An Improved Apparatus for the Measurement of the-~oule-~homson Coefficient of Gases Arthur M. Halpern and Saeed Gozashti Northeastern University. Boston. MA 02115 One of the common annlications of real eases nresented in undergraduate treatme& of thermodynakics is the JouleThomson (JT) effect. This tonic not onlv shows " ex~licitlv . how a nonzero J T coefficient arises from an equation of state for a real gas, but i t also appeals to the student's physical experience with the cooling associated with most expanding gases. In addition, the ability to calculate the J T coefficient (PJT)from an equation of state illustrates the computational nature of thermodynamics as well as the relative utilitv of equations of state. Experimental measurements of PJT nicely fit into the laboratory portion of physical chemistry. Accordingly, this experiment is described in Shoemaker et al. ( I ) . 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 described 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 cumbersome equipment. In this paper, we describe an apparatus that can be constructed from commercially available components and that has the sensitivity to measure FJT for He with reasonable accurwy. l'he strategy is to usegas fitting sand a porous plug made trom sti~inlesssteel. This material was chosen because of its h e r thermal ronducrivitv (relative to brass). Lnlike the glass used in the J T cells pre&usly described, dur stainless steel apparatus can withstand higher pressures, and, in the case of He, this contributes to the ability to measure pJT with reasonable accuracy. The two commonly used gases Np and Cop are easily studied with this apparatus. In addition, SFGis used; i t is a good choice for this experiment because it is presumably nontoxic, nonreactive, andrelatively inexpensive. 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 Dart of the J T cell is a 3/R-in.union cross (swagel;k SS-600-4j adapted on three sides to S/s-in. (SS-200-R-6). The gas inlet is coupled via a %-in. Teflon tube and the pressure is read via a 0-100 psi gauge also connected by '18-in. Teflon tubing (used to reduce heat trans~~~
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fer tolfrom the J T cell). A copperlconstantan thermocouple, sealed with an epoxy adhesive passes through a 'I8-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 pm) used was a 3/s-in. stainless steel HPLC bed support (43-38BS, Rainin Inst. Co.). The frit is contained in a 3/8-in. union (SS-600-6); the latter is connected to the cross via a 3/8-in. close-couple. The lowpressure thermocouple is fed through a #17 stainless steel syringe needle (the s h a r ~end removed) as a euide and held rigid hy a 3s-\G-in. reducing union (ss-600-6:l) with Teflon ferrules. The gas nutlet is provided by several holes drilled through a short length ( 2 in.) of ,*-in. tul~ingplaced betwen thr frit-containing union and the reducing union. 1Lo damp out flurtuatiuns in the temperature difference read hv the therrnocouplrs, the low-pressure thermocouple was fastened to a small brass cup attached to the end of the guide using a minute amount of epoxy adhesive, heavily impregnated with brass filinri to i m ~ r o v et h ~ thermal . conductivitv. The cun was prepared by simply filing down the lock-end of th'e syringe. T o provide additional insulation, a short length of Tygon tubing is inserted into the high-pressure side of the frit. Holes are provided for the thermocounle and nressure gauge. ina ally,-to krrp the entire apparatus as adinhatic as pussihle, it was wrapped in several la\ws of class wool. be very well The two therm&ouples were found 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 between the thermocouples, the voltage of the equilibrated, static apparatus was usually found to be less than 1pv. Best results were obtained under this condition which could be brought about by a very slow trickle of gas (He or Nz) through the apparatus. The potential developed by the thermocouples was directly read by a Hewlett-Packard model 419A null voltmeter. Alternatively, another readout device having an appruprtatrly high input resistance can be used. A cnlibratioti of :{!I p\'/Y: \confirmed hy the freezing point of benzene) was used in these experiments. The measurements for He were carried out between pressures 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 J T effect is larger, the highest pressure used could be reduced. 'l'he entireexperiment involving the measurement uf the four gases can he carried out in less than 3 h. The J T coefficients were determined by a linear regression of the data, (see Fig. - 2) assuming alow-nressure value of 1 ntm. The highest prtswre used is low enough to justify the asnnmption of P-inde~endvntJ T coefficients. These w e r ~ compared with ~ J a; T 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 he obtained from critical data while the latter incorporates five empirical parameters. ~
to
~
Figure 1. Cutaway diagram of the apparatus. The stainless steel fiuings and Other components are described in the text.
