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Researches on heat conduction by rarefied gases. II
Physica III. no 10
December 1936
RESEARCHES ON HEAT CONDUCTION BY RAREFIED GASES. II. THE THERMAL ACCOl\G\IODATION COEFFICIENT OF HELIUM, NEON, HYDROGEN AND NITROGEN ON GLASS AT 70-90°I{.
by W. H. KEESOl\I and G. SCH1\IIDT Communication Xo, 245b from' the Kamerlingh Ormes Laboratory at Lcidcn.
Summary These measurements form part of a series of investigations on heat conduction by rarefied gases, viz. helium, hydrogen. neon and nitrogen, at O°C, 70-90°l( and 14-20°1{. Some points of view in relation to these experiments arc discussed. The accommodation coefficient (a l • oo) with regard to glass appears to increase with decreasing temperature, to a degree which appears to bc connected with the critical temperature. From these experiments considered in connection with measurements on adsorption it follows: 1. T < Tedt.: adsorption. at. 00 = 1. 2. T> Tedt.: no measurable adsorption; at least for a certain temperature range from the critical temperature upwards a rather large increase of al' 00 with decreasing temperature. which can be conceived as an indication of approaching adsorption.
§ 1. Introduction. a. In Commun. No. 242c 1 ) we described a method
for measuring the thermal accommodation coefficients of helium, neon, hydrogen, and nitrogen at DoC, 70-90 oK and 14-20 0 K, on glass and on surfaces of copper, silver and gold performed by means of vaporization in high vacuum. Wecompared our results for a glass surface at DoC with those of K n u d sen 2). The results appeared to agree beyond expectation in spite of the circumstance that the kinds of glass used were probably not the same; K n u d sen does not mention what kind of glass he used. Perhaps this remarkable fact can be explained by assuming the glass surface always covered with at least one layer of H 20-dipoles, as it is an open question how far it is possible to discard the last -
1085-
1086
W. H. KEESO:\I AKD G. SCIDlIDT
layer of adsorbed water by heating the glass for some time at 300°e. b. In some respect we can check also our measurements at 7090 0 K and at 14-2)°K. At 70-90 o K for instance we may expect the accommodation coefficient of N 2 to be equal to unity since below' 90 0 K there is already a considerable adsorption of this gas on a glass surface. At lower temperature the average life of the gasmolecules on the wall will be very long in comparison with the collision time when there is no adsorption. In that case the wall behaves just like a perfectly porous surface, there will exist equilibrium of temperature between the wall and the molecules that leave the wall, and we shall find aI, 00 = 1 (the indices 1 and 00 in aI, 00 refer to the number of collisions a molecule will suffer with the one surface before it reaches the other). If the assumption, that adsorption goes together with al,oo = 1, appears to be right we may state the following experimental rule: the heat conduction in a rarefied gas between two walls becomes independent on the nature of the walls if gas and walls have temperatures below the critical point of the gas. As a matter of fact generally a gas will be measurably adsorbed by any solid wall as soon as the temperature becomes lower than its critical point. Though we examined the adsorption of several gases, viz. He, Ne 3) and later also H 2 and N 2 , on glass and on metal surfaces, we found no exception to that rule. c. In connection with Lan g m u i r's theory of adsorption it is a very interesting question whether al,oo will remain equal to 1 if the adsorption at lower temperatures increases so intensely, that the greater part of the wall is covered with a film of the adsorbed gas. To deduce his wellknown formula for the adsorption isotherm Lan g m u i r started from the assumption that a molecule, which strikes the wall at a place already taken, will be reflected. As a consequence of this assumption the complete covering of the surface will only be reached at p --+ 00. Measurements on Ne at 14-20 0 K 3) have shown, however, that complete covering is reached at about the saturated vapour pressure. Now it is to be expected that even a very short average life of the molecules on the places already covered enables these molecules to enter into thermal contact with the underlaying wall molecules, so that even a relative short average life may not be neglected as regards heat conduction. According to this it can be expected that, independently of the degree of covering,
RESEARCHES 0)< HEAT CONDUCTION' BY RAREFIED GASES. II 1087
aI' 00 = 1, whereas Lan g m u i r's assumption should admit the possibility that aJ> 00 decreases with increasing degree of covering. In this respect it is a happy circumstance that the method used in the experiments dealt with in this paper enables us to measure both heat conduction and adsorption. d. Having given above some idea concerning the. questions we meet in these experimental researches, we wish to point out the importance for helium gasthermometry, especially below 10 K , of investigating the heat conductivity. The rapidly increasing influence of the thermomolecular pressure effect and still more the adsorption of the helium gas oblige us to look for new methods in the gasthermometry in this region. Perhaps it may be possible to use molecular heat conduction for this purpose.
