Huygens Institute - Royal Netherlands Academy of Arts and Sciences (KNAW)
Citation:
Kuenen, J.P. & Visser, S.W., The viscosity of the vapour of normal butane, in:
KNAW, Proceedings, 16 I, 1913, Amsterdam, 1913, pp. 355-362
This PDF was made on 24 September 2010, from the 'Digital Library' of the Dutch History of Science Web Center (www.dwc.knaw.nl)
> 'Digital Library > Proceedings of the Royal Netherlands Academy of Arts and Sciences (KNAW), http://www.digitallibrary.nl'
-1-
355
whieh means a furtlier: :J:ise of the boiling point: the final value
may be taken at - 0.6° C.
A furtheL' confirmation of the presence of an admixture like ethane
is afforded by the mlue of the critical temperature (l50.8°). When
for the varions saturated hydrocarbons a gl'aphieal curve is drawn
with the molar weights as abscissae and the C'olTesponding critical
temperatures as ordinates, the value found for butane seems to be
a little too small. By representing the critical temperatures of ethane
(305°.3), pentane (470°.3), hexane (507°.9), heptane (539°.95) and
octane (569°.3) as an arithmetical series of the fom'th order, we
find fol' propane 370°.25 instead of the experimental value 370°.1
and for butane 424°.94, i.e. 1.°04: higher than what was obtained
by us. This r~bult also points to a d~viation of the critical temperatUl'e owing to the pl'esence of a more volatile admixh:re.
Physics. - "The viscosity of the vapOU7' of n01'mal butane". BJ'
J. P. KUENEN and S. W. VISSER.
(Communicated in the meeting of September 27, 1913).
For the determination of the vlscoslfy of butane vaponr RAN:KJNE's 1)
rranspÎl'ation method was used; a method' which is very simple and
requires very little vapour, ,tnd in whieh the \'aponr comes into
contact with glass and mercury onIy.
The apparatus consists of a long O-tube placed vertically and
capable of being turned over on a horizontal :1Xis. One arm of the
is capillary, the other one a wider tube. The vapoUl' is forced'
throllgh the capillary by a falling drop of mel'cury iJl the wide tube.
When the drop has arrivecl at the bottom of the tube, the appar~tlls
is simply turnecl upsicle down, and the drop now drÎ\'es the gas
through the capillary In the opposite direction. The time IS measured
between th~ moments a,t wbich the mercury passes two marl~:s on
the fall-tube. The whole tube is monntecl in a glass ,jacket, where
the temperature is kept constant.
In order to be able to work with a long capillary without making
the apparatlls umvieldy by its length, a capillal'y is used which is
twice b~nt l'ound: hereby it becornes al most thl'ee times as long as
the wide tube.
o
ft
1) A. O. RANKINE, Proc. Roy. Soc. Londoll A 83, 265, 516; 1910.
23~
-2-
3»6
Tbe apparatus is provided at the top and the bottom with sidetubes which serve for the purpose of cleaning and filling and are
sealed uff bef'ore the meaSUl'ementE>. At both ends the tube has a
slight enlal'gement fol' collecting the meI:cury.
Wh en the tube is used fol' l'elative measurements, lhe formula to
be used is
'fl1 : '1'/2
=t
1 :
t2
where '11 and '1'/2 are the viscosities of both vapours, t1 and t2 ' their
times of flow.
A correction has to be applied tor gliding by means of the relation
4G1
-
1+-
'l'/1=:: __!!:.-=~ \1 + 4G2(G
t
4G
t I
R G
t _
'1'/2
2
2
2
l+R
)l
1
,
2
where G1 and G2 are the mean f1'ee paths of the two vapours and
G
R is the radius of the capillary. When .; is known, a rongh approximation for
G
G
1
•
IS
ffi .
su CIent.
2
=
=
The !rinetic theol'y gives ,1/ l/a dG V and p 1/3 dP, where cl
is the density, V the square root of the mean velocity square, p
the pressure. Eliminating V we find '1'/
Vl/apdG and therefore
G1 = 1/1
G2 'fl2
G'itical velocity.
gases 1). For
V
d2 P2.
d1P1
criterion for liquids also holds for
REYNOLDS'
Ddv
OUI'
=
viscosimeter, -
'1
= 146 fol' air (admissible limit
.
