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Measurement of the thermal conductivity of argon using hot-wire type thermal diffusion columns
CHEMICAL PHYSICS LETTERS
Volume 2. number 1
MEASUREMENT OF
OF ARGON
THERMAL
THE
THERMAL
USING
1968
CONDUCTIVITY
HOT-WIRE
DIFFUSIOET
May
TYPE
COLUMNS
V. K. SWENA * Pizysics Departmenf , Rajasthan Universiiy , Jaipur, Rajasthan, India and S. C. %XENA Themnopltysical Properties Research Center. Purdnc University, Lafayette, Indiana, USA
Received 26 March 1968 Hot wire type of thermal diffusion columns have been used to determine
Convection.
temperature
jump
and end conduction
are
established
thermal
experimentally
conductivity of argon. small. The new
to be
data taken in the range 350 to 15OOOKare correlated by 105h = 1.355 + 1.091 x 10-2T - 1.876 x lo-6T2Here the thermal conductivity, 3. is in cal cm-lsec’ ldeg-l and temperature, T. in ?K. It is found that the new X values agree with all the existing data and theory well within the estimated total uncertainty of 2 29i,of our meas*Erement.
We [l] have been trying to explore the prospect of using hot wire type of thermal diffusion columns for measuring thermal conductivity of gases upto moderately high temperatures. about 3000°K. Subsequent experimentation with neon [2] upto 723’K and with helium 131 upto 1350°K turned out to be very encouraging. We report here our results on argon in the temperature xange 350 - 1500°K and compare with other available data as well as with the Chapman-Enskog kinetic theory. This gas was chosen particularly because it has been thoroughly investigated by other workers and also the rigorous theory describes its behaviour quite successfully. It is thus possible to have a good confirmation of this promising and valuable technique. The argon gas used in our investigations was supplied by British Oxygen Co., England, and was spectroscopically pure. The description of the apparatus, its theory and correction$ and procedure of making a run are already given in enough detail [1.2] and therefore here we-will briefly refer to the pertinent points and present our new results and their dis* Present address: Department of Pharmacy. sity of Saugar.
44
Ssgar.
M.P..
India.
univer-
cussion. The necessary constants of the two conductivity columns and platinum wires are given in table 1. The latter was supplied by M/S Ravindra Heracus and Co., Bombay. and was 99.99% pure. The change in the resistance of the platinum wire was used to determine its temperature according to the relation, Rf = Ro(l+At+Bt2).
(1)
The constants A and B for the two samples of platinum wires used were determined experimentally and are also reported in table 1. In the above relation. Ri and R, are the resistances of the platinum wire at t and O°C respectively. The thermal conductivity of the gas A’, is computed from the formula [l], A’
=
ln(r 3/‘~2) 2ikT
dw
( dt
c
J .)+r2 *
(2)
Here w, is the power conducted through the gas and is obtairied experimentally as a difference of the two powers needed to heat the platinum wire to a certain temperature in the presence and absence of the gas. YI and u2 are the radii of the tube and wi.re respectively and J the. mechanical .-qi;valeni: of heat. For the sake of brevity we do
Volume 2, number 1
May 1968
CHEMICAJ, DHYSICS LETTERS Table 1 The constants of the conductivity columns.
The length of the axial platinum
wire of column I at 25OC
91.05 cm
The length of the axial platinum
wire
62.73 cm
Internal
radius
External First
of the conductivity
radius
sample
Resistance
columns
of the conductivity
of the platinum
of column II at 250C
wire:
columns radius
0.427 cm
(ri)
0.512 cm
(rlt)
0.024 60 cm
(~2)
0.005 9972 ohm/cm
per unit length at OoC
Constant A.
33.55
eq. (I)
-49
Constant B. eq. (1) Second sample Resistance
-
wire:
radius
x 10-8pz=
C.02463 cm
(~2)
0 -005 447 ohm/cm
per unit length at O°C
Constant A. Constant
of the platinum
x ia-+%
36.25 x l&/%
eq. (1)
-49
B. eq. (1)
x lo-s/%2
lumns. The X’ values of column 7 zre obtained according to this differential procedure. The fact that these values of X’ agree with those given in columns 2 through 6 is not surprising and indicates that the error introduced in X’ due to the
not report the wc values but instead directly the X’ values in table 2. In columns 2 through 5 are
those values of ;i’ which were obtained from column II at four different pressures. As the four sets agree well with each other we conclude that convection and temperature jump effects are absent. In column 6 of table 2 are given the h’ values as obtained from measurements on column I. The two columns do not differ from each other in any respect except for length. Consequently differential measurements will refer to a small centra! portion of the longer wire of length equal to the difference of the two individual lengths of the co-
conduction of heat through the two ends of the wire is not significant for our columns and operating conditions. This possibility was indicated before [l] and is experimentaliy estabflshed here over a much longer temperature range. We have
graphically
smoothed all these 6 sets of measure,
values are reported in coLumn 8. The A’ va’iues after being corrected for the “wall effect” are &ported in column 9 and are adequaments
and these
Table 2 Uncorrected (A’) and corrected (A) experimental values of thermal conductivitv (in cal cm-lsec-ldeg-I) of argon at a and b signify that first and secdifferent pressures (p, cm Hg) as a function of temperature (t. OC). Superscripts ond samples of the platinum wires were used.
