JOURNAL OF THE, OPTtCAT, SOCIETY OF AMERICAV

Emissivity of Carbon Dioxide at 4.3 t

WILLIAM 0. DAVIES

LIT Research Institute, Chicago, Illinois 60616

(Received 15 August 1962)

The emissivity of carbon dioxide has been measured for temperatures from 1500° to 30000 K over thewavelength range from 4.40 to 5.30 p. Optical densities varied from 0.04 to 4.00 atm -cm; all measurementswere made at a total gas pressure of 1 atm. The test gas was heated to the desired temperature by shockcompression. The temperature and pressure of the test gas were determined by measuring initial concentra-tions and shock wave velocities. The emissivity of the hot gas was obtained in two ways: (1) the spectralradiance from the C02 was compared to that from a globar, which was calibrated with a blackbody sourceand (2) the transmission through the hot gas was measured, and emissivity obtained from Kirchhoff's law.The emissivity obtained with these two methods is in agreement within experimental error. The observedemissivities are reasonably well represented by values calculated with the weak line approximation, exceptthat the measured values are consistently higher than the calculated emissivities at the longer wavelengths.

INTRODUCTION

THE 4.3 -g carbon dioxide fundamental vibrationTband is an old and often studied subject ofmolecular spectroscopy. A theoretical determination ofenergy levels and line strengths'-3 successfully pre-dicted the observed frequencies and rotational lineintensities. 4-6 Several measurements7 -9 of the integratedabsorption of this band made at room temperature usingthe Wilson-Wells method1 0 are in agreement that thisvalue is 2700 atm-1 cm-2 . These results are also inagreement with the earlier dispersion studies which arereviewed in Ref. 4. The dependence of band absorptionon pressure and optical density at low temperatures isknown from empirical relations.1 1

At elevated temperatures there is a general shift ofabsorption and emission to longer wavelengths becauseof the broadening of the rotational structure and theanharmonicity of the vibrational energy levels.'2-'5 Be-cause of these factors, and the fact that a number ofadditional bands are excited,"6 the band structure be-comes very complex at high temperatures. A number oftransmittance measurements have been made at hightemperatures using jet burners,"," furnaces,1 9 20 and

1 D. M. Dennison, Rev. Mod. Phys. 3, 280 (1931).2 D. M. Dennison, Rev. Mod. Phys. 12, 175 (1940).3A. H. Nielsen, Phys. Rev. 53, 983 (1938).P. E. Martin and E. F. Barker, Phys. Rev. 41, 291 (1932).H. H. Nielsen, Phys. Rev. 60, 794 (1941).

6A. H. Nielsen and Y. T. Rao, Phys. Rev. 68, 173 (1945).'A. M.Thorndyke, J. Chem. Phys. 15, 868 (1945).O D. F. Eggers, Jr., and B. L. Crawford, Jr., J. Chem. Phys. 19,

1554 (1951).O D. Weber, R. J. Holm, and S. S. Penner, J. Chem. Phys. 20,

1820 (1952).10 E. B. Wilson, Jr., and A. J. Wells, J. Chem. Phys. 14, 578

(1946).1 J. N. Howard, D. E. Burch, and D. Williams, J. Opt. Soc. Am.

46, 237 (1956).12 F. Pashen, Wied. Ann. 52, 209 (1894).1 3 H. Schmidt, Ann. Phys. 42, 415 (1913).14 E. K. Plyler, J. Res. Natl. Bur. Std. 40, 113 (1948).B1 E. F. Daly and G. B. B. M. Sutherland, Symp. Combust.

3rd Madison Wis. 1948.16 J. H. Taylor, W. S. Benedict, and J. Strong, J. Chem. Phys.