§ 2. The method. a. For a more complete description we refer to Commun. No. 242c 1); we restrict ourselves here to some supplementary remarks. In this method the energy is measured which is delivered to the rarefied gas by a thin glass wire (Thuringian glass) with a platinum pith (15 fl.) which enables the wire to be heated by means of an electrical current. The glass wire is stretched out in the glass bulb of a gas thermometer. The gas pressure in this bulb can be determined by two different methods. If there is no adsorption of the gas on the inner wall of the glass bulb the pressure can be deduced from the volumes of the thermometer and of the gas pipette used for filling the thermometer. In case of adsorption the pressure is measured with a hot wire manometer placed in a bath of liquid oxygen. The difference between the calculated and the measured pressures gives the adsorption. In the latter case we must account for the thermomolecular pressure difference occurring in the capillary which connects manometer and bulb. A matter of importance is the choice of the diameter of this capillary. We consider that the gas must be rarefied to such a degree that practically the diameter of the glass wire may be neglected in comparison with the mean free path x of the gas molecules. At this rarefaction it is impossible to take the diameter 2 R of the capillary so large that the parameter 2Rj)" which determines the therrnomolecular pressure difference, remains> 1 along the whole capillary.
1088
w.
H. KEESOlll AND G. SCHlIIIDT
2RjI. ,......, 1 forms, however, the most uncertain part of the pressure.
region of this effect. Hence it is better to choose the diameter on the contrary so small that, considering that a pressure as low as possible is also chosen, the pressure effect approaches the limit: PJ!Pz--: YTJ!,\IT z. The nearer this approach the better we know the quotient pJ!pz by which we must correct. This quotient can be calculated from the formula for the thermomolecular pressure difference given in Commun. No. 246b 4). It is in every respect advantageous to place the hot wire manometer in a bath of liquid oxygen or nitrogen in stead of placing it in an ice bath; in this way pJ!pz is reduced to a much lower value. b. \Ve wish to discuss now how to correct for the heat developed in both short wire ends which have remained uncovered with glass. These ends take together 12% of the whole wire length. For that purpose we think the wire warmed up in the rarefied gas. If we suppose the temperature variation along the ends to be about linear it is evident that the temperature increase of the glass body amounts to 1.C6 ~ T, if ~ T is the mean temperature increase of the whole wire as derived from its resistance. Meanwhile for our calculations we may consider the temperature increases of the glass body to be ~ T provided that we diminish the measured value of the energy by 6%. Further we may suppose that about half the energy developed in the short wire ends is given off to the glass body, and that the rest flows away through the ends. To account for this loss we have to diminish the total energy again by 6%, so in total with 12%. As to the measurements in vacuum. we eliminate the heat developed in the ends in the same way. After all we subtract the corrected energy eo as measured in vacuum from the corrected e measured in the gas, both for the same ~ T of course; the difference is the energy given off to the gas by the glass body. c. In these measurements fig. 1 represents the resistance Q of the wire and moreover the corrected energy eo both as functions of the average temperature of the wire. The curves for eo give the temperature increase in vacuum for four different temperatures of the bath. A translation of the three lower curves in the vertical direction leads to coincidence with the higher one as we might expect. That these curves are not exactly straight is probably caused by a
lC89
RESEARCHES ON HEAT CONDUCTION BY RAREFIED GASES. II
small variation with temperature in the heat conductivity of the wire ends. 300 watts
.l75
.50 1 - - - - - + - - - - - + - - - - - l - - - - . ; : L - - - - + - - - - - 7 ' i 2 S0
.25!------I-----+-----If7L---------+---~q_---_7.
