- Email: [email protected]
The temperature dependence of the thermal diffusivities of organic vapours
.-
~.
Received 7 _Novembkr 1983 _
:
_-
-. __-
.-
.
.-.
;
The well established. thermal lens techni&e has been used to measure the the&&
diifusfvities-of c$Aopropa& ethyl chloride, nitrobenzene and toluene from_ 1 to 428 K. These vaiues have @en co_nve+ed to the_rmalcondu&vity &efficient$ by ’ .- ,_ applying~currently accepted heat capacities whereavailable. Compansbn with other. currentvalues-of this co&idient reveals,_in some cases, differences well beyond their quoted errors as well as beyc&d the error ass&d to the heat capackies: The ~oiu& of this error-is not always clear, but the:hot‘~ire~tranaient technique from-which previous thermal’conductivity coefficients have been derived is poorest at the low pressure available near room temperature with the compounds examined here. _
1. Introduct&
In design problems where it is necessary to calculate e.g. the rate of heat loss from a hot gas on the axis of a cylinder, the sample-dependent variable is the thermal difftisivity, K,-&en’ byK=
K/Pep,
where p is the sample density, K its thermal conductivity coefficient and Cp its constant pressure heat capacity_ The value of K is essential to the calculation of, e.g., heat loss from the axis _of a’cylinder as -in calculation of peak temperatures reached’ on- the axis of a cell in IR laser-induced photochemistry [I] where this tempcrature‘can be determined by transport -kinetics. Failure. to use correct thermal diffusivities to deduce’ appropriate-laser repetition rates has often led to temperature ‘mtegration from -_ -1 _’ I ‘. successile_!aser_pulses_-.shot @e_tranSient experiinehts [2] are probably ~‘the-most acc@rate:~s&kS ‘of $x&LI conductivity eoefficierits. .To.dedtice K-it i$ necessary ro know 6 and. Cp_.Pr$prently, these are poorly characterized -even. for, gases.-l$&ideal behaviour may affect. p,l but; :iri@ ser&sly,G C~values -are sometimesavailabIe of;ly _. tiuoti&idditivity~Scheiries [3] orri(jt at. -- -_ _‘-:-’
all: Of. the nitro compounds -only. nitromethane seems to have -a-measuredCp value; In these-cases a direct measure of K- is- desirible -&id this is available from thermal lens expe&nents~[4~~]. Additionally, corrections’ applied to_lhot tire measurements become increasingly. important [2] at,low pressu&( s 5.:atm)_Unless these .are‘haridled with: care;. accuracy is seriously impaired as -tiGressed’ b$ the reported -data .on.:toluene. The thermal. lens approkh d&s_.not zdepend on injection ._of energy, into. the--g& by contact with’ a surface, so,that-for.this technique the accommodation problem dokliiot exist.‘pf course; below -1-2 Tot-r thermal ~diffusivity becomes meaningless in cells- up _toa few-centimetkis~-diameter,. since heat removal‘kine~tics are then~dete’rminedby’gas:molecje/cell wall, accommodation _as the ::mean:-free path becomes comparable with the ct$ @ins._--;.-: _ _--. -_ ,; __ ..~_ __ I.’ . .- .-
126
R T. Bailq
er al. /
Thermal diffiicihzs
Pyrex, gas handling and storage system, the other to a short, vertical, Pyrex side arm. This latter was used .as reservoir for low vapour pressure liquids and was fitted with an independent heater to generate the desired vapour pressure. Pressures were measured on an MKS Baratron O-1000 Torr gauge directly connected to the thermai iens cell by a stainless-steel system. The cell, valves and Baratron transducer were contained in an electrically heated, air thermostat bath and careful calibrations of thermocouples embedded in the cell wall ensured an accuracy of temperature measurement better than t 1 K. Care was taken to ensure that the pressure transducer capsule was also at the cell temperature. Pyrophyllite tubes placed between the KC1 cell windows and the oven walls prevented distortion of the optical path by convection currents within the oven. The argon (BOC) was used as supplied at > 99.9% purity in sealed Pyrex flasks. The cyclopropane (BOC) and ethyl chloride (BDH) were outgassed and vacuum fraction-distilled at liquid nitrogen temperature before use. GC analysis confirmed purity > 99.9% Toluene (150 ml, AR, BDH) was washed with 10 ml aliquots of concentrated sulphuric acid until the acid layer was no longer brown. The toluene was then washed with 25 ml aliquots of water until the washings were at pH = 7. This toluene was then dried over molecular sieves in a desiccator_ The dry sample was fractionated over CaH?. Only the centre fraction was used and it was stored in darkness in vacua. Nitrobenzene (100 ml, AR, BDH) was added to diethyl ether (200 ml) and washed with four 50 ml aliquots of molar sulphuric acid followed by three 50 ml aliquots of water. The neutral solution was dried over anhydrous sodium sulphate. the ether removed by rotary evaporator, and the nitrobenzene fractionated in vacua over P205_ The clear, colourless centre fraction was stored in darkness, in vacua. To promote absorption of the 943 cm-’ CO2 laser line used, 1 Torr or 1% (whichever was lower) SF, was added to all systems. This has been shown experimentally [5] to introduce insignificant error in measuring thermal diffusivity.