=
is 2000) D was .0358 cm.; d
.001293; '1 = .0001t11; the volume
2.246 ccm.; the time of flow 57 seconds.
UORRECTION FOR THE CAPILI.ARY ACTION
m'
THE l\Ui:RCURY DROP.
In consequence of the difference in curvatnre of the two snrfaces
of the mel'cury drop, a correction has to be made in the pressure
which may be different fol' different gases and different temperatllres.
This corl'ection was determined by RANKINE by measuring the time
of flow for sevel'al, mercnry drops of different lengtIl. The relation
bet ween the mass 1n of the mercury and the time of fall t may be
l'epl'esented by the equation
.
1) RUCKES,
Ann. Pllys. 25, p. 9S3, 1908.
-3-
•
357 \
b
m=a+-t
whel'e a is the unknown cOl'rertiQn and b a constant, which is equal
to the product of the corrected mass and the time. From a series
of measurements with different rn the constants a and b may be
calculated.
In order to avoid tbe use of different masses which involved
opening, l'efilling and reclosing the tube, an attempt was made to
determine the correction in a different manner. By dividing a given
qnantity of mercury into a train of drops which falÏ down together
the capillary action is multiplied 1). If the influence of each separate
drop is the same, the cOl'rection must be proportional to the nl1mber
of drops. Calling the number of drops [IJ, RANKINE'S equation becomes
b
m=.va+-.
t
b may thus be calculated from sevel'ul meaSUl'ements with
different (1.', m being known. If rn is taken as unknown, the ratios a/m
and bJm may be found. Calling these ratios al and bI the equation
~~~e~m
.
a and
altll
+ bi -1t == 1
[IJ = 0
i.e. the time corrected for the
influence of capillarity. According to this equation the graphical
bi is th us the time fol'
relation , between
1
[IJ
and -t should be a stI'aight line.
In the application of this method some unexpected difficulties made
their appeal'ance.
(
To begin with the constants a and b were derived from t111'ee
observations by RANKINE'S method.
RANKINE'S rnet/tod rn
1.86
57.1
temp. 14.5°.
t
1.31
84.5
1.01
114.2
grms
seconds,.
These results give:
a == .160
b
= 97.10.
,
The observations with air were' now repeated by th.e drop-method.
1) By providing the wide tube with a smalt contraction on the inside of the
curve near one of the bulbs, it is easy to divide the mercury oolumn into two
Ol' more drops.
-4-
358
Drop-met7uJCt.
11>t
sel'les. m
31
1.09.
1
102.7
temp. 15.5°.
These points
very small
high and the
first two drops
2
119.7
3
143.3
4 :J 74.3
5
216.9
do not he eÀactly on a straight line. The deviation
fOl' the first tl1l'ec drops; the fourth point is too
fifth deviates still more in the same direction. The
gIve
a
.135
b
97.99.
A5 th is result does not agree with the former reslllt as regards
a, a fUl'thel' investJgatIon of the method was made w!th aIr aftel'
the completlOn of tho ob5ervations w!th butane. In tlus case threequanhties of mercury were taken, each of WhICh was used In a
dIfferent numbeI' of drops.
Tbe resuJts were as follows·
2
Drop-method 2nd series. x
1
3
49.0
54.4 62.0 temp. 19.8.
111 2.11
t
117, 1.~3
80.1 97.9 temp. 19.5.
t 69.1
m 1.06 t 103.6 129.9
temp. 19.5.
From this set the intluence of capillal'ity fbI' one, two Ol' three
drop5 mayaIso be calculated by RANKINE'S method.
The first column gives a = .121 b = 97.59 fol' one drop.
second"
" a = .306 b = 98.31 fol' two drops.
"
a = .533 b = 97.97 fbI' three drops.
"
third
"
"
The capillary effect pel' drop thns becomes:
IS
_0
=
=
.121
.153
.178.
it see~s therefo1'e to become gl'eater as the nllmbel' of drops
increases.
The vallle of b IS practleally constant: the deviations are 0.4%
and remain below the errors of ohservatioll.
