi8try,((3rd Ed., MeDrav-Hill, 1974, pp. 6Z70. (2) White. J.M.."PhysiealChemistryLaboratoryExperimen&" Pmtia-Hall, 1975,pp.
.".
,n,.,m
(3) Daniels F.. et al.,"ExperimentalPhysicelChemistry.'. 7th Ed., Mffirev-HiU, l970,pp. b.l .f.i
Nostrand. 1989, pp. 253-258. (5) Bcttllheim. F. A,, "Erperimentd Physical Chemietry." W. B. Saunders, 1971, p p
(4) Oelks. W. D.. "Laboratory Physical Chemiatry:'Van
3744.
(6) Besttie, J.A, and Staekmayer, W. H., in H. S. Taylor and S. Glasstone. (Editors),"A Treatise on Physics1 Chemistry." Van Nostrand. 1961,Vol. 2, pp. 204-206.