of organic uapours
As before, the thermal diffusivity of -argon was used to measure R, (l/e radius of the gaussian TEM, profile)_ In all cases the analysis of the time-dependent thermal lens signal, expressed as a fractional modulation, S, of the He/Ne laser beam, fitted the equation [4] [(1-~)-“~-l]-“2=C(t+7),
(I)
to within +2% (two standard deviations)_ The values of 7 so calculated were plotted against the sample pressure, P, for a range of pressurei and. according to the relation [4] r = PC,R24RTh-,
(2)
a linear plot invariably resulted with an error of *2% in the least-squares fitted slope. The thermal diffusivity, K, was calculated as a pressure-normalised quantity in N s -’ by multiplying the reciprocal of the slope of T against P by (Ri/4). Thermal conductivity coefficients were calculated by multiplying K by the appropriate (CJRT) value. The thermal lens signal was retrieved using a computer-controlled 2048 point, 16 bit signal averager [S], 20 to 130 runs being averaged for each set of sample conditions before analysis_ Time resolution was varied from 100 ns per point upwards as required.
3. Results Argon is ideal for evaluating the accuracy of these temperature-dependent studies, since its heat capacity is classically translational and accurate thermal conductivity coefficients are available over a range of temperatures. * The day to day reproducibility of R, was assessed by measuring R, in calibration thermal lens experiments at 291 K, using the thermal conductivity coefficient of argon at 291 K. This R, value was then applied to alI subsequent measurements on argon at temperatures up to 4’15 K. A typical plot of eq. (2) is shown in fig. 1 and the variation
* For a compilation of critically assessed rare gas data see ref. PI-
:
in k- with temperature shown in fig_ 2, I tog&&r ’ . _. wiih values from ref. [9]. At -2!l& K, the v&at& of._i- &&wn in-.fig.‘ 2 represents .the tiepr;odUcitiility in R$ i.e. this results in = __+2.5% e_rror. This is aiso shown‘ in the points pId!ted in fig. 1. Together with the- same’ error. in work at a different ~temperature the total expected error- in K based on calibra&on at 291 K is thus = +5%. In fig. 2 the greatest difference between our results and those of ref. [9] is 6.7% which we regard as satisfactory_ Errors larger than = 7% should therefore not arise from these thermal lens studies. It would be possible to reduce this error by stabilising the laser cavity. This- would require a completely redesigned system, and for our present purpose an accuracy of = 7% was acceptable. This error limit is consistent with our previous fixed temperature work on rare. gases [5]. R, having been calibrated and the maximum errors in the K measurement calculated, the technique was applied to the following compounds. 3. I. Cyclopropane Thermal diffusivities obtained as a function of temperature for cyclopropane are shown in table 1. The heat capacity is given by [lo], CP = 0_0471475T-
0.6716
cal mol-’
K-l,
161
3oo
350 T/K -
Fig. 2. Thermal conductivity 10-3,
K-1
s-1
,-I
as
400
coefficient
a functionof temperature.T. The solid
line represents data from ref.- [9]. The departure of the lowest temperature point from this line me-sures the reproducibility of the R, value over the extended period of this experimental work. since the initial calibration value (X) necessarily lies on the line.
with a quoted error of + 0.9% This relationship was used to calculate the thermal conductivity coefficients of table 1: The temperature variation of these is shown in fig_ 3 and compared with other data [ll-141. Immediately it is obvious that while agreement is within -experimental error around room temperature, the discrepancy at 413 K cannot be attributed to experimental error, being 40% higher than the previously quoted value_ Eq. (2) was used over the pressure range 20-520 Torr at 413 K and the error in its least-squares slope was withinthe 2% quoted-above. Accordingly, we see no reason to ascribe the discrepancy to the thermal lens work. Much of the -previous work relies on calibration of systems relative to the same Table 1 Cyclopropaue Thermal
Temperature
diffusivity (Ns-t)
(K)
lo3 xtbermal cdnductivity
--
loo
200 P/TORR
300
400
500
-
Fig: I. 7 versus pressure (P).graph for argon at 291 K. Points shown here vere randomly obtained over a 3-day period and abscncc of any systematic &end indicates the~stabitity of the system and iht& reliability of the R, value so obtained_
0.633 0.809 0.994 1.46 1.83
.-
_-
:
(J K-‘-s-?
m:‘)
291 ~323
15.1718.33
. -_
3295362~. 413
22.54 3324 41_88
I 0
.
coefficient.
