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Heat conductivity of glass at 1.3 °K
Physica
XI,
no 4
HEAT
December
CONDUCTIVITY
1945
OF GLASS AT 1.3”K
by P. H. KEESOM Communication No.
2686
from the Kamerlingh
Onnes Laboratory,
Leiden
Summary At 1.3”K deg-’ set-‘.
the heat conductivity
of thuringian
glass is 8. 1O-5 cal cm-1
To be able to estimate beforehand the degree. of heat of a glass calorimeter to be constructed, we wanted a the heat conductivity of thuringian glass at a temperature 1°K. We made some measurements with a very simple which gave an approximate value of the heat conductivity.
Introduction.
insulation value of of about apparatus
1. Af$arattis. Fig. 1 shows the measuring device consisting of two’tubes Al, API in which helium is condensed and two connecting tubes B,, B,, leading to a differential oilmanometer which make it possible to measure pressure differences between the liquids inside A, and A, and the bath. The two parts are similar except that the condenser tubes have different lengths viz. 5.8 and 2 cm. The diameters of the tubes are 0.95 cm and the thickness of the glass walls is 0.091 cm. The double-walled connecting tubes prevent condensation above the condenser tubes when heat is supplied to these and they define the area of flow through the glass. Each condenser tube contains a constantan resistance C, and C2 as heating element. 2. Measurement. It proved impossible to fill the tubes with liquid helium when the bath temperature was near the boiling point, but when we reduced the bath temperature below the A-point we could condense helium into them and filled them up to several ems above the rim of the condenser tubes. Some measurements were done with a bath temperature of 1.169”K but it was more convenient to work at a somewhat higher temperature viz. 1.324”K. -
339 -
340 Whether downwards flow being each tube
I’.
H.
KEESOM
a current is sent through C, and C, or not, heat wil flow along the inner walls of B, and B,, the amount W, of the practically the same for both tubes. This flow caused in a temperature difference between the liquids in bathand
A
E Fig.
1.
tube, which we denote by AT,,. Its magnitude was calculated from the corresponding pressure difference between bath and liquid in the tube, which was measured regularly. The latter was found to change slightly with varying temperature at the top of ‘B, and BZ, as was to be expected. For different values of the heating current, the ensuing temptrature differences AT between bath and tube’were likewisedetermined
HEAT
CONDUCTIVITY
OF GLASS
AT
34 1
1.3OK
from the pressure differences. In figure 2 the heat input is plotted as a function of AT and again of AT - AT,, for both tubes. The resulting curves are almost straight lines. the W vers. AT curves are easily extrapolated so as to intersect on the W-axis. 3. RCSI&S. For each tube we will have:
where A is the heat conductivity, 0 the effective area of the glass wall through which heat flows to the bath, and Ax the thickness of the glass wall. Mre can find A in either of two ways.
Fig. 2. 0 long
tube
9 short tube v ,I #>
1,324” K AT _ AT, > Tbatb = T bath = 1.169”K ?,
,#
T ,,
bath
=
1.324”K
342
HEAT
CONDUCTIVITY
OF
GLASS
AT
1.3’K
The first way is to eliminate W,-, by taking, for one and the same AT value, thk difference of both members of this equation for both tubes. Calling AW the difference in heat input and A0 (= 10.75 cmz) the difference in conducting areas, we find: AW A=m.m.
Ax
To AT = 0.4 corresponds AW = 16.8. lo4 ergs, and we find A = 3.5.1 O3 erg cm-’ deg-’ se& = 8.3.10” cal cm-’ deg-’ se&. The second way is to estimate W, from the intersection of the W vers. AT curve with the W axis, giving W,. For the larger tube we get in this way A = w + wo -Ax -
0
AT
8,2.1 Om5 cal cm-’
deg-’ see-*
0 is not so accurately defined. Due both to the fact that 0 is less well known and to the extrapolation this method is not so reliable as the former one. Ey the agreement of the two results the extrapolation is justified and although the accuracy is not very great, we conclude that at 1.3”K the heat conductivity of ordinary thuringian glass is 8.1 OM5 cal deg-’ cm-’ set-*. A comparison with measurements ai higher temperature, see E u c k e n ‘) (different kinds of glass) and S t e p h e n “) (Pyrex glass), shows a marked decrease of the heat conduction to lower temperatures. We have neglected the possibility of a temperature jump in passing from helium to glass and vice verse. For a normal liquid this is quite correct, for liquid helium we are not absolutely certain as to this point. As mentioned we measured some points at a somewhat lower temperature. Although we cannot give any reliable factor the points show very distinctly that the conductivity still decreases. Received
Oct.
15,
1945.
REFERENCES I) 2)
A. E u c k e n, Ann. Physik R. W. B. S t e p he n, Phil.
(4) 34, 185, 191 I. Mag. (7) 14, 897, 193’2.