105Az column II (O:)
100
p = 15.5a
5.20
p’= 29.8a
4.96
p = 50.2a
5.16
p =
sob 5.10
105ti.
column I
p = 15.0b 5.00
105X’, differential
p = 15.0
105k 105x Smooth Corrected
105h Eq. (3)
5.15
5.12
5.15
5.16
200
6.12
5.92
6.15
6.08
5.95
6.iY
6.08
6.09
G-09
300
7.15
7.10
6.90
6.95
7.10
7.20
7.06
7.01
7.00
400
8.00
7.95
7.88
8.09
8.00
7.96
7.88
7.96
7.85
8.50
8.50
8.66
8.6s
8.66
500 600
8.51 9.48
8.49 9.60
8.70 9.25
8.45 9.40
9.50
9.35
9.44
9.46
9.44
700
10.2
10.3
10.0
10.2
10.0
10.2
10.2
10.2
10.2
800
10.8
11.0
11.2
10.9
11.1
13.0
10.9
10 =
10-9
900
11.5
11.5
11.4
11.2
11.5
11.5
11.5
LI.5
Il.6
1000
12.0
12.1
11.9
11.8
12.0
12.1
12.2
12.2
12.2
1100
12.4
12.7
12.7
12.8
12.6
12.8
1200
13.5
13.4
13.6
13.4
13.4
13.4
45
Volume
2. number
Comparison (&
CHEMICAL
1
of the present
thermal
Present work
Ref. [4J
350
4.95
4.80(-3.0)
400
5.42
5.33(-l-7)
500
6.34
600 700
PHYSICS LETTERS
Table 3 conductivit_v values
May 1968
of argon with those of others
105X in cal cm-lsec-ldegl Ref. [5] Ref. l6J
and theory *. Theory
Ref. [7]
4.84(-2.2)
4.80(-3.0)
4.85(-2.0)
5.38(-0.7)
5.35(-1.5)
5.35(-1.3)
6.31(-0.5)
6.32(-0.3)
6.35(-O-Z)
6.25(-l
7.25
7.19(-0.6)
7.22(-0.1)
7.28(-0.7)
7.10(-1.8)
8.07
8.03(-0.5)
8.08(-0.1)
8.18(-+1.4)
800
8.88
8.82(-0.7)
8.88(
0.0)
8.92(-cO.6)
9.19(&3.5)
8.75(-1.5)
900
S-65
9.51(-1.5)
9.65(
0.0)
9.68(+0.3)
9.89(+2.5)
9.50(-1.6)
.
.4)
7.95(-1.5)
1000
10.4
10.2 (-1.9)
10.2 (-1.9)
10.4 ( 0.0)
10.6 (+J .S)
10.2 (-1.9)
1100
11.1
10.9
(-1.8)
10.8 (-2.7)
11.1 ( 0.0)
11.2
(to.9)
10.9 (-1.8)
1200
11.7
11.5
(-1.7)
11.4 (-2.6)
11.7 ( 0.0)
11.8 (+0.9)
11.5 (-1.7)
12.3 (-0.8)
12.4 ( 0.0)
12.2 (-1.6)
12.9 (-0.8)
12.8 (-1.5)
13.4 (-0.7)
13.4 (-0.7)
1300
12.4
12.2 (-1.6)
12.1 (-2.4)
14lJlJ
13.0
12.8 (-1.5)
12.5
1500
13.5
13.4
(-0.7)
from
values
* The percentage
tely correlated
deviations
by the foIlowing
of column
(-3.9)
2 are given in parenthesis
equation:
10% = 1.355 + 1.091 x 10_2T - 1.876 Y 10_6&(3) Here T is in oK. The above equation synthesises the h values within an average absolute deviation of 0.2%. In table 3 we compare our results with other experimental data as well as with theory. In columns 3 and 4 we present results of two independent studies [4.5].in which most probable values are recommended on the basis of most of the available data. Both-sets agree with our experimental values within an average absolute deviation of 1.5 per cent. Vargaftik and Zimina [6] measured the thermal conductivity using a Standard hot wire cell in the temperature range 0 to 1000°C. Their results are reproduced in column 5 and agree with the current values within an average absolute deviation of 0.8%. Timrot and Umanskii [7] have also reported that data in 800 2000’K using the same technique as ours and their values are listed in column 6. These are stated to be accurate within a maximum possible error of about 7%. Our values agree with theirs within an average absolute deviation of 1.4%. We thus find that our values agree with the existing data within the estimated precision of the measurement i.e. 5 2%. and this is also consistent with our error estimation 131. The decrease in h values and the increase in electrical stability (and hence in the accuracy of the measured or values) seem to present a good balance in keep
in each case.