In the calculatton by the drop-method ~combinatioll of the results
in the same l'ow) the third point appears to deviate downwards
I
this time.
,
The fh'st row gi ves fbl' 31=1 alld 31=2,' a = .192 b=94.1 fol' m=2.11
" second "
" "
a = .185 b=93.1"
1.53
" third"
" "
a = .179 b=91.6"
1.06.
The deviation from RANKINE'S method of cnlcu)ahon is also in
tbe opposite dlI'ection. The differences between the constants bare
again much smaller than ihose between the a's.
The conflicting resuIts of ihe two serie5 of observations make , it,
-5-
359
probable, that the differences between the two methods are aeciden tal, due to small dift'eI'ences in purity of the mel'cnry anel of
the walls of the tube. A further investigation is therefol'e desirabIe,
as the drop-method, if found tillstworthy, is much preferabie to the
method which depends on the Ufle of different masses.
For high temperatUl'es with air and for all tempel'atures wUh
butane the drop-method was the only one that could be used. It
appeared advisable fo nse the constants a and b as derived fi'om
the fÎl''3t series of the aboye detel'minations, because in the measurements at 100° and with butane the same quantitr of mel'cury was l1sed.
Aftel' the first series of determinations with air the time of flow
for air in steam of boiling water was measured. In order to get an
even temperature it was found necessal'y to admit steam by means
of two flasks one at each end of the vapour jacket. A side-tnbe in
the middle allowed the steam to pass oft'. When the apparatus was
rever5ed the condensed water could flow out thl'ough the sall1e tnbe.
As mentioned above the constants a and b were determined according tn the drop-method. As the results for air at orelinary temperature were fOllnd somewhat uncertain, the following l'esnlts must a1so
be consielered to be only approximately correct.
Obsel'vations at
100.1°
m == 1.09
2
1
3
t
121.9
139.4
161
The deviation for ()J = 3 is upwal'ds.
Fl'om ()J = 1 allel ()J = 2 follows
a
= .122
=
b
118.1.
The constants a, .135 at 15°.5 and .122 at 100°, thus appeal'
to dUfer but little, compared to the dift'erences between the ob~er­
vations with a different quantity of mercury.
We thus ûnel
'11 1001
"1 1.5 ~
== 118.1 = 1.205.
97.99
COl'rected fOI' gliding 1.205.
BREITENBAOH 1) gives 1115 = .0001807, RANKINF.~) 11
.0001803;
155
3
l\'IARKoWSKI ) "1996= .0002212; SCHIERLOOIl I) 1]09.9 = .0002218.
=
Phys. 5, 166 j 1901.
A. O. RANKINE 1. C.
H. MARKOWSKI, Ann. Phys. (4) 14 j 1904.
J. F. SClIIERLOCH, Diss. Halle 1908.
1) Ann.
ll)
S)
4)
-6-
"
360
These values which have been selected feom severaI which differ
consldel'ably glye;
11
~=1228.
1/ 15.5
DETERl\HNATION Ol!' THJ~ VrSCOSITY OF BUTANE VAPOUR.
The viscosimetel' was ronnected to the butane-reservoir, and two
\ or three times washed out with the vapour. Finally it was filled
with vapoul', while the reservoir, was cooled to - 8° O. At the
temperature of the room the vapoUl' is then so fat,- removed from ~
saturation, tbat il'l'egularities owing to condensation in the capillal'y
need not be feared.Again the results may contain a sma]) error owing to tbe uncertainty of the drop-method used.
m=
j
.09 grms.
t
1
46.6
temp.
14.7.
x
2
52.5
3
59.3
4
68.9
The deviations from the straight line. were much smaller than in
all the other determinations.
Oalculation gives
a= 11
b
45.69.
In steam
m = 1.09 grms.
aJ
1
2
3
4
86.5.
60.4
67.7
76.5
t'
=
The deviations are again upwards and more pl'OnOllllCed ihan in
the pl'eviouf:l detel'mination.
a
.11.
b
59.40.
=
=
Second observation at room-temperature.
m= 1.09
2
lIJ
1
3
47.0
53.4
60.8
temp.
16.0.