XI,
no 4
HEAT
December
CONDUCTIVITY
1945
OF GLASS AT 1.3”K
by P. H. KEESOM Communication No.
2686
from the Kamerlingh
Onnes Laboratory,
Leiden
Summary At 1.3”K deg-’ set-‘.
the heat conductivity
of thuringian
glass is 8. 1O-5 cal cm-1
To be able to estimate beforehand the degree. of heat of a glass calorimeter to be constructed, we wanted a the heat conductivity of thuringian glass at a temperature 1°K. We made some measurements with a very simple which gave an approximate value of the heat conductivity.
Introduction.
insulation value of of about apparatus
1. Af$arattis. Fig. 1 shows the measuring device consisting of two’tubes Al, API in which helium is condensed and two connecting tubes B,, B,, leading to a differential oilmanometer which make it possible to measure pressure differences between the liquids inside A, and A, and the bath. The two parts are similar except that the condenser tubes have different lengths viz. 5.8 and 2 cm. The diameters of the tubes are 0.95 cm and the thickness of the glass walls is 0.091 cm. The double-walled connecting tubes prevent condensation above the condenser tubes when heat is supplied to these and they define the area of flow through the glass. Each condenser tube contains a constantan resistance C, and C2 as heating element. 2. Measurement. It proved impossible to fill the tubes with liquid helium when the bath temperature was near the boiling point, but when we reduced the bath temperature below the A-point we could condense helium into them and filled them up to several ems above the rim of the condenser tubes. Some measurements were done with a bath temperature of 1.169”K but it was more convenient to work at a somewhat higher temperature viz. 1.324”K. -
339 -
340 Whether downwards flow being each tube
I’.
H.
KEESOM
a current is sent through C, and C, or not, heat wil flow along the inner walls of B, and B,, the amount W, of the practically the same for both tubes. This flow caused in a temperature difference between the liquids in bathand
A
E Fig.
1.
tube, which we denote by AT,,. Its magnitude was calculated from the corresponding pressure difference between bath and liquid in the tube, which was measured regularly. The latter was found to change slightly with varying temperature at the top of ‘B, and BZ, as was to be expected. For different values of the heating current, the ensuing temptrature differences AT between bath and tube’were likewisedetermined
HEAT
CONDUCTIVITY
OF GLASS
AT
34 1
1.3OK
from the pressure differences. In figure 2 the heat input is plotted as a function of AT and again of AT - AT,, for both tubes. The resulting curves are almost straight lines. the W vers. AT curves are easily extrapolated so as to intersect on the W-axis. 3. RCSI&S. For each tube we will have:
where A is the heat conductivity, 0 the effective area of the glass wall through which heat flows to the bath, and Ax the thickness of the glass wall. Mre can find A in either of two ways.
Fig. 2. 0 long
tube
9 short tube v ,I #>
1,324” K AT _ AT, > Tbatb = T bath = 1.169”K ?,
,#
T ,,
bath
=
1.324”K
342
HEAT
CONDUCTIVITY
OF
GLASS
AT
1.3’K
The first way is to eliminate W,-, by taking, for one and the same AT value, thk difference of both members of this equation for both tubes. Calling AW the difference in heat input and A0 (= 10.75 cmz) the difference in conducting areas, we find: AW A=m.m.
Ax
To AT = 0.4 corresponds AW = 16.8. lo4 ergs, and we find A = 3.5.1 O3 erg cm-’ deg-’ se& = 8.3.10” cal cm-’ deg-’ se&. The second way is to estimate W, from the intersection of the W vers. AT curve with the W axis, giving W,. For the larger tube we get in this way A = w + wo -Ax -
0
AT
8,2.1 Om5 cal cm-’
deg-’ see-*
0 is not so accurately defined. Due both to the fact that 0 is less well known and to the extrapolation this method is not so reliable as the former one. Ey the agreement of the two results the extrapolation is justified and although the accuracy is not very great, we conclude that at 1.3”K the heat conductivity of ordinary thuringian glass is 8.1 OM5 cal deg-’ cm-’ set-*. A comparison with measurements ai higher temperature, see E u c k e n ‘) (different kinds of glass) and S t e p h e n “) (Pyrex glass), shows a marked decrease of the heat conduction to lower temperatures. We have neglected the possibility of a temperature jump in passing from helium to glass and vice verse. For a normal liquid this is quite correct, for liquid helium we are not absolutely certain as to this point. As mentioned we measured some points at a somewhat lower temperature. Although we cannot give any reliable factor the points show very distinctly that the conductivity still decreases. Received
Oct.
15,
1945.
REFERENCES I) 2)
A. E u c k e n, Ann. Physik R. W. B. S t e p he n, Phil.
(4) 34, 185, 191 I. Mag. (7) 14, 897, 193’2.