In the last column of table 3 are given the theoa retical values of h according to the third approximation expression [83 and the exp-six intermolecular potential with parameters of Mason and Rice [9]. The calculated values agree with our data within an average absolute deviation of 1.7% This is quite satisfactory. We are grateful to the Department of Energy. Bombay. and to the Ministry of New Delhi, for supporting this research the award of a research fellowship to V. na.
Atomic Defence. and for K. Saxe-
Re_fct-ewes M. P. Saksena ( I 966) 1595. V. I<. Saksena.
and S. C. Sasenn. M. P. Saksena
Whys. Fluids
and S. C. S,zuena.
dian .J. I’hys. 40 (1966) 597. V. K. Saltsena and S. C. Saxena.
9 In-
to be published. Proc.Phvs.Soc. (London). Purdue cniversity Thermophysical Properties Research Center Data Book. cci. Y.S. Touloukian. Vol. 2 (December 1966) Ch. 1. J. Chem. Eng. Data. 151 J. M. Gandhi and S. C.Saxena. in press. 2 [61 5. B. Vargaflik and h’. Zimina. High Temperature (19641 645. High Temperature 17) D. L. Timrot and A. S. Umanskii. 4 (1966) 285. C. F.Curtiss and R. B. Bird. t81 J.O.Hirschfelder. Molecular Theory of Gases and Liquids (John Wile! and Sons. Xew York. lYG4). r91 E-.4. Mason and W. E. Rice. J. Chem. Phgs. 22 (1954) 522.
Volume 2. number 1
MEASUREMENT OF
OF ARGON
THERMAL
THE
THERMAL
USING
1968
CONDUCTIVITY
HOT-WIRE
DIFFUSIOET
May
TYPE
COLUMNS
V. K. SWENA * Pizysics Departmenf , Rajasthan Universiiy , Jaipur, Rajasthan, India and S. C. %XENA Themnopltysical Properties Research Center. Purdnc University, Lafayette, Indiana, USA
Received 26 March 1968 Hot wire type of thermal diffusion columns have been used to determine
Convection.
temperature
jump
and end conduction
are
established
thermal
experimentally
conductivity of argon. small. The new
to be
data taken in the range 350 to 15OOOKare correlated by 105h = 1.355 + 1.091 x 10-2T - 1.876 x lo-6T2Here the thermal conductivity, 3. is in cal cm-lsec’ ldeg-l and temperature, T. in ?K. It is found that the new X values agree with all the existing data and theory well within the estimated total uncertainty of 2 29i,of our meas*Erement.
We [l] have been trying to explore the prospect of using hot wire type of thermal diffusion columns for measuring thermal conductivity of gases upto moderately high temperatures. about 3000°K. Subsequent experimentation with neon [2] upto 723’K and with helium 131 upto 1350°K turned out to be very encouraging. We report here our results on argon in the temperature xange 350 - 1500°K and compare with other available data as well as with the Chapman-Enskog kinetic theory. This gas was chosen particularly because it has been thoroughly investigated by other workers and also the rigorous theory describes its behaviour quite successfully. It is thus possible to have a good confirmation of this promising and valuable technique. The argon gas used in our investigations was supplied by British Oxygen Co., England, and was spectroscopically pure. The description of the apparatus, its theory and correction$ and procedure of making a run are already given in enough detail [1.2] and therefore here we-will briefly refer to the pertinent points and present our new results and their dis* Present address: Department of Pharmacy. sity of Saugar.
44
Ssgar.
M.P..
India.
univer-
cussion. The necessary constants of the two conductivity columns and platinum wires are given in table 1. The latter was supplied by M/S Ravindra Heracus and Co., Bombay. and was 99.99% pure. The change in the resistance of the platinum wire was used to determine its temperature according to the relation, Rf = Ro(l+At+Bt2).