20, 1884 (1952)." D. K. Edwards, J. Opt. Soc. Am. 50, 617 (1960).i8 C. C. Ferriso, J. Chem. Phys. 37, 1955 (1962).

shock tubes2 l to elevate the gas to the desired tempera-ture. The empirical description of the band absorptionas a function of optical density and pressure has beenextended to temperatures of 1200 0K,17 and spectraltransmittance has been measured with a furnace forvarious optical densities and pressures at temperaturesup to 12700 K.'9 Transmittance measurements, obtainedusing a supersonic burner,1 8 yielded spectral absorptioncoefficients that are within 10% of those obtained in ashock tube study21 at temperatures of the order of20000 K, and it has been shown' 0 that the apparentinconsistency of these results with the measurementsmade in a furnace1 are due to the inapplicability of theBeer-Lambert law. The spectral absorption coefficientand emissivity for this band have been calculated inboth the strong and weak line approximation for tem-peratures up to 30000K.2 '

In this paper the measurements of carbon dioxidespectral emissivity in the 4.3-A region are presented fortemperatures from 1500° to 30000 K. The high tempera-tures were obtained by passing a plane shock wavethrough the test gas, and the radiation from the testgas monitored spectrophotometrically, utilizing a rapidresponse infrared detector. The temperature and pres-sure of the test gas were determined from initialpressures and measured shock wave velocities. Theemissivities were obtained primarily from a comparisonof spectral radiance of the hot gas with blackbodyradiance, through the intermediary of a calibratedglobar lamp. As a check on this system some additionaldata were obtained from measurements of infraredtransmittance through the hot gas and application ofKirchhoff's law. The emissivity was determined for anumber of optical densities at temperatures of 15000,20000, 2500°, and 30000 K. The carbon dioxide opticaldensity was varied while maintaining a constant totalgas pressure of 1 atm by altering the carbon dioxide

19 R. H. Tourin, J. Opt. Soc. Am. 51, 175 (1961).20

U. P. Oppenheim and Y. Ben-Aryeh, J. Opt. Soc. Am. 53, 344(1963).

21 M. Steinberg and W. 0. Davies, J. Chem. Phys. 34, 1373(1961).

2X W. Malkmus, J. Opt. Soc. Am. 53, 951 (1963).

467

V(>ITMIJ-F 54, NUTMBE4R 4 APRIL 1964

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concentration in argon. The results are compared to thecalculated emissivities22 in both strong and weak lineapproximations. The data are reasonably well repre-sented by the weak line approximation, except that themeasured values are consistently higher than the calcu-lated emissivities at longer wavelengths. This appearsto be consistent with the approximations made in theemissivity calculations, e.g., a determination of vibra-tional energy level population with a harmonic oscillatorapproximation. The observation of spectral radiance asa function of pressure also indicates that the weak lineapproximation should apply.

EXPERIMENTAL PROCEDURE

The gas mixtures were heated by shock compressionin a 3-in. i.d. uniform-bore shock tube. The shock tubeand associated instruments were previously described ina report of measurements of absorption of carbondioxide21 and carbon monoxide,23 and the oxidation rateof carbon monoxide.24 Helium was used as the drivergas, at initial pressures up to 100 psig. Carbon dioxide-argon mixtures were prepared in Pyrex flasks, andallowed to stand 24 h before use. The carbon dioxideused was Matheson bone dry grade (99.8% minimum

0' \X

: 40 B.0+6 .040 4050505D 40*040*> 8 9 c 1 2I1~LXT 1 ). *NEEO~ S

4.40 ... 40 7 4

FIG. 2. Carbon dioxide emissivity vs wavelength. Temperature= 1500'K; total pressure= 1 atm; o, emission; 0, absorption;Curve 1, strong line; Curve 2, weak line.

23 WV. 0. Davies, J. Chem. Phys. 36, 292 (1962).24 M. Steinberg and W. 0. Davies, ARL Technical Report

60-312, ARDC, Wright-Patterson AFB, Ohio, December 1960.

purity); the argon used was 99.98(%80 minimum purity.Shock wave velocities were determined from measure-ments of shock wave transit time between two thinfilm platinum gauges. When the shock wave passes, theresistance of each film increases. Resulting changes ofpotential drop, of a few millivolts, are amplified andused to start and stop a microsecond time-intervalmeter. Shock wave velocities over the 375-mm path canbe measured with a 4% accuracy, corresponding toabout a 1%0 uncertainty in the temperature behind theshock wave.