DOI-----+-----j-~---1I--__j:f_-t----_,+_---____lf50
751-----I-r----+----;e'F--J----r-f-----+----r--j
t--;,,<-----t----r'-----j----r--1I-----t----:;P>---+-r-----!SO
1:.10'
l
BO
75
Fig. J.
n
BS
95
100 'K
and eo as fun ctic ns of the temperature of the wire.
§~. The results. a. In table ITo represents the bath temperature; il T the temperature increase; e: the corrected energy in watts; TV the energy in watts given off to the gas per em- glass surface and per micron mercury gas pressure. Since the wire diameter cannot entirely be neglected in comparison with the mea n free path of the rarefied gas, the gas molecules coming back from the wire have a small chance to reach the wire again aft er only one collision with a molecule of the gas. The correction factor 1 krj"A, in which r is the radius of the glass wire, refers not only to this circumstance, but moreover to possible smaller other corrections linearly dependent 011 the pressure.
+
Physica III
69
1090
W. H. I{EESO:lI AND G. SCIDIIDT TABLE I Accommodation coefficient of He, II" Xe and X, on glass at 70-100°1{ Hydrogen, To = 90.10°1{
Helium, 'fo = 77.20°1{
t1 T
I'
I ~.lo'l
co.IO'/...!.!..:- .10' (watts) (watts) t1T (watts)
Ia"oo
p (mm Hg) = 0.02060
+ rIJ. =
1
t1 1'1 C.IO"
co.10'j...!.!..:-.IO' (watts) (watts) t1T (watts)
P (mm Hg) = 0.02607
1.045
+ rIJ. =
I
2L16 21.27 20.92
12.481 693.71 104.61 14.60. 815.5 123.3 17.11 955.7 157.7
Ia,,=
0 3 84 1 0.386 . 0.380
5.841762.51 52.1 60.2 6.72 879.0 8.80 1130.79.0 102.3 a"oo= 0.383 11.31 1463.-
1.08
I
501 44. 44.46 43.73 44.00
0.560 0.559 0.550 0.554 a,,= = 0.555
Xeon, To = 90.11°1{
Nitrogen, 1'0=70.08°1{ and 86.58°1{
p (mm Hg) = 0.0293
P (mm Hg)=0.00388, 1'0=70.08°1{
1 5.32\ 336.1 7.72 494.2 11.08 713.0
+ rIA =
I
1.085 17.67\ 18.02 18.62
47.41 68.7 82.1
a" 00
I
P = 0.0586
I
+ rIA =
= 1.04 75 33. 1 32.99 32.93 ·a"oo =
1.022 0.999 0.996 1.005
= 86.58°1{ = 1.045
P = 0.00602, To
1.170
10.471 1170.94.2 1 11.78 1328.- 1 106.8
+ rIA
0.786 9.521 210.3\ 74.81 0.797 12.52 274.0 99.5 166.0 0.824 20.39 I 449.3 = 0.802
18. 09 1 0.800 7.141210.1 18.28 0.808 9.37 274.7 a"oo = 0.804 12.02 351.8
I
+ rIA
I
64.61 85.5 111.0
1.051 1.040 1.032 a"oo = 1.041
22 31. 1 30.92 30.68
P = 0.0879
1 9.2811420.11.60 1774.-
+ rIJ.
!
= 1.255
83.2 105.0
I
0.803 18. 161 18.14 0.802 a"oo = 0.802'
From our earlier measurements at O°C we found k = 1.0. Table I shows for Ne that the same k leads to data for al,oo which are independent on the pressure. It will be shown later that k = 1.0 also may be applied at 14-20°K. In the calculation of the molecular heat conduction for hydrogen according to the K n u d sen's formula we assumed for this gas cp/cv = 1.58 in this region of temperatures; here this gas behaves almost as if it were monoatomic. b. Comparison of the results here obtained for al,oo with the earlier ones at O°C shows: 70 0 K < To < 90 0 K : He 0.383; H 2 0.555; Ne 0.803; N 2 1.02. To = 273.1 oK: 0.336; 0.283; 0.670; 0.855.
