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Absorption coefficients for water vapor in the 600–1000 cm-1 region
1. Quonr. Sprrrrosc.
Rodiar.
Transfer. Vol. 8. pp. 1531-l 541. Pe.rgamon Pm
1968. Printed
in Great
Britain
NOTE
ABSORPTION COEFFICIENTS FOR WATER IN THE 600-lOOOcm_’ REGION*
VAPOR
P. VARANASI Department
of Mechanics,
State University
of New York, Stony Brook, Long Island, New York and
S. CHOU Department
of the Aerospace
and
S. S. PENNER
and Mechanical Engineering Sciences, University La Jolla, California 92037
of California/San
Diego
(Received 7 March 1968) Abstract-Experimental determinations of absorption coefficients of water vapor are presented for temperatures between 400 and 5OO’K and pressures of 2 and IO atm. All measurements were made by using the technique of self-broadening, moderate resolution ( - 25 cm _ ‘), and a supply source of liquid water at variable temperatures. The observed results are consistent with the idea that hydrogen bonding contributes to the absorption coefficient of water vapor in the spectral region between 600 and 1000 cm- ‘.
1. INTRODUCTION procedure used by us in the determination of absorption coefficients with self-broadening follows standard techniques, which have been adequately described in the literature.“’ The water supply source was a container of liquid water submerged in an oil-heating bath. This liquid container is connected to the absorption cell through a The temperature ofthe absorption a’ in. wide, heated tube (in order to prevent condensation). cell was controlled independently by using a furnace with separate temperature regulation. A schematic diagram of the apparatus is shown in Fig. 1. The experimental technique suggested by Fig. 1 has been employed by one of us (S. S. Penner) for at least 10 years in spectroscopic measurements of absorption coefficients for self-broadening gases produced by evaporation from a liquid reservoir. Previous examples of the use of this procedure in our laboratory have been published.‘24’ It is interesting to note that the non-isothermal experimental arrangement described by Fig. 1 is a system without significant and measurable pressure gradients. This fact is easily established experimentally and may also be shown to be consistent with theoretical results derivable by use of the methodology of irreversible thermodynamics.‘5’ In the present studies, two stainless-steel cells with Irtran-6 (Cd Te) windows and teflon gaskets were used. The remaining aspects of the experimental procedure involve standard techniques (e.g. a Globar light source, mechanical chopper, PerkinElmer model 13 infrared spectrometer with thermocouple detector, etc.).
THE EXPERIMENTAL
* Supported by the Physics Branch of the Office of Naval Research under Contract No. Nonr 2216(24), NR 015401. Reproduction in whole or in part is permitted for any purpose of the United States Government. 1537
1538
P. VARANASI, S. CHOU and S. S. PENNER
En=ERf
PRESSURE GAGE7
ZORPTION
CELL
OBSERVATION
CONSTANT-TEMPERATURE OIL BATH MONOCHROMATOR
VACUUM ‘8s VL\LVE M,, hlprM3~ FIG
I. Schematic
MIRRORS
diagram of the experimental arrangement used in determining coefficients for the pure rotation spectrum of water vapor.
II.
RECORDER
AMPU FIER
EXPERIMENTAL
absorption
RESULTS
The results of the experimental studies are summarized in Figs. 2 and 3, where we show data of the measured spectral absorption coefficients (in cm-’ atm-‘) at 2 and 10 atm, respectively, for temperatures between 400 and 500°K. The data shown in Fig. 2 are close to the values given at 500°K in a previous Note, which also contained some results at 20 and 25 atm for 500”K.‘6’ Some apparent differences in spectral structure are attributable to differences in instrumental resolution. 111.
INTERPRETATION
OF
RESULTS
Absorption coefficients P,T (cm- ‘-atm -l-OK), averaged over the frequency range from 6OOcm-’ to lOOOcm-‘, and derived from the measurements shown in Figs. 2 and 3 pw=2atm 0.03 -.
-
Tw=4000K
____
450°
K
w(cm-‘1 FIG.2. Experimental
results showing P, (in cm- ‘-atm _ ‘) at a pressure of 2 atm and at temperatures of 400.450 and 500°K ; cell length = 30.48 cm.