-~
.-
_.
.
:--
128
R. 7: Bailey er al. /
Thermal diff/usiuiries of organic oapours
-_
Table 2 Ethyl chloride
Fig. 3. Thermal conductivity coefficient (K) of cyclopropane in units of lo-’ J K-’ s-’ m-I as a function of temperature. T. (0) = prurnt work, (A) = ref. [12]. (X) = ref. [?4], (0) = ref. [ 131. (I) = r& [Ill_ The solid tine is the suggested best fit to our
Thermal
Temperature
1(j3Xthennal
diffusivity (N s-l)
W)
conductivity coefficient (J K-’ s-* m:‘j
0.456 0.491 0.609 0.798 0.847 0.901 1.10
201 291 329.5 348 365 390. 414
11.63 12.5 14.96 19.31 20.23 21.15 25.44
_
sured value within 2.5%. The previous thermal conductivity coefficients are spread + = 4% about a mean.
data.
3.3. Tolirefre
dry air [15] data. This calibration is frequently the major error in some of the recent hot wire work [14] and the error is assessed at 1% Together with the 0.9% C, error this would be quite insufficient to account for the observed disagreement at the higher temperatures.
Thermal diffusivity as a function of temperature is listed in table 3. A heat capacity given by [231 C, = 0_08383T+
0.1764 cal mol-’
K-r.
with a quoted error of &1.2% was used to calcu-
3.2. Ethyl chloride Thermal diffusivity as a function of temperature for ethyl chloride is listed in table 2. Over our temperature range the heat capacity is given by C’ = O.O348215T+ 4.63 cal mol-’
K-r.
with a quoted 1161error of 0.17% and this relation was used to generate the thermal conductivity coefficients of table 2. These are compared with current data [17-221 in fig. 4. As for cyclopropane. hot wire equipment was used. often traceable to the calibration data of ref. [15]. As before, our room temperature data are in closest agreement. A 14% discrepancy is found at the highest temperature, less if only the data of Keyes [20] are considered. This is somewhat beyond the combined experimental errors of both sets of data. The quoted heat capacity is a statistical thermodynamic value which agrees with a mea-
10 303
350
LOO
Lsa
T/K--+
Fig. 4. Thermal conductivity coefficient (IL) of ethyl chloride in units of lo-’ J K-t s-t m-’ as a function of temperature, T. (0) = present work, (A)= ref. [ll]. (x) = ref. [!7], (0) = ref. [IS]. (0) = ref. [19]. (I) = ref. 1201. (A) = ref. [21]. (I)= ref. (221.
Table.3. ;Tolueke
~
I. :
.
.~
Ther+ diffusivity‘-
-.
:
_.:
_
~empera&e(K)
‘_
-. .,
_,.
-_ ...- --. --_I
I~ .:: l Ip’X_ttier&al ; co&&iiy_
:.._ ‘-
; :. 1 1
_.
_,
co&ici&ii’ --. _’ ~ .- (J K-y s-’ m-1,
(N s--l).
0.516 0.561 0.583
~.
..364
:.
~385.5 419.5
late the thermal conductivity
21.62 23.51 -. 24.44
coefficients
of table
3. These
coefficients are compared. with current data [24,25] in fig. 5; The two sets of current data disagree by up to 25%. Both are hot wire measurements and these will not be at their best at low sample pressures. The saturated vapour pressure of toluene at 323 K, for example, is = 85 Torr, so that low pressures have to be used. In the thermal lens experiments great care was taken to work well below saturated vapour pressure limits and to prevent condensing vapour within the system. Should liquid toluene be present during a measurement, C’!,.,,‘and not C’ would have to be used [26] in evaluating thermal conductivities from diffusivities. It has been shown [26] that for pressures near atmospheric C:jl,,, = C,?:, - 10R. Now for toiuene C,?fz = 113 - 146 J J mol-’ moi-’ K-t, so that C*g s+ I.#?#130-63 lower than CP over the temK-t, i.e. = 25-438 perature range. Thus the presence of two phases may explain the lower set of values in fig. 5. Our
* t
%
temperature span was restricted due to the need to cover- a sufficiently--wide pressure range to .obtain an accurate T versus -P plot. and still keep. well below the relevant saturated vapour pressure. Our three points shown in fig.-5 agree with the higher set of previous values [24]. . 3.4. Nittobenzene The thermal diffusivity of nitrobenzene is-listed in table 4 ‘at 429 K:. There appear to be no current data for comparison nor is -there a published CP value. Again only one -temperature (the highest) was studied due to pressure range limitations. The r versus Pi plot is shown in fig. 6. A value of heat capacity has been deduced [27] from a thermochemical cycle, but since it is almost certainly a c:Yr, m value it has not been used to_ generate a thermal conductivity coefficient.
4. Conclusions It has been shown, in the case of argon, that the thermal lens technique can measure reliable thermal diffusivities within S-7% in the present con-
6.
