Huygens Institute - Royal Netherlands Academy of Arts and Sciences (KNAW)
Citation:
Kuenen, J.P. & Visser, S.W., The virial-coefficient B for normal butane, in:
KNAW, Proceedings, 16 I, 1913, Amsterdam, 1913, pp. 350-355
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-1-
350
Physics. J. P.
"Tlze vi1'ial-coeJficient B J01'
KUENEN
and S. W.
n01'n J al
butane.;' By Prof. -
VISSER.
(Communicated in lhe meeting of September 27, 1913).
Deterroinations of the vapour density of normal butane have
enabled us 10 calculate the virial-coefficient B in the empirical
equatlOn of state as established by KAl\iERUNGH ONNES 1). In the
course of these calculations anomalies appeared which may be
explained by the pl'esence of a &mall quantity of a lightel' admixture: a confirmation of this supposition wa& obtained by detel'mi:
nations of Lhe boilmg point and fi'om the critical temperature.
The vapoul' density was determined uy weighing. For this purpose
a glass bulb of ábout .4 litre was, used, pl'ovided with a stopcock
and ground joint by means of which it could be connected to a
butaJle-reservou', a merclU'y pump, and an open merCtlry manometel'.
The volnme of the bulb was determined by weighing with air.
First the weight of the bulb was determined aftel' having" been
exhfLustèd as completely as posslblè by the mercul'y pump. In all
the weighings a tarra-bulb of about the same external volume was
suspended from the other arm of the balance: the reading was
not taken nniil the equilibrium had becomE( constant.
The pressure of the air and afterwards of butane was first of
all taken eLJ.ual to the atmospheric pressure, the temperature being
that of the room. For Ihis purpose a tube some metres long witb
a stûpcock was attached to the filling-apparatus. The gab was
admitted to a pressure of about 1 m.m. _above the atmospheric:
by opening the tap at the end of the long tube for a moment,
the excess pl'essure could be let oif without appreciable change of
temperature and withont fear of outside air penetrating into the
bulb. Immediately aftel' closing the' bulb the temperature alld pres~
sure were read. The bulb was then weighed. In filling the bulb
with butane vapoul' It was thl'ee tunes washed out with the vapour
and exhansted.
'fhe harometl'ic pressnres were redllCed to 0° and m the weights
at tempel'atUl'es above 0° a cOl'l'ection was applied fol' the expansion of the glass.
was made at
In
the same manner a determination with butsJne
•
I
0°, the bllib baving been kept in ice for at least balf an hour.
Dllring/lhe operation the bntane·l'eservoir was also placed in iee to
1) Leiden Cllmm. Suppl. 23 j § 36 j p. 114}
-2-
sqq,
CIRCUS
ROLLING MOVEMENT A:-ID ALUED
MOVEMENT
CONDITiONS
VESTIBULARY ROOT
DEI~ERS" A~~E;;', _I
,- 'I
FASe.
,---
I,
I
GROUP I.
L
L;; PLB'I '
.
AREA,
lAND
•
FASe. DElT. Ase.
R
RE:.IARKS ABOUT OTHER DEG
t-;ERATJONS
_
Direet leSIon of the Vestibulary nerve.
I ACllstico·vestibulary
23.5.00
.
A s· c end i n g
DURATION
onR.side
IDeg'"'''t'dl~'~
!JmeL.>R
RnbbitV
42
R.: AC\1stico·l'fstlbular exit
61
I
ol
Destmction R. K. Vestib. and ganglion ventrale; proximalendofincision
ia lateral pm-t Clf Fase. Ddt. asc.
"
,
,~
I'
,
,0
JJ'
I
8days
I
0
I<lay
!
0
Sdays
I
I~~
I
0
GRüUP IJ. Indirect, lntramedullary, sligbt Iesion of N. ve~nbularja, by shiffing of cranlal cOlltenUi or vlclulty of a malacial head.
l\uc: commiss. pos!., corp. quad. anI., corp. ~~nic.l!l.t
lG'J
108
R
I
~
1
o
lateral IQ nue. cor.:miss. pos:. (aue. interstitial.) cayal}
\
h~ben.