The optical system, shown in Fig. 1, permits a directcomparison of the spectral radiance from a knownquantity of hot gas with that from a globar lamp. Theglobar is then calibrated by comparison with a black-body source. The radiation from the shock tube iscollimated by slits S1, condensed by spherical mirrorM9, and focused on the entrance slit of a Perkin-Elmer Model 98 monochromator which has a CaF2prism. The radiation is then focused by mirror M13 onthe sensitive surface of an InSb photovoltaic detector,which has a time constant of less than 0.5-,usec. Theoutput of the detector is amplified, displayed on anoscilloscope, and photographed. Radiation from theglobar (G2) collimated by slits S2, is directed by theplane mirror M8 to the detector through the sameoptical system as is radiation from the test gas. Whenthe calibration signal is being observed, an electricallydriven chopper is placed in front of the monochromatorentrance slit, and the ac calibration signal from thelamp is displayed on the oscilloscope and photographed.

The emissivity of the hot gas is given by

e= (AQ/V2 0 )EB(XT)/eB(XT,)

where (A Q) is the product of area and solid angle of theglobar lamp, (AQ,) is the product of volume and solidangle of the hot gas, E is the ratio of hot gas to globarsignal obtained from the oscilloscope traces, e, is theglobar emissivity, and B (XTo) and B (XT) are theblackbody radiation functions at the temperature ofglobar and the hot gas. The area or volume and thesolid angle for each emitter is determined by thegeometry of the system. The brightness temperature ofthe globar is measured with a micro-optical pyrometer,and the true temperature is obtained from the expressionT= [T1 -±+ (X lnE,)/C2 }-, where C2 is the second radia-tion constant and TB is the brightness temperature.

The globar emissivity was obtained by comparing thespectral radiance of the globar with that of a blackbodysource. The emissivity of a globar, or a of silicon carbiderod, has been measured by a number of investiga-tors.25 -2 8 Although the results are similar, there aredeviations from one sample to another, and the emis-

25 W. Brugel, Z. Phys. 127, 400 (1950).26J. E. Stewart and J. G. Richmond, J. Res. Natl. Bur. Std.

59, 405 (1957).27 S. Silverman. J. Opt. Soc. Am. 38, 989 (1948).2 8

J. C. Morris, J. Opt. Soc. Am. 51, 798 (1961).

Vol. 54

EMISSIVITY OF CARBON DIOXIDE AT 4.34u

sivity varies with the operating time of the lamp. Theemissivity of the globar rod used for this calibration wasmeasured a number of time during the course of theexperiment using the optical system described aboveand the relatively large monochromator slitwidths usedfor the hot gas studies. These measurements are in-tended to provide a convenient comparison of the hotgas and blackbody radiance for this experiment, but thedeviation from other measurements is not emphasized.The globar emissivity at a given wavelength varied byless than 4% for a total of ten measurements and theemissivity showed essentially no wavelength depend-ence. No dependence of emissivity on operating timewas observed. Measurements made at globar tempera-tures of 11000 to 1300'K yielded the same emissivity.Of the published values of globar emissivity thesemeasurements are in best agreement with those ofBrugel,25 and deviate from his by not more than 2%over the wavelength range considered.

The use of the globar as a calibration source has theadvantage that calibration records can be obtained

.1 - W 'OASC

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9 - 9-

L.3

. 4 IWAVLEGT .1 - .. , - .1 ..)

939 460 9.39 .. 90 o -99 -o 0 999 99 3 .- 0-- -VLE.- ~1/. WAVLE-T j,)

FIG. 3. Carbon dioxide emissivity vs wavelength. Temperature=2000'K; total pressure =1 atm; O, emission; *, absorption;Curve 1, strong line; Curve 2, weak line.

regularly during testing, so that effects of variations inthe optics or the atmosphere are minimized. A directcalibration with the blackbody source requires dis-mantling either the shock tube or the optical system.The uncertainty of globar emissivity is minimized by acalibration of a particular rod with the optical systemused for the hot gas studies, and it is believed that theregular check on the calibration contributes more tothe accuracy than is lost by the indirect calibrationand uncertainty of the globar emissivity.