OQJ
K
Fig. 5. Thermal conductivity coefficient (K) of tohene in units of 10:” J K-’ s-t m-?. as a function of temperature, T. (0) = present work, (X) = ref..[24], (r> = ref. [25]:
/ 0‘
20.
Fig. 6. z versus presst&
40
P/TcmR-%
80
P, -graph for &obenzene
.
100
ai 429 k.
130
R T. Bailey et al. /
figuration. proved
Although
this precision
with a more stable laser.
can
be
it is clear
Themal
im-
that.
even at this level, in the case of the organic vapours studied here, there are substantial differences beour data and hot wire transient data at elevated temperatures for gases other than argon. The source of this error is not definable as yet. It may be in the CP values used to convert our K to K. but this is unlikely_ We feel that, since the thermal lens technique depends on principles totaliy different from those involved in the hot wire work. it provides an important check on these values. On the timescale of our measurement, convection is absent. Accommodation kinetics and the need to operate at high pressures are also removed in thermal lens work. Our calibration is based on pure argon rather than “dry COz-free air” and we feel this is a more reproducible standard. From the above it is clear that further investigation of both techniques is required, so that the results may be reconciled and confidence in the coefficient values attained. tween
Acknowledgement The authors thank Imperial Chemical Industries Ltd. and the Royal Society (London) for provision of some of the equipment used and the Science and Engineering Research Council for a research studentship (IJMW).
References [I] R-T. Bailey. F.R. Cruickshank.
D. Pugh. R. Guthrie and K. hliddlrton. J. Chem. Phys. 77 (1982) 3453. [2] JJ. Hcaly. J.J. de Groat and J. Kestin. Physica 82C (1976) 392.
diffiivities
of organic vapors
F-R Cruick.&mk. D&f_ Golden. G-R (31 S.W. %nsou. Haugen. HE. O’NeaI. AS. Rodgers. R Shaw and R Walsh. Chem; Rev. 69 (i969) 279. [41 R-T. Bailey. F-R. Cruickshank. D. Pugh and W. Johnstone, J. Chem. Sot. Faraday Trans. II. 76 (1980) 633. Bailey, F.R. Ct-uickshank. D. Pugh and W. Johnstone, J. Chem. Sot. Faraday Trans. II 77 (1981) 1387. 161 R-T_ Bailey. F.R. Cruickshank. D. Pugh and A_ M&XXI, Chem. Phys. 68 (1982) 351. I71 R.T. Bailey. F-R. Cruickshank. D. Pugh, S. Guthrie. W.S. Foulds. W.R. Lee and S. Venkatesh, Chem. Phys. 77
Es1 RT.
(1983) 243. [S] R-T. Bailey. ER. Cruickshank and N. Wagstaffe, Comp. Enh. Spectry. 1 (1983) 63. [9] J.T.R. Watson. Thermal conductivity of gases in metric units. (H.M.S.O.. London, 1973). [IO] K.A_ K&e and R.E_ Pennington. Petrol. Refiner 29 (1950)
PII Wl
93. J.D. Lambert, K.J. Cotton, M.W. Pailtbotpe. A.M. Robinson. J. Scrivins. W.R.F. Vale and R.M. Young, Proc. Roy. Sot. 231A (1955) 280. R.G. Vines and LA Bennett. J. Chem. Phys. 22 (1954)
360. ]131 A. Eucken. Physik Z. 14 (1913) 324. ]14] C. Parkinson and P. Gray, J. Chem. Sot. Faraday Trans. I 68 (1972) 1065. ]151 W.G. Kannuluik and EH. Carman, Proc. Phys. Sot. B 65 (1952)
701.
I161 J.H.S. Green and D.J. Holden. J. Phys. Chem. 66 (1962) 1794. ]171 M. El Nadi and E. Salam. Z. Physik. Chem. 215 (1960) 121. I181 B. Schramm. Allg. Warm. Technik 12 (1966) 125. 1191 A. Manna. A. Das Gupta and B-N. Srivastava. J. Phys. A 2 (1968) 272. F-G. Keyes, Trans. Am. Sot. Mech. Eng. 76 (1954) 807. RG. Vines. Austr_ J_ Chem. 6 (1953) 1. H. Senftleben. Z. Angew. Physik 17 (1964) 86. D.W. Scott. G.B. Guthrie, J-F_ Messerly. S.S. Todd, W.T. Berg. LA. Hosscnlopp and J.P. McCullough. J. Phys. Chem. 66 (1962) 911. [24] A. Zade, Dokla Akad. Nauk. Azerb. SSR 3 (1947) 3. [25] LS. Zaitsrva. Fii Zh. 31 (1976) 826. 1261 M.L. McGlashan, ed.. Chemical thermodynamics (Academic Press. New York. 1979) p. 129 ff. [27] A. Charlton and J-1. McNab, private communication.