109
lndsion from L. ganglion
134
R.' ExtirpatiQn of anl.lob. tr.rebell. (nut. glob. indllS.)
113
R.: :'>luc, tria;]g. Vll!, nuc. intral'esl.
118
R.: Dor,~al rnag~ocel1lIlar part Q[nU~ ..Deit., (also med. group and nue.lnang.)
I
L.: middle (md proximal part Itegencrllted
0
o
b:J.
R.
Sdays
HEad ,'olated to L.
[day
Te'1de<1cy to [al1to L.
~.nd
Rêels ol'erL. siile
medial grOllpS (Fusc.)
I)
o
I
I
'I
L.: Commiss. post. and nuc. interstitialls (I'. Valkenburg) ')
Rabbit I
Cire~$
0
0
1
'
I~~
o
I ~ ~ 1RI R,lmw,d, d"",reli,"
hll R. eorp. qlla.dr. ant
R.: Nu.c. Bechterew and nuc. brachil pontis sup.
95
I
I
medio·
lateml
::~:~~
]lateral
Head rolated: to
Falls to
, ","Imi;
0
·Ialera.
ventr~1
dlifllse
R.
R
~~
~~
io ""I ,f "pioo,,~b,I1oe I",,, ,,' cocp, ce;lil,~"; m,dio,I,I,,,1 poel of
m"i'IP"tl~~
FaUs t<1 R, with eye-ball fot~llüll
I
(1~6
Vill
99
1
b~ regarded a9 such 113, 118, <lod 95, beca~oC Ihe sUght d~ger.cralir.n of thc vestibulary root cao hardly Oe considered responsiblc for the symptoms. Also gO, 91j 92, and 93, anc1 the sagittal lesion În the vesti bnlary
GRQUP 111. Excluslve Iesion of vestibulary nuclei.
and 158) may be consulted.
R:
,Cy~t in caudal part of Ram. des,.
L" Rnmus tese. nuc. VllI, nue. hiang.
fibres
nur.. VliJ
L.>R.I
o
L.: Sagitt~l lesion : Deiters complexcompletely cutoffraphe, and L. fromal
pole removed
Lesion of
I L>R.I
RoUs fu 1..; head cmd ry<'_~ rotaled to L.
lillle
I
~ ~ I ~~ ~~~~f (~ro~.)~e;;~~u~;~;i~~à
2 d,; 4 d.
~
little
GROUP IV.
UWe
'~nd BechtQrewfullofdegel1erated
longitudlnal-flbre~,
I
R. ánd L.: littl"
I'
Hili,!
\-.....'-.....0 0/A
~
9d",
I'
lateral Ilalcral
ascendillg from vestiblllary complex, belween nue. VI and nUl!, IV, except 1!4
B~chteICW
0
0:D
'Ilittle
a~d
TI
dlfJls
I
cut off from rapIIe
Falls 10 L.; eyes rotaferJ
crlls cerebell.llnt. aod F. Deiters ase.
((J
""I'
L.
part
HearJrolafedto R.
Rails 10 R.,· falls to R.
Laleral
Lat~rnl
Rails fa R.
Head rotated
RoUs
Se!},ejIll
1~ith
Swgg~rs.
~.~:á~l;
Circlis 10 L.
UWe
Circ\!s 10 R.
68
122~
I
and Kn.rplus I)) Cat R.: Pes pcdunculi and P. L. B.
Head bent to L.