RESEARCHES ON HEAT CONDUCTION BY RAREFIED GASES. II
1091
There appears to be an increase of al. co with decrease of temperature for each of the four gases. For N 2 we find practically unity for 70 < To < 90 as was expected (§ Ib). We intend to publish shortly the results obtained for the adsorption of N 2 , in combination with : those for H 2 at 14-20°K. The dependence of ai, 00 on the temperature can perhaps be best expressed by forming the ratio of the difference of the two values of al,co to the difference between ai, co at O°C and unity: He 0.07; H 2 0.38; Ne 0.40; N 21.00. The ciritical points of these four gases are: He 5.2°1{; H 2 33°1{; Ne 44°1{; N2 126°K. Here appears a remarkable relation between both series of numbers; the ratio mentioned above increases with the critical point. At the other side we may consider the critical point practically as about the upper limit of the region of measurable adsorption on glass as follows from our adsorption measurements on He, Ne 3) and later on H 2 and N2 on glass. The joint results can be summarised as follows: 1. T Tent.: no measurable adsorption: at least for a certain temperature range from the critical temperature upwards a rather large increase of al. co with decreasing temperature, which can be conceived as an indication of approaching adsorption. 3. al. co increases with the molecular weight of the gases as has been observed already by I{ n u d sen. \Ve add the remark that probably the dependence on molecular weight becomes more evident at temperatures sufficiently higher than the critical points. Finally we remark that in these experiments it has not been possible to decide anything about the question, as to whether al. oo remains equal to unity with increasing degree of covering of the surface (§ Ie). For a decision of this question we refer to a report soon to be published on the measurements on H 2 at 14-200 IC
1092
RESEARCHES ON HEAT CONDUCTION BY RAREFIED GASES. II REFERE!\CES
1) \Y. H. K e \) s 0 m and G. S c h mid t, Commun. Kamerlingh Ormes Lab., Leiden xo, 242c; Physica, 's-Grav.Tl, 590,1936. 2) ~1. K n u d sen, Ann. Physik (4) 4H, 641,1915. \\'e also referred to the measurements of G r n s t e i n and van \\' ij k. These scientists found a"oo '0.32 for He on glass at 377'C, K n u d sen and we found 0.34 at O'C. 3) \V. H. K e e s 0 m and G. S c h mid t, Commun. Kamerlingh Ormes Lab., Leiden Nos. 226a and b; Proe. roy. Acad. Amsterdam aH, 825,1933. 4) S. Web e rand G. S c h mid t, Cornmun. Kamerlingh Onnes Lab., Leiden No, 246c; Rapp. Commun. Lab. Kamerlingh Ormes septieme Congr. into Froid No. 8, 1936.
December 1936
RESEARCHES ON HEAT CONDUCTION BY RAREFIED GASES. II. THE THERMAL ACCOl\G\IODATION COEFFICIENT OF HELIUM, NEON, HYDROGEN AND NITROGEN ON GLASS AT 70-90°I{.
by W. H. KEESOl\I and G. SCH1\IIDT Communication Xo, 245b from' the Kamerlingh Ormes Laboratory at Lcidcn.
Summary These measurements form part of a series of investigations on heat conduction by rarefied gases, viz. helium, hydrogen. neon and nitrogen, at O°C, 70-90°l( and 14-20°1{. Some points of view in relation to these experiments arc discussed. The accommodation coefficient (a l • oo) with regard to glass appears to increase with decreasing temperature, to a degree which appears to bc connected with the critical temperature. From these experiments considered in connection with measurements on adsorption it follows: 1. T < Tedt.: adsorption. at. 00 = 1. 2. T> Tedt.: no measurable adsorption; at least for a certain temperature range from the critical temperature upwards a rather large increase of al' 00 with decreasing temperature. which can be conceived as an indication of approaching adsorption.
