Abstract

The spectral emissivity of the ν3 band of methane was measured at temperatures of 297, 673, and 923 K. Use was made of absorption cells of various lengths in order to obtain curves of growth. Application of the Goody statistical band model to small frequency intervals within the band allowed the spectral band parameters to be obtained at the above-mentioned temperatures. The spectral absorption coefficient was found by two independent methods: by multiplication of the spectral-band parameters and by direct observation of the transmittance in the linear region. The integrated band intensity was also derived as a function of temperature up to 923 K.

© 1969 Optical Society of America

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References

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  1. G. Herzberg, Molecular Spectra and Molecular Structure II (D. Van Nostrand Co., Inc., New York, 1945).
  2. D. R. J. Boyd, H. W. Thompson, and R. L. Williams, Proc. Roy. Soc. (London) A213, 42 (1952).
  3. E. K. Plyler, J. Res. Natl. Bur. Std. (U. S.) 64A, 201 (1960).
    [Crossref]
  4. R. S. McDowell, J. Mol. Spectry. 21, 280 (1966).
    [Crossref]
  5. G. N. Plass, J. Opt. Soc. Am. 48, 690 (1958).
    [Crossref]
  6. R. M. Goody, Atmospheric Radiation, Vol. I: Theoretical Basis (Oxford University Press, Oxford, 1964).
  7. U. P. Oppenheim and Y. Ben-Aryeh, J. Opt. Soc. Am. 53, 344 (1963).
    [Crossref]
  8. U. P. Oppenheim and Y. Ben-Aryeh, J. Quant. Spectry. Radiative Transfer 4, 559 (1964).
    [Crossref]
  9. A. Goldman and U. P. Oppenheim, J. Opt. Soc. Am. 55, 794 (1965).
    [Crossref]
  10. E. Finkman, U. P. Oppenheim, and A. Goldman, J. Opt. Soc. Am. 57, 1130 (1967).
    [Crossref]
  11. D. E. Burch and D. Williams, Appl. Opt. 1, 587 (1962).
    [Crossref]
  12. D. Vanderwerf, Appl. Opt. 4, 209 (1965).
    [Crossref]
  13. L. D. Gray and S. S. Penner, J. Quant. Spectry. Radiative Transfer 5, 611 (1965).
    [Crossref]
  14. J. C. Breeze, C. C. Ferriso, C. B. Ludwig, and W. Malkmus, J. Chem. Phys. 42, 402 (1965).
    [Crossref]
  15. W. Malkmus, J. Opt. Soc. Am. 57, 323 (1967).
    [Crossref]
  16. C. B. Ludwig, C. C. Ferriso, and L. Acton, J. Opt. Soc. Am. 56, 1685 (1966).
    [Crossref]
  17. C. B. Ludwig, C. C. Ferriso, and C. N. Abeyta, J. Quant. Spectry. Radiative Transfer 5, 281 (1965).
    [Crossref]
  18. A. Goldman and T. G. Kyle, Appl. Opt. 7, 1167 (1968).
    [Crossref] [PubMed]

1968 (1)

1967 (2)

1966 (2)

1965 (5)

L. D. Gray and S. S. Penner, J. Quant. Spectry. Radiative Transfer 5, 611 (1965).
[Crossref]

J. C. Breeze, C. C. Ferriso, C. B. Ludwig, and W. Malkmus, J. Chem. Phys. 42, 402 (1965).
[Crossref]

C. B. Ludwig, C. C. Ferriso, and C. N. Abeyta, J. Quant. Spectry. Radiative Transfer 5, 281 (1965).
[Crossref]

D. Vanderwerf, Appl. Opt. 4, 209 (1965).
[Crossref]

A. Goldman and U. P. Oppenheim, J. Opt. Soc. Am. 55, 794 (1965).
[Crossref]

1964 (1)

U. P. Oppenheim and Y. Ben-Aryeh, J. Quant. Spectry. Radiative Transfer 4, 559 (1964).
[Crossref]

1963 (1)

1962 (1)

1960 (1)

E. K. Plyler, J. Res. Natl. Bur. Std. (U. S.) 64A, 201 (1960).
[Crossref]

1958 (1)

1952 (1)

D. R. J. Boyd, H. W. Thompson, and R. L. Williams, Proc. Roy. Soc. (London) A213, 42 (1952).

Abeyta, C. N.