(1)
The constants A and B for the two samples of platinum wires used were determined experimentally and are also reported in table 1. In the above relation. Ri and R, are the resistances of the platinum wire at t and O°C respectively. The thermal conductivity of the gas A’, is computed from the formula [l], A’
=
ln(r 3/‘~2) 2ikT
dw
( dt
c
J .)+r2 *
(2)
Here w, is the power conducted through the gas and is obtairied experimentally as a difference of the two powers needed to heat the platinum wire to a certain temperature in the presence and absence of the gas. YI and u2 are the radii of the tube and wi.re respectively and J the. mechanical .-qi;valeni: of heat. For the sake of brevity we do
Volume 2, number 1
May 1968
CHEMICAJ, DHYSICS LETTERS Table 1 The constants of the conductivity columns.
The length of the axial platinum
wire of column I at 25OC
91.05 cm
The length of the axial platinum
wire
62.73 cm
Internal
radius
External First
of the conductivity
radius
sample
Resistance
columns
of the conductivity
of the platinum
of column II at 250C
wire:
columns radius
0.427 cm
(ri)
0.512 cm
(rlt)
0.024 60 cm
(~2)
0.005 9972 ohm/cm
per unit length at OoC
Constant A.
33.55
eq. (I)
-49
Constant B. eq. (1) Second sample Resistance
-
wire:
radius
x 10-8pz=
C.02463 cm
(~2)
0 -005 447 ohm/cm
per unit length at O°C
Constant A. Constant
of the platinum
x ia-+%
36.25 x l&/%
eq. (1)
-49
B. eq. (1)
x lo-s/%2
lumns. The X’ values of column 7 zre obtained according to this differential procedure. The fact that these values of X’ agree with those given in columns 2 through 6 is not surprising and indicates that the error introduced in X’ due to the
not report the wc values but instead directly the X’ values in table 2. In columns 2 through 5 are
those values of ;i’ which were obtained from column II at four different pressures. As the four sets agree well with each other we conclude that convection and temperature jump effects are absent. In column 6 of table 2 are given the h’ values as obtained from measurements on column I. The two columns do not differ from each other in any respect except for length. Consequently differential measurements will refer to a small centra! portion of the longer wire of length equal to the difference of the two individual lengths of the co-
conduction of heat through the two ends of the wire is not significant for our columns and operating conditions. This possibility was indicated before [l] and is experimentaliy estabflshed here over a much longer temperature range. We have
graphically
smoothed all these 6 sets of measure,
values are reported in coLumn 8. The A’ va’iues after being corrected for the “wall effect” are &ported in column 9 and are adequaments
and these
Table 2 Uncorrected (A’) and corrected (A) experimental values of thermal conductivitv (in cal cm-lsec-ldeg-I) of argon at a and b signify that first and secdifferent pressures (p, cm Hg) as a function of temperature (t. OC). Superscripts ond samples of the platinum wires were used.
105Az column II (O:)
100
p = 15.5a
5.20
p’= 29.8a
4.96
p = 50.2a
5.16
p =
sob 5.10
105ti.
column I
p = 15.0b 5.00
105X’, differential
p = 15.0
105k 105x Smooth Corrected
105h Eq. (3)
5.15
5.12
5.15
5.16
200
6.12
5.92
6.15
6.08
5.95
6.iY
6.08
6.09
G-09
300
7.15
7.10
6.90
6.95
7.10
7.20
7.06
7.01
7.00
400
8.00
7.95
7.88
8.09
8.00
7.96
7.88
7.96
7.85
8.50
8.50
8.66
8.6s
8.66
500 600
8.51 9.48
8.49 9.60
8.70 9.25
8.45 9.40
9.50
9.35
9.44
9.46
9.44
700
10.2
10.3
10.0
10.2
10.0
10.2
10.2
10.2
10.2
800
10.8
11.0
11.2
10.9
11.1
13.0
10.9
10 =
10-9
900
11.5
11.5
11.4
11.2
11.5
11.5
11.5
LI.5
Il.6
1000
12.0
12.1
11.9
11.8
12.0
12.1
12.2
12.2
12.2
1100
12.4
12.7
12.7
12.8
12.6
12.8
1200
13.5
13.4
13.6
13.4
13.4
13.4
45
Volume
2. number
Comparison (&
CHEMICAL
1
of the present
thermal
Present work
Ref. [4J
350
4.95
4.80(-3.0)
400
5.42
5.33(-l-7)
500
6.34
600 700
PHYSICS LETTERS
Table 3 conductivit_v values
May 1968
of argon with those of others
105X in cal cm-lsec-ldegl Ref. [5] Ref. l6J
and theory *. Theory
Ref. [7]
4.84(-2.2)
4.80(-3.0)
4.85(-2.0)
5.38(-0.7)
5.35(-1.5)
5.35(-1.3)
6.31(-0.5)
6.32(-0.3)
6.35(-O-Z)
6.25(-l
7.25
7.19(-0.6)
7.22(-0.1)
7.28(-0.7)
7.10(-1.8)
8.07
8.03(-0.5)
8.08(-0.1)
8.18(-+1.4)
800
8.88
8.82(-0.7)
8.88(
0.0)
8.92(-cO.6)
9.19(&3.5)
8.75(-1.5)
900
S-65
9.51(-1.5)
9.65(
0.0)
9.68(+0.3)
9.89(+2.5)
9.50(-1.6)
.