Absorption coefficients for water vapor in the 600-1000 cm-’
1539
pw= IO atm
0.06 -
T,= 460° K
._
480.K 500.K
__--
0
region
I 700
I
I 000
w
900
1000
(cm-‘)
FIG. 3. Experimental results showing P, (in cm ‘-atm I) at a pressure of 10 atm and at temperatures of 460,480 and 500°K ; cell length = 2 cm.
for 400°K and 450°K at 2 atm and for 460°K and 500°K at 10 atm may be compared with approximate theoretical estimates obtained from the intensity tables of BENEDICT and KAPLAN.“)
Since Benedict and Kaplan did not cover the temperature range in which our experimental measurements were performed, we have employed a semi-empirical procedure to extend their theoretical compilations. The temperature dependence of line intensities, without the induced emission term, is expected to be of the form S(&‘) -
$
exp[ - E(J;.)/kT). R
Here S(J:‘,,) is the integrated intensity (in cm-‘-atm- ’ ) of the rotational line with the lower state identified by J;, and energy E(Jr,.); QR is the rotational partition function of an asymmetric rotor ; N/p is the number of Hz0 molecules per unit volume and unit pressure at temperature T. Within any narrow spectral region, several transitions with completely different lower-state energy levels contribute to the pure rotation spectrum and make it impossible to obtain a theoretical expression for the temperature dependence of a “mean” spectral absorption coefficient. However, a semi-empirical estimate may be made from the tables of Benedict and Kaplan if we define an average absorption coefficient per particle through the relation
P,Tz
[Sum of the intensities (in g- ‘-cm) of all the lines between 600 cm- ’ and 1000 cm- ‘1 4QOR,
where R, is the gas constant per unit mass. We may then plot the quantity log{ T3’2(P,T)j against l/T and obtain an effective mean energy level for the lower state; the factor T3j2 arises because QR y T312. The resulting plot is shown in Fig. 4, where the circles represent values of T312(P,T) derived from Benedict and Kaplan’s tabulations at 220”K, 260°K and
P. VARANASI, S. CHOU and S. S. PENNER
I540
10212, 2.0
30
4.0
50
f x IO+3pKj FIG. 4. Temperature
extrapolation
of mean absorption
coefficients.
for the 600-1000
cm
I region
300°K. A straight line is seen to join the three theoretical data points at low temperatures; the extrapolated curve yields estimates for (P,T) at temperatures between 400°K and 500°K. Comparison of the extrapolated theoretical estimates for the average absorption coefficient with the results of the present experimental studies shows again that the measured values of P,Tare markedly higher. However, the difference between the experimental and extrapolated theoretical results decreases as the temperature is increased. This observation is consistent with the idea@) that association of water vapor molecules due to hydrogen bonding increases the absorption coefficient in the 600-1000 cm- ’ region. As the temperature of water is raised at constant pressure, hydrogen bonds between associated water molecules are probably broken and may provide an explanation for decrease of the quantity
with temperature.
Assuming
A(is,T)
that
x the number
-
E exp $7 i
of hydrogen
bonds at a given temperature
1 ,
we have estimated the “energy E, _” of hydrogen bonding”. Using the data shown in Fig. 2 400°K and 450°K) and in Fig. 3 (pHzO = IOatm, THro = 460°K and 2 arm. THzo = (Pn,o = 500°K). respectively. we obtain 5 kcal/mole and 3 kcal/mole. respectively. These estimates are close to the value of 5 kcal/mole given by PAULING ‘s’ for water in the vapor phase. The numerical estimates for E,_, have been verified in independent experiments that are not described in this Note. The conclusions described in the present Note are not changed significantly when allowance is made for the far wings of strong, distant lines, in accord with the approximate procedure described in Ref. 6, which probably yielded an
Absorption coefficients for water vapor in the 600-1000 cm-’ region
1541
bound for the wing correction in view of much smaller estimates for this effect made earlier by ELSASSER.(” The salient assumptions made in the present Note, namely, negligibly small wing corrections and a theoretical dependence of is, on temperature of the type shown in Fig. 4, have been verified by careful numerical calculations performed recently by P. Varanasi. upper
REFERENCES I S. S. PENNERand D. WEBER,J. Chem. Phys. 19,807. 1361 (1951). 2. A. GUTTMAN and S. S. PENNER,.I. Chem. Phys. 36.98 (1962). 3. A. GUTTMAN, JQSRT 2, 1 (1962). 4. R. GOLDSTEIN. JQSRT4.343 (1963). 5. R. BECKER.Theory q/ Heaf (English translation by G. LEIBFRIED). pp. 358-363. Springer Verlag. New York, New York (1967). 6. S. S. PENNERand P. VARANASI, JQSRT 7,687 (1967). 7. W. S. BENEDICT and L. D. KAPLAN,unpublished calculations, which are reproduced, in part, on p. 184 of Armospheric Radiufion. I. Theoretical Basis by R. hi. GtmDY. Oxford University Press, London (1964). 8. L. PAULINE;,The Nuturr qf rhe C’hrmical Bond. Third ed.. p. 469. Cornell University Press. Ithaca (1960). 9. W. M. ELSASSER, Phys. Rev. 53,768 (1938); Asrrophys. J. 87,497 (1938).