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Volume 63 Number 11 November 1986
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~
1001
Critical Data, Heat Capacnies, vdW, RK,and BB Parameters for He, N,, CO,, and SF8 ( 9 ) ,as well as Calculated, Measured, and Literature Values ( lo, 11) for fin
"4 :Ti
a(vdW)
-20
HE
0
40
20 AP.
60
80
0.02677 1.3445 0.05046 4.20 X 10'
C pdvdW) P~RK) wdBB)
-0,101 -0.0774 -0.0596
0.250 0.224 0.229
pdmeas) pdlit)
-0.066 -0.0624
0.230 0.2217
&
0
15.38 0.03862 1.350
0.01636 0.0216 0.0140 40
b (RK) Ao
40
0.07651 0.02369 0.03397
PSI
F w r e 2 Plots of AVversus APfar the gases s t d w he. N,. SF,, and C02 The ammen11emperstLre is 298 K
The J T coefficient, defined as (aTlap)xcan be expressed in terms of the T and Vpartial derivatives of the equation of state explicit in P (see also 7,8),
The well-known vdW equation is P = RTI(V- b) - a l p
and the RK equation, which is a very useful two parameter state function reads
+
P = RTI(V - b ) - ~ V ( Vb)~l"I
(2)
The vdW o and b parameters expressed in terms of the critical temperature, T,, and pressure PC,are a = 2.8408 x 10-3T:/P,
and
p~~= ( ~ I c ~ ) [ - T ~ J P / ~ ~ ~ V) I ( J P I ~ ~ (6) ~ The application of equation 6 to the vdW, RK, and BB equations of state ~rovides.in the limit of laree - V.. the following V-independent expressions for wT: p
=
PJT =
PJ'JT=
where units of dm3, atm, and K are implied. Likewise, for the RK equation a = 2.879 X IO-~(T~")/P,
(l/Cp)IZa/(RT) - bl ( 1 / ~ ~ ) 1 5 a / ( 2 ~7 0bl~ ~ )
(udW) (RK)
(7) (8)
+
(BB)
(9)
(11Cp)12Ad(RTj 4 c l P - BB,J
Thevalues of ~ J Tcalculated , 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.
and Literature Cited
The BB equation, containing the five parameters, a, b, Ao, Bo, and c is
(11 Shoemaker, D. P.; Gsrknd, C. W.: Steinfeld, J. I.; Nibler, J . W. -~xperimenkin Phyrieal Chemistry)',4th od.; McCraw-Hill: New York, 1961; p 6 5 (21 Hecht. C. E.: Zimmermsn. G. J. Chem. Edue. 1954.31.530. (8, Levine.1. N."Physical Chemir~y",2nd ed.: McCrsw~Hill:New York, 1981:pp 2W-
-.... 9°K
The BB equation can he cast into the more convenient virial form ( 6 ) ,
1002
Journal of Chemical Education
I 4 Redlich, 0.;Kwong, J. N.S.ChamReu. 1949.44.283. ( 5 ) Beattie.J.A.: Brideeman.0. C. J.Amer. Chem.Sor. 1928.50.8133. 161 Catellan, G. W. "Physicsl Chemistry", 3rd ed.: Addison-Wesley: Reading. MA, 1983:
."
pw.
(7) Ryho1t.T. R. J.Chom.Educ. 1981.58.621. (61 Nwde. J. T . "Phyaieal Chemistry"; Liltle. Brown: Boaton, 1985: pp 105-110. (91 "Lange'sHsndhmkofChemiatcy': 13Lhed.; Dean. J. A.ed.:MeGraw-Hill: New York, 1985; pp9-180, 9-4. 1101 "Chemical Engineers' Hsndboolt': 5th ed.; Perry, R. H.; Chilfon. C. H., Eda.: McCraw-Hill: New York. ,978: p3102. 1111 Bier, K.; Mauier, G.:Sand,H. Rer. Runsewes.Phya. Chcm. 1980,81,480.