I
j'day
5days
Underllned in lhjs table ar<' the tru<:t5, degerlcratcd, whicb
te
Dteg~uerated
R. (chin to L. and upward)
later~!
filled. Most of
ascc[ldî~g P .. L.·B. fitJfe5 stop
R.: Vestibulo.spinal b.; Gowers nnd Flech5ig b.;
'
wlb Imd L, P,cern, Ic,
R ~~~Rr'L: c\;;,:;;.v,~:;'~,~;;,',;;:;fb ~~i~1to::1 ~~~":,;i; ~[,~;:::;oiC~;;):;~mh;:-:::J ~~j ;~;' I;:::"~l
'A
I L.:
(f5/' j,
ft:
,:
~
,
\...~
tlays
Lies Ol! L. sida
la~t
Falls on R.; lias down bn R. side
14 days
I,j ,
Ij,
Middle part
.. 'U'
I::P>'~
I m,ddi"blcil poel
M!ddle part
Middle part
c;'lif" ""', ,Iobo<" OM ~"b,11i m,d, m,d "I.; locm,1. ",,,,1. P'",ti5 and
'R I
~""-.JJ
1;;)../.../~a::/""...4
<:el'ebcl1. mM. aml ant. (with descending collaterals,
mesencep~,alic
R.: Motor and
Y foof; rUbrO.S,PlIlal and (lateral pa,'I,Of) p.l'ram;dal trad; lateral fillet.
R.andL.:nue.tec\iandnllddlethirdpartofdescendmgVnudeus
~,9. ~j '
R.: Gowcrs' 31ld rubro·sp,nal bundIe; ems
~~
T,"I ",t",,'oo i Towl d'"""i,"'e ,I ~
FaUs to R. in epileptic fit:
Rubro·spinal trad; nue.lV. R. alld !-.: Nuc. Delters and Bec<Jterew, in their oralparts,cutoftfrornraphe;
lai.eralfillEl.R.:crusmed.eerebelh.
I Haemorr1l>lge 011 L. P. L. B, R. and L.: ems cerebelli ad pOlltem (éeep l~\'er). R.: c~lIS,cerebellian!.(medial
part). L.: lateral fillet.
•
\l'-U
~
rJ7'Á
\.
Degenerated
locomolion to L.
Telld;nQ/ te tie down on L, side
Tota!
Latere: alld media!j' ~'"
8d.;2i!d
6 days
Rol/sta R.
littk,
lateral
1
L.: VeslibulO"spinal b.;
I
139
!ida}';
, 91
"êiil 'V
mediai part
1\.:
rs/'A
-3-
rcgion
R.:
~
R.I
~erebell.
ant. and med. (oral part); nuc. of P. L. B. contains
a:::Oa::~~ol,V(t:~:;~c:: ~~e:~;i ~~~uu:.a~:chterew(?). R. and L. hooklike bund/e.
"d 0,1~,1 1'' 1 of} pyc.mid,1 ',mdl" m"i,1 dU,I; W'm''',k', commiS;"; m,di,l poel
many degeneraled eens;
~ ~ :R,' :~i;,:~):':,~~:~~~:~:~~~:::~~:,f~~'~:?~:;~:~~::1:~::~~:~::~~;f~?~;~;11'::Oi~!;':;:;_~I;~:~·::~1
I
~~
~ (!JJJfJf:.~
R.: Crlls cerebeHi ant. (with
,'R:.: Pyramidal and
'~escending
coll;J.terals -
Thomas, Probot).
R..!IUc. IV fu11 of
mesenccPhnlo,oli~~r)' ,tr~d; cr\!s allt. cel'~bclli and 1ool11nisclis. -
d~generation.
Both rubro·spillal trael$..
3!H
Pl'event distillation of liquid into the bulb. Aftel' the weighing thB
weight of the empty uulb was determined a second time as a test.
Subsequently determinations at room temperature were made at
pl'essures of 1/2 and 1/4 atm. The pressure was in this case rBad on
the mercury-gauge.
It appeared necessary to eletermine the contraction of the bul u
by the diminution of the internal pressure. For tbis pnl'pose the
weight qf air rontained in the bulb at a pressure of I/lOf an atm.
was measured.
Finally two weighings were made with bntane-vapour at 0° anel
at 1/. and 2/3 of an atm.
MEASUREMENTS
1).