Rodiar.
Transfer. Vol. 8. pp. 1531-l 541. Pe.rgamon Pm
1968. Printed
in Great
Britain
NOTE
ABSORPTION COEFFICIENTS FOR WATER IN THE 600-lOOOcm_’ REGION*
VAPOR
P. VARANASI Department
of Mechanics,
State University
of New York, Stony Brook, Long Island, New York and
S. CHOU Department
of the Aerospace
and
S. S. PENNER
and Mechanical Engineering Sciences, University La Jolla, California 92037
of California/San
Diego
(Received 7 March 1968) Abstract-Experimental determinations of absorption coefficients of water vapor are presented for temperatures between 400 and 5OO’K and pressures of 2 and IO atm. All measurements were made by using the technique of self-broadening, moderate resolution ( - 25 cm _ ‘), and a supply source of liquid water at variable temperatures. The observed results are consistent with the idea that hydrogen bonding contributes to the absorption coefficient of water vapor in the spectral region between 600 and 1000 cm- ‘.
1. INTRODUCTION procedure used by us in the determination of absorption coefficients with self-broadening follows standard techniques, which have been adequately described in the literature.“’ The water supply source was a container of liquid water submerged in an oil-heating bath. This liquid container is connected to the absorption cell through a The temperature ofthe absorption a’ in. wide, heated tube (in order to prevent condensation). cell was controlled independently by using a furnace with separate temperature regulation. A schematic diagram of the apparatus is shown in Fig. 1. The experimental technique suggested by Fig. 1 has been employed by one of us (S. S. Penner) for at least 10 years in spectroscopic measurements of absorption coefficients for self-broadening gases produced by evaporation from a liquid reservoir. Previous examples of the use of this procedure in our laboratory have been published.‘24’ It is interesting to note that the non-isothermal experimental arrangement described by Fig. 1 is a system without significant and measurable pressure gradients. This fact is easily established experimentally and may also be shown to be consistent with theoretical results derivable by use of the methodology of irreversible thermodynamics.‘5’ In the present studies, two stainless-steel cells with Irtran-6 (Cd Te) windows and teflon gaskets were used. The remaining aspects of the experimental procedure involve standard techniques (e.g. a Globar light source, mechanical chopper, PerkinElmer model 13 infrared spectrometer with thermocouple detector, etc.).
THE EXPERIMENTAL
* Supported by the Physics Branch of the Office of Naval Research under Contract No. Nonr 2216(24), NR 015401. Reproduction in whole or in part is permitted for any purpose of the United States Government. 1537
1538
P. VARANASI, S. CHOU and S. S. PENNER
En=ERf
PRESSURE GAGE7
ZORPTION
CELL
OBSERVATION
CONSTANT-TEMPERATURE OIL BATH MONOCHROMATOR
VACUUM ‘8s VL\LVE M,, hlprM3~ FIG
I. Schematic
MIRRORS
diagram of the experimental arrangement used in determining coefficients for the pure rotation spectrum of water vapor.
II.
RECORDER
AMPU FIER
EXPERIMENTAL
absorption
RESULTS
The results of the experimental studies are summarized in Figs. 2 and 3, where we show data of the measured spectral absorption coefficients (in cm-’ atm-‘) at 2 and 10 atm, respectively, for temperatures between 400 and 500°K. The data shown in Fig. 2 are close to the values given at 500°K in a previous Note, which also contained some results at 20 and 25 atm for 500”K.‘6’ Some apparent differences in spectral structure are attributable to differences in instrumental resolution. 111.
INTERPRETATION
OF
RESULTS
Absorption coefficients P,T (cm- ‘-atm -l-OK), averaged over the frequency range from 6OOcm-’ to lOOOcm-‘, and derived from the measurements shown in Figs. 2 and 3 pw=2atm 0.03 -.
-
Tw=4000K
____
450°
K
w(cm-‘1 FIG.2. Experimental
results showing P, (in cm- ‘-atm _ ‘) at a pressure of 2 atm and at temperatures of 400.450 and 500°K ; cell length = 30.48 cm.