~.
Received 7 _Novembkr 1983 _
:
_-
-. __-
.-
.
.-.
;
The well established. thermal lens techni&e has been used to measure the the&&
diifusfvities-of c$Aopropa& ethyl chloride, nitrobenzene and toluene from_ 1 to 428 K. These vaiues have @en co_nve+ed to the_rmalcondu&vity &efficient$ by ’ .- ,_ applying~currently accepted heat capacities whereavailable. Compansbn with other. currentvalues-of this co&idient reveals,_in some cases, differences well beyond their quoted errors as well as beyc&d the error ass&d to the heat capackies: The ~oiu& of this error-is not always clear, but the:hot‘~ire~tranaient technique from-which previous thermal’conductivity coefficients have been derived is poorest at the low pressure available near room temperature with the compounds examined here. _
1. Introduct&
In design problems where it is necessary to calculate e.g. the rate of heat loss from a hot gas on the axis of a cylinder, the sample-dependent variable is the thermal difftisivity, K,-&en’ byK=
K/Pep,
where p is the sample density, K its thermal conductivity coefficient and Cp its constant pressure heat capacity_ The value of K is essential to the calculation of, e.g., heat loss from the axis _of a’cylinder as -in calculation of peak temperatures reached’ on- the axis of a cell in IR laser-induced photochemistry [I] where this tempcrature‘can be determined by transport -kinetics. Failure. to use correct thermal diffusivities to deduce’ appropriate-laser repetition rates has often led to temperature ‘mtegration from -_ -1 _’ I ‘. successile_!aser_pulses_-.shot @e_tranSient experiinehts [2] are probably ~‘the-most acc@rate:~s&kS ‘of $x&LI conductivity eoefficierits. .To.dedtice K-it i$ necessary ro know 6 and. Cp_.Pr$prently, these are poorly characterized -even. for, gases.-l$&ideal behaviour may affect. p,l but; :iri@ ser&sly,G C~values -are sometimesavailabIe of;ly _. tiuoti&idditivity~Scheiries [3] orri(jt at. -- -_ _‘-:-’
all: Of. the nitro compounds -only. nitromethane seems to have -a-measuredCp value; In these-cases a direct measure of K- is- desirible -&id this is available from thermal lens expe&nents~[4~~]. Additionally, corrections’ applied to_lhot tire measurements become increasingly. important [2] at,low pressu&( s 5.:atm)_Unless these .are‘haridled with: care;. accuracy is seriously impaired as -tiGressed’ b$ the reported -data .on.:toluene. The thermal. lens approkh d&s_.not zdepend on injection ._of energy, into. the--g& by contact with’ a surface, so,that-for.this technique the accommodation problem dokliiot exist.‘pf course; below -1-2 Tot-r thermal ~diffusivity becomes meaningless in cells- up _toa few-centimetkis~-diameter,. since heat removal‘kine~tics are then~dete’rminedby’gas:molecje/cell wall, accommodation _as the ::mean:-free path becomes comparable with the ct$ @ins._--;.-: _ _--. -_ ,; __ ..~_ __ I.’ . .- .-
126
R T. Bailq
er al. /
Thermal diffiicihzs
Pyrex, gas handling and storage system, the other to a short, vertical, Pyrex side arm. This latter was used .as reservoir for low vapour pressure liquids and was fitted with an independent heater to generate the desired vapour pressure. Pressures were measured on an MKS Baratron O-1000 Torr gauge directly connected to the thermai iens cell by a stainless-steel system. The cell, valves and Baratron transducer were contained in an electrically heated, air thermostat bath and careful calibrations of thermocouples embedded in the cell wall ensured an accuracy of temperature measurement better than t 1 K. Care was taken to ensure that the pressure transducer capsule was also at the cell temperature. Pyrophyllite tubes placed between the KC1 cell windows and the oven walls prevented distortion of the optical path by convection currents within the oven. The argon (BOC) was used as supplied at > 99.9% purity in sealed Pyrex flasks. The cyclopropane (BOC) and ethyl chloride (BDH) were outgassed and vacuum fraction-distilled at liquid nitrogen temperature before use. GC analysis confirmed purity > 99.9% Toluene (150 ml, AR, BDH) was washed with 10 ml aliquots of concentrated sulphuric acid until the acid layer was no longer brown. The toluene was then washed with 25 ml aliquots of water until the washings were at pH = 7. This toluene was then dried over molecular sieves in a desiccator_ The dry sample was fractionated over CaH?. Only the centre fraction was used and it was stored in darkness in vacua. Nitrobenzene (100 ml, AR, BDH) was added to diethyl ether (200 ml) and washed with four 50 ml aliquots of molar sulphuric acid followed by three 50 ml aliquots of water. The neutral solution was dried over anhydrous sodium sulphate. the ether removed by rotary evaporator, and the nitrobenzene fractionated in vacua over P205_ The clear, colourless centre fraction was stored in darkness, in vacua. To promote absorption of the 943 cm-’ CO2 laser line used, 1 Torr or 1% (whichever was lower) SF, was added to all systems. This has been shown experimentally [5] to introduce insignificant error in measuring thermal diffusivity.