4
68.3
The deviations have increased and agree in magnitude with those
in the othel' observations
a=.12.
-7-
b = 45.74.
361
The d ifferen ces in the two sets of meaSlll'ements at room-temperat ure al80 point to accidental changes of the rapillal'y action,
possib1y due to the formation or disappearance of a layer ofvapour
on the wall of the tube.
The relaq.vfl viscosity follows fi'om the equation
11 =:s.l 1+ 4G (G
11 t 1 R G
1
2
I
2
2
--
2
1) I ,
I
where the indices 1 and 2 refel' to butane and air of 15.°5 respectiv61y, while
I
~hese
equations give fol' the viscosity of butane vaponr l'elatively
to Ithat of air at 15.5°
"
at 14.70
I
'fJ 1
= .4661.
at 16.0~
.4666.
0
.6059.
at 100
The viscosity of all' at 15.°5 is giveh by RANKINE equa1 to 0.0001803.
The viscosity of normal butane thus becomes
temp. 14.7
')1 .00008404
160
08413
100.0
1092
Of the other satnl'ated hydl'ocarbons the on1y OlIes th at we found
mentioned are
.0001040
methane temp.
1201
08851 RAPPENECKER 2)
isopentalle
1164
formuIa which gives a conllection between the temperature and the viscosity of the vapour is
1'0+0 1'1 8/ 2
'1/1
')10 T;;"3i"2- 1'1+C'
SUTHEHLAND'S
=
For isopentalle RAPPENECKER deduces from his observations C = 500;
for normal butane we find from the above data C 349. GRAHAM'S
data 1'01' methane give a negative C.
180pentane at 100.0° U. corresponds with llormal butaIle at 70.°0
(l'educed
tempeI'ature t = .809). SUTHHRLAND'S formula gives for the
I
=
1) GRAHAM,
Pbil. Trans Land. Hl, p. 57H; 1864.
Zs. Ph. Oh. 72, 695; 1910.
2) RAPPENECKER,
-8-
362
viseosity of butane at this temperature .0001005. In ol'der to compare the two resuIts at t = .809 we have calculated fol' these
vapours the constant 'tl-i M 1/2 Tk- 1/ a Pk2/ 3, which KAlIIERLINGH ONNES 1)
has given for liquids. Fo!' comparison~ we have added the valnes
ralculated for methyl chloride, benzene and nÏtl'ons oxide, with data
taken from,IJANDOLT'S Tables (4th edition).
C
r,X 107
n. butane
349
1005
isopentane
500
t = .809
T
M
Pk M1/2Tk"I/6Pk 2/3
Tk
r,- lM1/2Tk"I/6Pk 2/3
343.1° 58.08 423.9 37·5
31.15
310 X I10 3
885.1 373.1° 72.10 460.9 32.9
31.37
354 X 103
I
methyl chloride 454
1082
366.6° 50.48 416.1 66.0
42.47
393 X 103
benzene
700
1249
455.0° 78.05 562.4 47.9
40.25
323 X 103
nitrous oxide
313
1342
249.6° 44.02 308.5 75.0
45.38
388 X 10 3
I
I
The agreement as regards the hydrocal'bons is not so near as\for
the liquids. For the rest the numbel's do not diverge more than fol'
the liquids, the data fol' which are given below for comp:trison. \rn
the computation we have used. fol' butane 2) our own determination,
for the saturated hydrocal'bons the data of TIJORPE and RODGER 3),
for the re~aining substances the figures g'iven by M. DE HMS 4).
1
, =.60
, 1=.58
"
"
X I05
1
,,-1 M 1/2 Tk- I/6Pk 2/3
n. butane
250
12460
n. pentane
270
11600
n. hexane
287
10950
n. heptane
301
10470
n. octane
322
9747
isopentane
263
11940
benzene
420
9700
toluene
334
11720
methyl chloride
288
14790
butyl iodide
533
11250
ethyl ether
286
11720
"
»
r,
1
1) Comm. Leiden Suppl. 23, p. 85.
2) Comm. Leiden, 136.
and RODGER, Phil. Trans, 185A; 440; 1894.
4) Comm. Leiden 12, p. 12; 1894.
3) THORPE
-9-