Absorption coefficients for water vapor in the 600-1000 cm-’
1539
pw= IO atm
0.06 -
T,= 460° K
._
480.K 500.K
__--
0
region
I 700
I
I 000
w
900
1000
(cm-‘)
FIG. 3. Experimental results showing P, (in cm ‘-atm I) at a pressure of 10 atm and at temperatures of 460,480 and 500°K ; cell length = 2 cm.
for 400°K and 450°K at 2 atm and for 460°K and 500°K at 10 atm may be compared with approximate theoretical estimates obtained from the intensity tables of BENEDICT and KAPLAN.“)
Since Benedict and Kaplan did not cover the temperature range in which our experimental measurements were performed, we have employed a semi-empirical procedure to extend their theoretical compilations. The temperature dependence of line intensities, without the induced emission term, is expected to be of the form S(&‘) -
$
exp[ - E(J;.)/kT). R
Here S(J:‘,,) is the integrated intensity (in cm-‘-atm- ’ ) of the rotational line with the lower state identified by J;, and energy E(Jr,.); QR is the rotational partition function of an asymmetric rotor ; N/p is the number of Hz0 molecules per unit volume and unit pressure at temperature T. Within any narrow spectral region, several transitions with completely different lower-state energy levels contribute to the pure rotation spectrum and make it impossible to obtain a theoretical expression for the temperature dependence of a “mean” spectral absorption coefficient. However, a semi-empirical estimate may be made from the tables of Benedict and Kaplan if we define an average absorption coefficient per particle through the relation
P,Tz
[Sum of the intensities (in g- ‘-cm) of all the lines between 600 cm- ’ and 1000 cm- ‘1 4QOR,
where R, is the gas constant per unit mass. We may then plot the quantity log{ T3’2(P,T)j against l/T and obtain an effective mean energy level for the lower state; the factor T3j2 arises because QR y T312. The resulting plot is shown in Fig. 4, where the circles represent values of T312(P,T) derived from Benedict and Kaplan’s tabulations at 220”K, 260°K and
P. VARANASI, S. CHOU and S. S. PENNER
I540
10212, 2.0
30
4.0
50
f x IO+3pKj FIG. 4. Temperature
extrapolation
of mean absorption
coefficients.
for the 600-1000
cm
I region
300°K. A straight line is seen to join the three theoretical data points at low temperatures; the extrapolated curve yields estimates for (P,T) at temperatures between 400°K and 500°K. Comparison of the extrapolated theoretical estimates for the average absorption coefficient with the results of the present experimental studies shows again that the measured values of P,Tare markedly higher. However, the difference between the experimental and extrapolated theoretical results decreases as the temperature is increased. This observation is consistent with the idea@) that association of water vapor molecules due to hydrogen bonding increases the absorption coefficient in the 600-1000 cm- ’ region. As the temperature of water is raised at constant pressure, hydrogen bonds between associated water molecules are probably broken and may provide an explanation for decrease of the quantity
with temperature.
Assuming
A(is,T)
that
x the number
-
E exp $7 i
of hydrogen
bonds at a given temperature
1 ,
we have estimated the “energy E, _” of hydrogen bonding”. Using the data shown in Fig. 2 400°K and 450°K) and in Fig. 3 (pHzO = IOatm, THro = 460°K and 2 arm. THzo = (Pn,o = 500°K). respectively. we obtain 5 kcal/mole and 3 kcal/mole. respectively. These estimates are close to the value of 5 kcal/mole given by PAULING ‘s’ for water in the vapor phase. The numerical estimates for E,_, have been verified in independent experiments that are not described in this Note. The conclusions described in the present Note are not changed significantly when allowance is made for the far wings of strong, distant lines, in accord with the approximate procedure described in Ref. 6, which probably yielded an
Absorption coefficients for water vapor in the 600-1000 cm-’ region
1541
bound for the wing correction in view of much smaller estimates for this effect made earlier by ELSASSER.(” The salient assumptions made in the present Note, namely, negligibly small wing corrections and a theoretical dependence of is, on temperature of the type shown in Fig. 4, have been verified by careful numerical calculations performed recently by P. Varanasi. upper
REFERENCES I S. S. PENNERand D. WEBER,J. Chem. Phys. 19,807. 1361 (1951). 2. A. GUTTMAN and S. S. PENNER,.I. Chem. Phys. 36.98 (1962). 3. A. GUTTMAN, JQSRT 2, 1 (1962). 4. R. GOLDSTEIN. JQSRT4.343 (1963). 5. R. BECKER.Theory q/ Heaf (English translation by G. LEIBFRIED). pp. 358-363. Springer Verlag. New York, New York (1967). 6. S. S. PENNERand P. VARANASI, JQSRT 7,687 (1967). 7. W. S. BENEDICT and L. D. KAPLAN,unpublished calculations, which are reproduced, in part, on p. 184 of Armospheric Radiufion. I. Theoretical Basis by R. hi. GtmDY. Oxford University Press, London (1964). 8. L. PAULINE;,The Nuturr qf rhe C’hrmical Bond. Third ed.. p. 469. Cornell University Press. Ithaca (1960). 9. W. M. ELSASSER, Phys. Rev. 53,768 (1938); Asrrophys. J. 87,497 (1938).