§ 1. Introduction. a. In Commun. No. 242c 1 ) we described a method
for measuring the thermal accommodation coefficients of helium, neon, hydrogen, and nitrogen at DoC, 70-90 oK and 14-20 0 K, on glass and on surfaces of copper, silver and gold performed by means of vaporization in high vacuum. Wecompared our results for a glass surface at DoC with those of K n u d sen 2). The results appeared to agree beyond expectation in spite of the circumstance that the kinds of glass used were probably not the same; K n u d sen does not mention what kind of glass he used. Perhaps this remarkable fact can be explained by assuming the glass surface always covered with at least one layer of H 20-dipoles, as it is an open question how far it is possible to discard the last -
1085-
1086
W. H. KEESO:\I AKD G. SCIDlIDT
layer of adsorbed water by heating the glass for some time at 300°e. b. In some respect we can check also our measurements at 7090 0 K and at 14-2)°K. At 70-90 o K for instance we may expect the accommodation coefficient of N 2 to be equal to unity since below' 90 0 K there is already a considerable adsorption of this gas on a glass surface. At lower temperature the average life of the gasmolecules on the wall will be very long in comparison with the collision time when there is no adsorption. In that case the wall behaves just like a perfectly porous surface, there will exist equilibrium of temperature between the wall and the molecules that leave the wall, and we shall find aI, 00 = 1 (the indices 1 and 00 in aI, 00 refer to the number of collisions a molecule will suffer with the one surface before it reaches the other). If the assumption, that adsorption goes together with al,oo = 1, appears to be right we may state the following experimental rule: the heat conduction in a rarefied gas between two walls becomes independent on the nature of the walls if gas and walls have temperatures below the critical point of the gas. As a matter of fact generally a gas will be measurably adsorbed by any solid wall as soon as the temperature becomes lower than its critical point. Though we examined the adsorption of several gases, viz. He, Ne 3) and later also H 2 and N 2 , on glass and on metal surfaces, we found no exception to that rule. c. In connection with Lan g m u i r's theory of adsorption it is a very interesting question whether al,oo will remain equal to 1 if the adsorption at lower temperatures increases so intensely, that the greater part of the wall is covered with a film of the adsorbed gas. To deduce his wellknown formula for the adsorption isotherm Lan g m u i r started from the assumption that a molecule, which strikes the wall at a place already taken, will be reflected. As a consequence of this assumption the complete covering of the surface will only be reached at p --+ 00. Measurements on Ne at 14-20 0 K 3) have shown, however, that complete covering is reached at about the saturated vapour pressure. Now it is to be expected that even a very short average life of the molecules on the places already covered enables these molecules to enter into thermal contact with the underlaying wall molecules, so that even a relative short average life may not be neglected as regards heat conduction. According to this it can be expected that, independently of the degree of covering,
RESEARCHES 0)< HEAT CONDUCTION' BY RAREFIED GASES. II 1087
aI' 00 = 1, whereas Lan g m u i r's assumption should admit the possibility that aJ> 00 decreases with increasing degree of covering. In this respect it is a happy circumstance that the method used in the experiments dealt with in this paper enables us to measure both heat conduction and adsorption. d. Having given above some idea concerning the. questions we meet in these experimental researches, we wish to point out the importance for helium gasthermometry, especially below 10 K , of investigating the heat conductivity. The rapidly increasing influence of the thermomolecular pressure effect and still more the adsorption of the helium gas oblige us to look for new methods in the gasthermometry in this region. Perhaps it may be possible to use molecular heat conduction for this purpose.
§ 2. The method. a. For a more complete description we refer to Commun. No. 242c 1); we restrict ourselves here to some supplementary remarks. In this method the energy is measured which is delivered to the rarefied gas by a thin glass wire (Thuringian glass) with a platinum pith (15 fl.) which enables the wire to be heated by means of an electrical current. The glass wire is stretched out in the glass bulb of a gas thermometer. The gas pressure in this bulb can be determined by two different methods. If there is no adsorption of the gas on the inner wall of the glass bulb the pressure can be deduced from the volumes of the thermometer and of the gas pipette used for filling the thermometer. In case of adsorption the pressure is measured with a hot wire manometer placed in a bath of liquid oxygen. The difference between the calculated and the measured pressures gives the adsorption. In the latter case we must account for the thermomolecular pressure difference occurring in the capillary which connects manometer and bulb. A matter of importance is the choice of the diameter of this capillary. We consider that the gas must be rarefied to such a degree that practically the diameter of the glass wire may be neglected in comparison with the mean free path x of the gas molecules. At this rarefaction it is impossible to take the diameter 2 R of the capillary so large that the parameter 2Rj)" which determines the therrnomolecular pressure difference, remains> 1 along the whole capillary.
1088
w.