of organic uapours
As before, the thermal diffusivity of -argon was used to measure R, (l/e radius of the gaussian TEM, profile)_ In all cases the analysis of the time-dependent thermal lens signal, expressed as a fractional modulation, S, of the He/Ne laser beam, fitted the equation [4] [(1-~)-“~-l]-“2=C(t+7),
(I)
to within +2% (two standard deviations)_ The values of 7 so calculated were plotted against the sample pressure, P, for a range of pressurei and. according to the relation [4] r = PC,R24RTh-,
(2)
a linear plot invariably resulted with an error of *2% in the least-squares fitted slope. The thermal diffusivity, K, was calculated as a pressure-normalised quantity in N s -’ by multiplying the reciprocal of the slope of T against P by (Ri/4). Thermal conductivity coefficients were calculated by multiplying K by the appropriate (CJRT) value. The thermal lens signal was retrieved using a computer-controlled 2048 point, 16 bit signal averager [S], 20 to 130 runs being averaged for each set of sample conditions before analysis_ Time resolution was varied from 100 ns per point upwards as required.
3. Results Argon is ideal for evaluating the accuracy of these temperature-dependent studies, since its heat capacity is classically translational and accurate thermal conductivity coefficients are available over a range of temperatures. * The day to day reproducibility of R, was assessed by measuring R, in calibration thermal lens experiments at 291 K, using the thermal conductivity coefficient of argon at 291 K. This R, value was then applied to alI subsequent measurements on argon at temperatures up to 4’15 K. A typical plot of eq. (2) is shown in fig. 1 and the variation
* For a compilation of critically assessed rare gas data see ref. PI-
:
in k- with temperature shown in fig_ 2, I tog&&r ’ . _. wiih values from ref. [9]. At -2!l& K, the v&at& of._i- &&wn in-.fig.‘ 2 represents .the tiepr;odUcitiility in R$ i.e. this results in = __+2.5% e_rror. This is aiso shown‘ in the points pId!ted in fig. 1. Together with the- same’ error. in work at a different ~temperature the total expected error- in K based on calibra&on at 291 K is thus = +5%. In fig. 2 the greatest difference between our results and those of ref. [9] is 6.7% which we regard as satisfactory_ Errors larger than = 7% should therefore not arise from these thermal lens studies. It would be possible to reduce this error by stabilising the laser cavity. This- would require a completely redesigned system, and for our present purpose an accuracy of = 7% was acceptable. This error limit is consistent with our previous fixed temperature work on rare. gases [5]. R, having been calibrated and the maximum errors in the K measurement calculated, the technique was applied to the following compounds. 3. I. Cyclopropane Thermal diffusivities obtained as a function of temperature for cyclopropane are shown in table 1. The heat capacity is given by [lo], CP = 0_0471475T-
0.6716
cal mol-’
K-l,
161
3oo
350 T/K -
Fig. 2. Thermal conductivity 10-3,
K-1
s-1
,-I
as
400
coefficient
a functionof temperature.T. The solid
line represents data from ref.- [9]. The departure of the lowest temperature point from this line me-sures the reproducibility of the R, value over the extended period of this experimental work. since the initial calibration value (X) necessarily lies on the line.
with a quoted error of + 0.9% This relationship was used to calculate the thermal conductivity coefficients of table 1: The temperature variation of these is shown in fig_ 3 and compared with other data [ll-141. Immediately it is obvious that while agreement is within -experimental error around room temperature, the discrepancy at 413 K cannot be attributed to experimental error, being 40% higher than the previously quoted value_ Eq. (2) was used over the pressure range 20-520 Torr at 413 K and the error in its least-squares slope was withinthe 2% quoted-above. Accordingly, we see no reason to ascribe the discrepancy to the thermal lens work. Much of the -previous work relies on calibration of systems relative to the same Table 1 Cyclopropaue Thermal
Temperature
diffusivity (Ns-t)
(K)
lo3 xtbermal cdnductivity
--
loo
200 P/TORR
300
400
500
-
Fig: I. 7 versus pressure (P).graph for argon at 291 K. Points shown here vere randomly obtained over a 3-day period and abscncc of any systematic &end indicates the~stabitity of the system and iht& reliability of the R, value so obtained_
0.633 0.809 0.994 1.46 1.83
.-
_-
:
(J K-‘-s-?
m:‘)
291 ~323
15.1718.33
. -_
3295362~. 413
22.54 3324 41_88
I 0
.
coefficient.
-~
.-
_.
.