.4)
7.95(-1.5)
1000
10.4
10.2 (-1.9)
10.2 (-1.9)
10.4 ( 0.0)
10.6 (+J .S)
10.2 (-1.9)
1100
11.1
10.9
(-1.8)
10.8 (-2.7)
11.1 ( 0.0)
11.2
(to.9)
10.9 (-1.8)
1200
11.7
11.5
(-1.7)
11.4 (-2.6)
11.7 ( 0.0)
11.8 (+0.9)
11.5 (-1.7)
12.3 (-0.8)
12.4 ( 0.0)
12.2 (-1.6)
12.9 (-0.8)
12.8 (-1.5)
13.4 (-0.7)
13.4 (-0.7)
1300
12.4
12.2 (-1.6)
12.1 (-2.4)
14lJlJ
13.0
12.8 (-1.5)
12.5
1500
13.5
13.4
(-0.7)
from
values
* The percentage
tely correlated
deviations
by the foIlowing
of column
(-3.9)
2 are given in parenthesis
equation:
10% = 1.355 + 1.091 x 10_2T - 1.876 Y 10_6&(3) Here T is in oK. The above equation synthesises the h values within an average absolute deviation of 0.2%. In table 3 we compare our results with other experimental data as well as with theory. In columns 3 and 4 we present results of two independent studies [4.5].in which most probable values are recommended on the basis of most of the available data. Both-sets agree with our experimental values within an average absolute deviation of 1.5 per cent. Vargaftik and Zimina [6] measured the thermal conductivity using a Standard hot wire cell in the temperature range 0 to 1000°C. Their results are reproduced in column 5 and agree with the current values within an average absolute deviation of 0.8%. Timrot and Umanskii [7] have also reported that data in 800 2000’K using the same technique as ours and their values are listed in column 6. These are stated to be accurate within a maximum possible error of about 7%. Our values agree with theirs within an average absolute deviation of 1.4%. We thus find that our values agree with the existing data within the estimated precision of the measurement i.e. 5 2%. and this is also consistent with our error estimation 131. The decrease in h values and the increase in electrical stability (and hence in the accuracy of the measured or values) seem to present a good balance in keep
in each case.
In the last column of table 3 are given the theoa retical values of h according to the third approximation expression [83 and the exp-six intermolecular potential with parameters of Mason and Rice [9]. The calculated values agree with our data within an average absolute deviation of 1.7% This is quite satisfactory. We are grateful to the Department of Energy. Bombay. and to the Ministry of New Delhi, for supporting this research the award of a research fellowship to V. na.
Atomic Defence. and for K. Saxe-
Re_fct-ewes M. P. Saksena ( I 966) 1595. V. I<. Saksena.
and S. C. Sasenn. M. P. Saksena
Whys. Fluids
and S. C. S,zuena.
dian .J. I’hys. 40 (1966) 597. V. K. Saltsena and S. C. Saxena.
9 In-
to be published. Proc.Phvs.Soc. (London). Purdue cniversity Thermophysical Properties Research Center Data Book. cci. Y.S. Touloukian. Vol. 2 (December 1966) Ch. 1. J. Chem. Eng. Data. 151 J. M. Gandhi and S. C.Saxena. in press. 2 [61 5. B. Vargaflik and h’. Zimina. High Temperature (19641 645. High Temperature 17) D. L. Timrot and A. S. Umanskii. 4 (1966) 285. C. F.Curtiss and R. B. Bird. t81 J.O.Hirschfelder. Molecular Theory of Gases and Liquids (John Wile! and Sons. Xew York. lYG4). r91 E-.4. Mason and W. E. Rice. J. Chem. Phgs. 22 (1954) 522.