H. KEESOlll AND G. SCHlIIIDT
2RjI. ,......, 1 forms, however, the most uncertain part of the pressure.
region of this effect. Hence it is better to choose the diameter on the contrary so small that, considering that a pressure as low as possible is also chosen, the pressure effect approaches the limit: PJ!Pz--: YTJ!,\IT z. The nearer this approach the better we know the quotient pJ!pz by which we must correct. This quotient can be calculated from the formula for the thermomolecular pressure difference given in Commun. No. 246b 4). It is in every respect advantageous to place the hot wire manometer in a bath of liquid oxygen or nitrogen in stead of placing it in an ice bath; in this way pJ!pz is reduced to a much lower value. b. \Ve wish to discuss now how to correct for the heat developed in both short wire ends which have remained uncovered with glass. These ends take together 12% of the whole wire length. For that purpose we think the wire warmed up in the rarefied gas. If we suppose the temperature variation along the ends to be about linear it is evident that the temperature increase of the glass body amounts to 1.C6 ~ T, if ~ T is the mean temperature increase of the whole wire as derived from its resistance. Meanwhile for our calculations we may consider the temperature increases of the glass body to be ~ T provided that we diminish the measured value of the energy by 6%. Further we may suppose that about half the energy developed in the short wire ends is given off to the glass body, and that the rest flows away through the ends. To account for this loss we have to diminish the total energy again by 6%, so in total with 12%. As to the measurements in vacuum. we eliminate the heat developed in the ends in the same way. After all we subtract the corrected energy eo as measured in vacuum from the corrected e measured in the gas, both for the same ~ T of course; the difference is the energy given off to the gas by the glass body. c. In these measurements fig. 1 represents the resistance Q of the wire and moreover the corrected energy eo both as functions of the average temperature of the wire. The curves for eo give the temperature increase in vacuum for four different temperatures of the bath. A translation of the three lower curves in the vertical direction leads to coincidence with the higher one as we might expect. That these curves are not exactly straight is probably caused by a
lC89
RESEARCHES ON HEAT CONDUCTION BY RAREFIED GASES. II
small variation with temperature in the heat conductivity of the wire ends. 300 watts
.l75
.50 1 - - - - - + - - - - - + - - - - - l - - - - . ; : L - - - - + - - - - - 7 ' i 2 S0
.25!------I-----+-----If7L---------+---~q_---_7.
DOI-----+-----j-~---1I--__j:f_-t----_,+_---____lf50
751-----I-r----+----;e'F--J----r-f-----+----r--j
t--;,,<-----t----r'-----j----r--1I-----t----:;P>---+-r-----!SO
1:.10'
l
BO
75
Fig. J.
n
BS
95
100 'K
and eo as fun ctic ns of the temperature of the wire.
§~. The results. a. In table ITo represents the bath temperature; il T the temperature increase; e: the corrected energy in watts; TV the energy in watts given off to the gas per em- glass surface and per micron mercury gas pressure. Since the wire diameter cannot entirely be neglected in comparison with the mea n free path of the rarefied gas, the gas molecules coming back from the wire have a small chance to reach the wire again aft er only one collision with a molecule of the gas. The correction factor 1 krj"A, in which r is the radius of the glass wire, refers not only to this circumstance, but moreover to possible smaller other corrections linearly dependent 011 the pressure.