:--
128
R. 7: Bailey er al. /
Thermal diff/usiuiries of organic oapours
-_
Table 2 Ethyl chloride
Fig. 3. Thermal conductivity coefficient (K) of cyclopropane in units of lo-’ J K-’ s-’ m-I as a function of temperature. T. (0) = prurnt work, (A) = ref. [12]. (X) = ref. [?4], (0) = ref. [ 131. (I) = r& [Ill_ The solid tine is the suggested best fit to our
Thermal
Temperature
1(j3Xthennal
diffusivity (N s-l)
W)
conductivity coefficient (J K-’ s-* m:‘j
0.456 0.491 0.609 0.798 0.847 0.901 1.10
201 291 329.5 348 365 390. 414
11.63 12.5 14.96 19.31 20.23 21.15 25.44
_
sured value within 2.5%. The previous thermal conductivity coefficients are spread + = 4% about a mean.
data.
3.3. Tolirefre
dry air [15] data. This calibration is frequently the major error in some of the recent hot wire work [14] and the error is assessed at 1% Together with the 0.9% C, error this would be quite insufficient to account for the observed disagreement at the higher temperatures.
Thermal diffusivity as a function of temperature is listed in table 3. A heat capacity given by [231 C, = 0_08383T+
0.1764 cal mol-’
K-r.
with a quoted error of &1.2% was used to calcu-
3.2. Ethyl chloride Thermal diffusivity as a function of temperature for ethyl chloride is listed in table 2. Over our temperature range the heat capacity is given by C’ = O.O348215T+ 4.63 cal mol-’
K-r.
with a quoted 1161error of 0.17% and this relation was used to generate the thermal conductivity coefficients of table 2. These are compared with current data [17-221 in fig. 4. As for cyclopropane. hot wire equipment was used. often traceable to the calibration data of ref. [15]. As before, our room temperature data are in closest agreement. A 14% discrepancy is found at the highest temperature, less if only the data of Keyes [20] are considered. This is somewhat beyond the combined experimental errors of both sets of data. The quoted heat capacity is a statistical thermodynamic value which agrees with a mea-
10 303
350
LOO
Lsa
T/K--+
Fig. 4. Thermal conductivity coefficient (IL) of ethyl chloride in units of lo-’ J K-t s-t m-’ as a function of temperature, T. (0) = present work, (A)= ref. [ll]. (x) = ref. [!7], (0) = ref. [IS]. (0) = ref. [19]. (I) = ref. 1201. (A) = ref. [21]. (I)= ref. (221.
Table.3. ;Tolueke
~
I. :
.
.~
Ther+ diffusivity‘-
-.
:
_.:
_
~empera&e(K)
‘_
-. .,
_,.
-_ ...- --. --_I
I~ .:: l Ip’X_ttier&al ; co&&iiy_
:.._ ‘-
; :. 1 1
_.
_,
co&ici&ii’ --. _’ ~ .- (J K-y s-’ m-1,
(N s--l).
0.516 0.561 0.583
~.
..364
:.
~385.5 419.5
late the thermal conductivity
21.62 23.51 -. 24.44
coefficients
of table
3. These
coefficients are compared. with current data [24,25] in fig. 5; The two sets of current data disagree by up to 25%. Both are hot wire measurements and these will not be at their best at low sample pressures. The saturated vapour pressure of toluene at 323 K, for example, is = 85 Torr, so that low pressures have to be used. In the thermal lens experiments great care was taken to work well below saturated vapour pressure limits and to prevent condensing vapour within the system. Should liquid toluene be present during a measurement, C’!,.,,‘and not C’ would have to be used [26] in evaluating thermal conductivities from diffusivities. It has been shown [26] that for pressures near atmospheric C:jl,,, = C,?:, - 10R. Now for toiuene C,?fz = 113 - 146 J J mol-’ moi-’ K-t, so that C*g s+ I.#?#130-63 lower than CP over the temK-t, i.e. = 25-438 perature range. Thus the presence of two phases may explain the lower set of values in fig. 5. Our
* t
%
temperature span was restricted due to the need to cover- a sufficiently--wide pressure range to .obtain an accurate T versus -P plot. and still keep. well below the relevant saturated vapour pressure. Our three points shown in fig.-5 agree with the higher set of previous values [24]. . 3.4. Nittobenzene The thermal diffusivity of nitrobenzene is-listed in table 4 ‘at 429 K:. There appear to be no current data for comparison nor is -there a published CP value. Again only one -temperature (the highest) was studied due to pressure range limitations. The r versus Pi plot is shown in fig. 6. A value of heat capacity has been deduced [27] from a thermochemical cycle, but since it is almost certainly a c:Yr, m value it has not been used to_ generate a thermal conductivity coefficient.
4. Conclusions It has been shown, in the case of argon, that the thermal lens technique can measure reliable thermal diffusivities within S-7% in the present con-
6.