Some additional data were obtained from transmit-tance measurements and application of Kirchhoff's law.The transmittance was determined by observing theattenuation of an ac infrared beam resulting fromabsorption by the hot gas. The radiation from a globar(GI in Fig. 1) is focused by mirrors MI to M3 on the slitof a high speed chopper, which modulates the beam at50 kc/sec. The ac infrared beam is then directed throughthe shock tube by mirrors M4 to M7. to the same optical

:V 6 - >

ToI .0 WOG .0 4t 9 0 , 2

.^t~T 1, ,

FIG. 4. Carbon dioxide emissivity vs wavelength. Temperature=2500'K; total pressure= 1 atm; o, emission; O, absorption;Curve 1, strong line; Curve 2, weak line.

system used for the spectral radiance measurements. Inthis case the oscilloscope trace contains two signals. Oneprovides a measure of transmittance through the coldgas and the other indicates transmitatnce through thehot shocked gas.23 As these measurements were madeoutside the range of atmospheric absorption, the trans-mittance is given by the relative heights of these twoenvelopes. While the measurement of spectral radianceand transmittance should yield the same emissivity,each method offers an advantage at some combinationof pressure, temperature, and wavelength. The calibra-tion of the transmittance record is self-contained, andrequires no calculation of the radiance and solid angle ofthe emitter. The transmittance method is more reliablewhen gas properties are such that transmittance isneither close to zero nor unity. The advantage of theradiance method is that once the optical system iscalibrated, equivalent accuracy can be obtained over awide range of test gas properties by altering the gain ofthe instrument.

RESULTS AND DISCUSSION

The spectral emissivity of carbon dioxide is shown inFigs. 2 to 5 for various optical densities at temperatures

- -- - - - - - -- --- - - - - - - - - - - - - -

FIG. 5. Carbon dioxide emissivity vs wavelength. Temperature=3000'K; total pressure= 1 atm; o, emission; O. absorption;Curve 1, strong line; Curve 2, weak line.

469April 1964

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TOTAL PRESSURE (ATM)

11G. 6. Relative emittance of carbon dioxide vs totalpressure. T=2000°K; u=0.93 atm/cm; X=4.40, 4.60, and4k.80.J

of 1500°, 20000, 25000, and 3000°K. A total pressure of1 atm was maintained by varying the carbon dioxideconcentration in argon. The radiation in this wavelengthregion is primarily from the vibrational transition(n 1,112

1 ,n3+1 -- nn 2l,1,n3), i.e., the fundamental vibra-tion band and transitions from excited states for whichAn3= 1 while the other vibrational quantum numbersand the angular momentum I do not change. Thesemeasurements were made for wavelengths from 4.40 ,uto wavelengths where emissivity becomes very small,which for these combinations of temperature, pressure,and optical density is between 5.00 and 5.30 ,u. Mostof the data were obtained with a monochromator slit-width of 0.30 mm, which corresponds to pass bands of0.046 ,. For lower temperatures and longer wavelengthssome observations were made with a band pass of 0.080,u. The emissivity was found to be independent of thepass band from within 0.020 to 0.080 jL, within the limitsof experimental accuracy.

To determine the effect of gas impurities on theseresults, the spectral radiance of water-argon and carbonmonoxide-argon mixtures was observed at these tem-peratures, using the same instrument sensitivities as forthe carbon dioxide measurements. For 2% water inargon the spectral radiance is negligible compared tothat of carbon dioxide. As a small amount of water inthe mixture does not affect the emissivity measure-ments, but does increase the vibrational relaxation rate29

no effort was made to remove it from the test gas. Theemissivity measurements of carbon monoxide showedthat the carbon dioxide emissivity results would bealtered by less than 10% even if the carbon monoxideand carbon dioxide concentrations are equal. Thespectral radiance and transmittance measurements weremade after vibrational relaxation but before appreciable

29 W. C. Griffith, Phys. Rev. 102, 1209 (1956).

dissociation so the results are not affected by dis-sociation products.