+
Empty bulb. The tarra-bulb
8 grammes made equilIbrium with
the empty bulb
.84036 grms. A later weighing gave .84033, a
thirel .84036. The mean of these i8 .84035. This weight is in
error by an amount a." owing to the change of the extern al volume
by exhaustion.
Bulb with dry air. At 18°.58 and 76.73~ ems. the weight of the
air was found to be .47370 grms; a secOlId welghing gave
.47735 grms. at 16°.88 and 76.805 cms. For the weight at 0° and
76 ems. they give .5009 gems and .5014 grms. the mean of which
is .5012 grms. This fignre has to be increased by the amount x
rnentioned above.
Bulb witA d1'y air at 10we7' internal lJressure. At á pressure of
-26.816 ems and a tempemtm'e of 16°.71 the air weighed .16596
gl'ms, The weight of tbe ail' contained in the bulb at 0°, and 76 ems
would have been .49899 gl·ms. It]s easily proved, that the el J'or
of thi'l figure owing to the change of extern al volume is approximately
equal to x. The dlffel'enee bet ween .5010 and :4989~ is thel'efol'e
independent of x and repl'esents the diminution of weight due to
the' diminution of internal volume at the lower p.ressure: as the
diminution may be taken Pl'opol·tional to the change of pl'eSSllre, it
follows that the diminution of weight for 1 atmosphere would be
.00333 grms. The externul change of volume being approximately
equal to the intel'nal change, this latter weight is equal to the
.0033 =
correction tIJ. The weight at 0° and 1 atm. is thus .5012
.5045 gl'n;ts. Fl'olIl this weight (be vohune is found by dividing by
the nOl'l~lal densitj of ni~·. The measul'ed weights of butane have
+
+
1) Tbe calculations as given here diITer sllghtly from those in the Dulch echtlOll
owing 10 a corl'eclion which had been overlooked.
-4-
352
'also to be corrected by amounts proportional to .x and to the pres:sure expresse cl as a frartion of 76 cmb.
Bulb with butane vapouJ'.
The following table gives the results of the 6 weighings.
Temp.
I.
n.
lIl.
IV.
V.
VI.
16°.63
o .00
21 .02
19 .94
o .00
o .00
Pl'essul'e
Weight.
0.98219 Gram
1.04400
O.b0339
0.22935
0.31244
0.66184
76.08 cm.
75.68
40.4:2
18.57
23.48
48.89
EMPIRICAJ, REDUCED EQUATION
Weight
corrected.
0.98513
1.04733
0.50469
0.23016
0.31347
0.66398
OF
Volume.
390.1 CCIn.
390.1
/'
388.9
388.1
388.3
389.2
STATE.
The equation of state was taken in the form (Comm. Leiden,
Suppl. 23)
pv=A ( 1
B C D E F)
+-+-;+-+-+.....
v
vv
'ilo
v
4
B
(1)
whel'e 13 is the pressure 111 atmospheres at 45° latitude, v the volume
of 1 gramme expressed in the theoretical nOl'IIlal volume as unit,
flll'ther:
1
'A=:RT; B
R k lS; C = R~~k2 ~; etc.
=
Pk-
Pk
iS, ~, etc. represent the "rednced virial coefficients", quantities
which depend on T only and must be equal for different substances,
except for small individual devlations.
D and the subsequent coefficients may be neglected for pressul'es
smaller than 1/7 Pk.
- By mtroducmg p as the mdependent variabie ill'3tead of v equauon
(:1) assumes the form.
pv _- R'l'
(1 + RTF
B
+C -
B~ ~) . . . . . (2)
R~l;;J P
The theoretical normal volume of pure butane is
386.0
22412 : 58.08
where 22412 is the nOl'mal volume of one gramme~molecule and
58.08 the molar weight of butane. When the constallts were calcuIated on tlllS baSIS, large deviations fI'om the reduced equation of
state were found. This finds a ready explanation in thE' fact, that
=
-5-
353
the butane was not absolutely pnre. It seemed therefore prefel'able
to tr'eat the theoretical nOl'mn,l volume as an unknown quantityand
deduce it together wlth the othel' contants fi'om the observations.