+
Physica III
69
1090
W. H. I{EESO:lI AND G. SCIDIIDT TABLE I Accommodation coefficient of He, II" Xe and X, on glass at 70-100°1{ Hydrogen, To = 90.10°1{
Helium, 'fo = 77.20°1{
t1 T
I'
I ~.lo'l
co.IO'/...!.!..:- .10' (watts) (watts) t1T (watts)
Ia"oo
p (mm Hg) = 0.02060
+ rIJ. =
1
t1 1'1 C.IO"
co.10'j...!.!..:-.IO' (watts) (watts) t1T (watts)
P (mm Hg) = 0.02607
1.045
+ rIJ. =
I
2L16 21.27 20.92
12.481 693.71 104.61 14.60. 815.5 123.3 17.11 955.7 157.7
Ia,,=
0 3 84 1 0.386 . 0.380
5.841762.51 52.1 60.2 6.72 879.0 8.80 1130.79.0 102.3 a"oo= 0.383 11.31 1463.-
1.08
I
501 44. 44.46 43.73 44.00
0.560 0.559 0.550 0.554 a,,= = 0.555
Xeon, To = 90.11°1{
Nitrogen, 1'0=70.08°1{ and 86.58°1{
p (mm Hg) = 0.0293
P (mm Hg)=0.00388, 1'0=70.08°1{
1 5.32\ 336.1 7.72 494.2 11.08 713.0
+ rIA =
I
1.085 17.67\ 18.02 18.62
47.41 68.7 82.1
a" 00
I
P = 0.0586
I
+ rIA =
= 1.04 75 33. 1 32.99 32.93 ·a"oo =
1.022 0.999 0.996 1.005
= 86.58°1{ = 1.045
P = 0.00602, To
1.170
10.471 1170.94.2 1 11.78 1328.- 1 106.8
+ rIA
0.786 9.521 210.3\ 74.81 0.797 12.52 274.0 99.5 166.0 0.824 20.39 I 449.3 = 0.802
18. 09 1 0.800 7.141210.1 18.28 0.808 9.37 274.7 a"oo = 0.804 12.02 351.8
I
+ rIA
I
64.61 85.5 111.0
1.051 1.040 1.032 a"oo = 1.041
22 31. 1 30.92 30.68
P = 0.0879
1 9.2811420.11.60 1774.-
+ rIJ.
!
= 1.255
83.2 105.0
I
0.803 18. 161 18.14 0.802 a"oo = 0.802'
From our earlier measurements at O°C we found k = 1.0. Table I shows for Ne that the same k leads to data for al,oo which are independent on the pressure. It will be shown later that k = 1.0 also may be applied at 14-20°K. In the calculation of the molecular heat conduction for hydrogen according to the K n u d sen's formula we assumed for this gas cp/cv = 1.58 in this region of temperatures; here this gas behaves almost as if it were monoatomic. b. Comparison of the results here obtained for al,oo with the earlier ones at O°C shows: 70 0 K < To < 90 0 K : He 0.383; H 2 0.555; Ne 0.803; N 2 1.02. To = 273.1 oK: 0.336; 0.283; 0.670; 0.855.
RESEARCHES ON HEAT CONDUCTION BY RAREFIED GASES. II
1091
There appears to be an increase of al. co with decrease of temperature for each of the four gases. For N 2 we find practically unity for 70 < To < 90 as was expected (§ Ib). We intend to publish shortly the results obtained for the adsorption of N 2 , in combination with : those for H 2 at 14-20°K. The dependence of ai, 00 on the temperature can perhaps be best expressed by forming the ratio of the difference of the two values of al,co to the difference between ai, co at O°C and unity: He 0.07; H 2 0.38; Ne 0.40; N 21.00. The ciritical points of these four gases are: He 5.2°1{; H 2 33°1{; Ne 44°1{; N2 126°K. Here appears a remarkable relation between both series of numbers; the ratio mentioned above increases with the critical point. At the other side we may consider the critical point practically as about the upper limit of the region of measurable adsorption on glass as follows from our adsorption measurements on He, Ne 3) and later on H 2 and N2 on glass. The joint results can be summarised as follows: 1. T
1092
RESEARCHES ON HEAT CONDUCTION BY RAREFIED GASES. II REFERE!\CES
1) \Y. H. K e \) s 0 m and G. S c h mid t, Commun. Kamerlingh Ormes Lab., Leiden xo, 242c; Physica, 's-Grav.Tl, 590,1936. 2) ~1. K n u d sen, Ann. Physik (4) 4H, 641,1915. \\'e also referred to the measurements of G r n s t e i n and van \\' ij k. These scientists found a"oo '0.32 for He on glass at 377'C, K n u d sen and we found 0.34 at O'C. 3) \V. H. K e e s 0 m and G. S c h mid t, Commun. Kamerlingh Ormes Lab., Leiden Nos. 226a and b; Proe. roy. Acad. Amsterdam aH, 825,1933. 4) S. Web e rand G. S c h mid t, Cornmun. Kamerlingh Onnes Lab., Leiden No, 246c; Rapp. Commun. Lab. Kamerlingh Ormes septieme Congr. into Froid No. 8, 1936.