The observed emissivities are compared to the cal-culated values given by Malkmus, 22 which provide car-bon dioxide emissivity as a function of pressure andoptical density for temperatures from 3000 to 3000'K.The plots in Figs. 2-5 are representative of the relationbetween the calculated and observed values at alloptical densities.A0 At 20000 and 2500'K the weak linetheory generally overestimates the emissivity measuredat the shorter wavelengths and at longer wavelengthsthe measured emissivity is greater than the calculatedemissivity. At the longest optical paths, emissivitiesfor the shorter wavelengths could perhaps fit the strong-line approximation as well, since for both methods theemissivity approaches unity; for shorter path lengthsthe superiority of the weak line approximation is quiteclear. The same comments apply to a comparison ofcalculated and measured emissivities at a temperatureof 3000'K, except that the weak line theory predicts alower intensity at all the wavelengths examined. At1500'K the weak line approximation is also in fairagreement with the measured emissivities. However, thedisagreement with the strong line approximation is notas striking, as the emissivities given by these twoapproximations are closer together at this temperature.

The experimental errors are expected to introduce anuncertainty of approximately 12% in the values ofemissivity, so that the magnitude of disagreement atshorter wavelengths is probably not significant. How-even, the persistent disagreement at longer wave-length bears further investigation. Possible sources oferror in the measured emissivities include globaremissivity, temperature, area and solid angle, and thegas volume and solid angle. The only one of these thatvaries with wavelength and could conceivably reducethe disagreement at longer wavelengths is globaremissivity. However, the globar emissivity varies byless than 2% in the wavelength interval from 4.40 to5.00 g at the temperature used in this study. Perhapsthe agreement is at least as good as could be expected,considering the difficulty of the measurement and theapproximations made in computing the emissivities.

In the emissivity calculations, Malkmus used aharmonic oscillator approximation to calculate vibra-tional line strengths and the population of uppervibrational levels. In addition to grouping bands havingnearly the same energies, he further simplified theproblem by neglecting the effect of vibration on therotational constant, and the contribution of the 4.8 and5.2 , bands. It is clear that some of these approximationswould reduce the calculated emissivity at increasingwavelengths, but a quantitative assessment wouldprobably require further computational study.

30 W. 0. Davies, Armour Research Foundation Report 1200-2June 1962.

470 Vol. 54

EMISSIVITY OF CARBON DIOXIDE AT 4.3k

The regions of validity of the strong and weak lineapproximations for various band models have beengiven by Plass3 ' in terms of the parameters N = 27rad andx= Su/27ra, where a is the rotational line half-width andd is the distance between rotational lines. The weakline approximation is valid with an error of less than10% for all band models if j>4. For the temperatures,pressures, and wavelengths used in these tests, Malk-mus' calculations yield values of N the order of 10 to100, which indicates the weak line approximationshould be valid for all optical densities considered. Theobservation of emission intensity over a range of totalpressures strengthens the selection of the weak lineapproximation. In the strong line approximation,emission is proportional to exp(-Pi), where P is thetotal gas pressure while in the weak line approximationthe emission is insensitive to pressure variations.

31 G. N. Plass, J. Opt. Soc. Am. 50, 868 (1960).

Tourin1 has found, at a temperature of 12700 K, anoptical density of 0.84 atm cm and at total pressuresfrom 0.06 to 0.26 atm that emissivity does depend onpressure, but the effect virtually disappears at pres-sures above 0.26 atm. The relative emission intensity ofcarbon dioxide at a temperature of 20000K has beenobserved (Fig. 6) for an optical density of 0.93 atm * cm,and total pressures of 0.10 to 2 atm for several wave-lengths. These results indicate that although the pres-sure dependence is significant for total pressures some-what less than 0.50 atm, above this pressure the emissionof carbon dioxide is independent of pressure at 20000 K.

ACKNOWLEDGMENT

The completely thorough and reliable assistanceof Mr. David A. Gast in the operation of the shocktube and reduction of the data is gratefully acknowl-edged.

April 1964 471