OQJ
K
Fig. 5. Thermal conductivity coefficient (K) of tohene in units of 10:” J K-’ s-t m-?. as a function of temperature, T. (0) = present work, (X) = ref..[24], (r> = ref. [25]:
/ 0‘
20.
Fig. 6. z versus presst&
40
P/TcmR-%
80
P, -graph for &obenzene
.
100
ai 429 k.
130
R T. Bailey et al. /
figuration. proved
Although
this precision
with a more stable laser.
can
be
it is clear
Themal
im-
that.
even at this level, in the case of the organic vapours studied here, there are substantial differences beour data and hot wire transient data at elevated temperatures for gases other than argon. The source of this error is not definable as yet. It may be in the CP values used to convert our K to K. but this is unlikely_ We feel that, since the thermal lens technique depends on principles totaliy different from those involved in the hot wire work. it provides an important check on these values. On the timescale of our measurement, convection is absent. Accommodation kinetics and the need to operate at high pressures are also removed in thermal lens work. Our calibration is based on pure argon rather than “dry COz-free air” and we feel this is a more reproducible standard. From the above it is clear that further investigation of both techniques is required, so that the results may be reconciled and confidence in the coefficient values attained. tween
Acknowledgement The authors thank Imperial Chemical Industries Ltd. and the Royal Society (London) for provision of some of the equipment used and the Science and Engineering Research Council for a research studentship (IJMW).
References [I] R-T. Bailey. F.R. Cruickshank.
D. Pugh. R. Guthrie and K. hliddlrton. J. Chem. Phys. 77 (1982) 3453. [2] JJ. Hcaly. J.J. de Groat and J. Kestin. Physica 82C (1976) 392.
diffiivities
of organic vapors
F-R Cruick.&mk. D&f_ Golden. G-R (31 S.W. %nsou. Haugen. HE. O’NeaI. AS. Rodgers. R Shaw and R Walsh. Chem; Rev. 69 (i969) 279. [41 R-T. Bailey. F-R. Cruickshank. D. Pugh and W. Johnstone, J. Chem. Sot. Faraday Trans. II. 76 (1980) 633. Bailey, F.R. Ct-uickshank. D. Pugh and W. Johnstone, J. Chem. Sot. Faraday Trans. II 77 (1981) 1387. 161 R-T_ Bailey. F.R. Cruickshank. D. Pugh and A_ M&XXI, Chem. Phys. 68 (1982) 351. I71 R.T. Bailey. F-R. Cruickshank. D. Pugh, S. Guthrie. W.S. Foulds. W.R. Lee and S. Venkatesh, Chem. Phys. 77
Es1 RT.
(1983) 243. [S] R-T. Bailey. ER. Cruickshank and N. Wagstaffe, Comp. Enh. Spectry. 1 (1983) 63. [9] J.T.R. Watson. Thermal conductivity of gases in metric units. (H.M.S.O.. London, 1973). [IO] K.A_ K&e and R.E_ Pennington. Petrol. Refiner 29 (1950)
PII Wl
93. J.D. Lambert, K.J. Cotton, M.W. Pailtbotpe. A.M. Robinson. J. Scrivins. W.R.F. Vale and R.M. Young, Proc. Roy. Sot. 231A (1955) 280. R.G. Vines and LA Bennett. J. Chem. Phys. 22 (1954)
360. ]131 A. Eucken. Physik Z. 14 (1913) 324. ]14] C. Parkinson and P. Gray, J. Chem. Sot. Faraday Trans. I 68 (1972) 1065. ]151 W.G. Kannuluik and EH. Carman, Proc. Phys. Sot. B 65 (1952)
701.
I161 J.H.S. Green and D.J. Holden. J. Phys. Chem. 66 (1962) 1794. ]171 M. El Nadi and E. Salam. Z. Physik. Chem. 215 (1960) 121. I181 B. Schramm. Allg. Warm. Technik 12 (1966) 125. 1191 A. Manna. A. Das Gupta and B-N. Srivastava. J. Phys. A 2 (1968) 272. F-G. Keyes, Trans. Am. Sot. Mech. Eng. 76 (1954) 807. RG. Vines. Austr_ J_ Chem. 6 (1953) 1. H. Senftleben. Z. Angew. Physik 17 (1964) 86. D.W. Scott. G.B. Guthrie, J-F_ Messerly. S.S. Todd, W.T. Berg. LA. Hosscnlopp and J.P. McCullough. J. Phys. Chem. 66 (1962) 911. [24] A. Zade, Dokla Akad. Nauk. Azerb. SSR 3 (1947) 3. [25] LS. Zaitsrva. Fii Zh. 31 (1976) 826. 1261 M.L. McGlashan, ed.. Chemical thermodynamics (Academic Press. New York. 1979) p. 129 ff. [27] A. Charlton and J-1. McNab, private communication.