It was fol' this purpose, that the above weighings at 0'" at thl'ee
different pressures were made.
Substituting in l2) P5' V 5 and Pa' Vu respectively and dividing the
two resultmg equations, we obtain the relation
In this equation we may take for V 5 and Va the volumes of
1 gramme in r.cm. The tE'rm containing C is of minor importitnCe:
C may therefore be calclllated with sllfficient accllracy from the
reduced coefficient €, which is lmown from measurements on a
number of other substances.
From equation (3) was found B
.0430
In the same mannel' the second and six.th weighings gave
B
.0431; as the mean was taken .0431.
The theoretical normal volume of the butane used may now be
calculated from equation (2): it becomes 388.1.
The ditference of this fignre from the value for pure butane
(386.0) gives an indicatlOn as to tbe amonnt of the impurity : It points
to the pres en ce of a light el' ad mixture. The ditference is .5%'
Using the normal volume founcl in this manner we may 110W
deduce the vi rial coeffirients B in the measurements at othel'
te1p peratllres.
=-
=-
0°
16.63
19.94
21.02
B
B calculatecl.
-.0431
381
371
359
-.0465
393
382
376
In the last column are given the values of B, as ,calculated from
the mean redllcecl vil'ial coefficient IS fol' a number of substances.
The correspondence is satisfactory considered the degree of accuracy
of the method by which B was here determin~d. An error in the
fl'action on the left side of equation (3) appeal's in B one hundred
times enlarged; an error of 5 % in B corresponds to all error of
observation of 1/ 2000 ,
Moreover a complete correspondence can in any case not be
expeeted, as the eql1atlon of state is aftel' all only nn nppl'oximn.tloJl
23
Proceedings Royal Acad. AmsleldaUl. VLI. .À. Vi.
\ I
-6-
354
Dwing to the mutual deviations of the various substances with l'egard _
to the law of cOl'1'esponding states. This is shown bJ the following
table containing variOlIs vaiues of m.
Reduced temperature .644.
mean reduced virial-coefficent Q3 = -1,12.
t
lD
ammonia 1)
-12°
metlly I chloride 1) - 5
isopentane 2)
23.7
n. butane 3)
00
O.
-1.22
-0.961
-1.02
-1.04.
Test of the' irnpurity. The theoretical normal volume found 388.1
leads to a molar weight of 57.77. If we assume the admixture to
be ethane, its amount may be calculated from the molar weights
of ethane (30.05) and butane (58.08): the amount of ethane would
appeal' to be 1 % ,
The above resllit respecting the nature of the admixture finds
contil'mation in the boiling point of our butane. This point (-1°.0) 4)
was del'ived from determinations of tbe vapoul' pressure in tbe
neighbourhood of 0°:
temp.
press. (atm.)
12.0
0.00
0.00
-6.2
1.6
1.049
1.046
0.79
Owing to the pl'esence of a more volatile admixtllre (ethane) tbe
boiling point will be too low. In order to remove it to a cel'tain
extent the butane was cooled in solid carbon dioxide ana vapoul"
was pumped oIf. Aftel" thi& opm'ation the vaponr pressure at 0° was
again measul'ed; it was now 1,035 atm. The boiling point has therefore
actually been raised: it now oecomes - 0.8°. In repeating the same
opel'ation a large pOl'tIon of the vapour coming otf was coUected
in the bulb of tbe mercnr)' pnmp. The pressnre above tlJe small
qnanttty of liquid left, appeared to have diminished to 1.027 atm.,
1) Fol' these data ',-:e are indebted to Mr. G. HOLST, ",hose res.ults, wbieh were
worked out in the Leiden Laboratory, will shortly be publishect a,s a thesis at
Zürich.
2) Galculatetl from S. YOUNO'S data.'
3, Deduced from the above value of B.
1} in Comm. 125 p. 4 by a clerical error the boiling point was given as - 0.1°,
-7-
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~
-8-