C. B. Ludwig, C. C. Ferriso, and C. N. Abeyta, J. Quant. Spectry. Radiative Transfer 5, 281 (1965).
[Crossref]

Acton, L.

Ben-Aryeh, Y.

U. P. Oppenheim and Y. Ben-Aryeh, J. Quant. Spectry. Radiative Transfer 4, 559 (1964).
[Crossref]

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

Boyd, D. R. J.

D. R. J. Boyd, H. W. Thompson, and R. L. Williams, Proc. Roy. Soc. (London) A213, 42 (1952).

Breeze, J. C.

J. C. Breeze, C. C. Ferriso, C. B. Ludwig, and W. Malkmus, J. Chem. Phys. 42, 402 (1965).
[Crossref]

Burch, D. E.

Ferriso, C. C.

C. B. Ludwig, C. C. Ferriso, and L. Acton, J. Opt. Soc. Am. 56, 1685 (1966).
[Crossref]

C. B. Ludwig, C. C. Ferriso, and C. N. Abeyta, J. Quant. Spectry. Radiative Transfer 5, 281 (1965).
[Crossref]

J. C. Breeze, C. C. Ferriso, C. B. Ludwig, and W. Malkmus, J. Chem. Phys. 42, 402 (1965).
[Crossref]

Finkman, E.

Goldman, A.

Goody, R. M.

R. M. Goody, Atmospheric Radiation, Vol. I: Theoretical Basis (Oxford University Press, Oxford, 1964).

Gray, L. D.

L. D. Gray and S. S. Penner, J. Quant. Spectry. Radiative Transfer 5, 611 (1965).
[Crossref]

Herzberg, G.

G. Herzberg, Molecular Spectra and Molecular Structure II (D. Van Nostrand Co., Inc., New York, 1945).

Kyle, T. G.

Ludwig, C. B.

C. B. Ludwig, C. C. Ferriso, and L. Acton, J. Opt. Soc. Am. 56, 1685 (1966).
[Crossref]

C. B. Ludwig, C. C. Ferriso, and C. N. Abeyta, J. Quant. Spectry. Radiative Transfer 5, 281 (1965).
[Crossref]

J. C. Breeze, C. C. Ferriso, C. B. Ludwig, and W. Malkmus, J. Chem. Phys. 42, 402 (1965).
[Crossref]

Malkmus, W.

W. Malkmus, J. Opt. Soc. Am. 57, 323 (1967).
[Crossref]

J. C. Breeze, C. C. Ferriso, C. B. Ludwig, and W. Malkmus, J. Chem. Phys. 42, 402 (1965).
[Crossref]

McDowell, R. S.

R. S. McDowell, J. Mol. Spectry. 21, 280 (1966).
[Crossref]

Oppenheim, U. P.

Penner, S. S.

L. D. Gray and S. S. Penner, J. Quant. Spectry. Radiative Transfer 5, 611 (1965).
[Crossref]

Plass, G. N.

Plyler, E. K.

E. K. Plyler, J. Res. Natl. Bur. Std. (U. S.) 64A, 201 (1960).
[Crossref]

Thompson, H. W.

D. R. J. Boyd, H. W. Thompson, and R. L. Williams, Proc. Roy. Soc. (London) A213, 42 (1952).

Vanderwerf, D.

Williams, D.

Williams, R. L.

D. R. J. Boyd, H. W. Thompson, and R. L. Williams, Proc. Roy. Soc. (London) A213, 42 (1952).

Appl. Opt. (3)

J. Chem. Phys. (1)

J. C. Breeze, C. C. Ferriso, C. B. Ludwig, and W. Malkmus, J. Chem. Phys. 42, 402 (1965).
[Crossref]

J. Mol. Spectry. (1)

R. S. McDowell, J. Mol. Spectry. 21, 280 (1966).
[Crossref]

J. Opt. Soc. Am. (6)

J. Quant. Spectry. Radiative Transfer (3)

C. B. Ludwig, C. C. Ferriso, and C. N. Abeyta, J. Quant. Spectry. Radiative Transfer 5, 281 (1965).
[Crossref]

U. P. Oppenheim and Y. Ben-Aryeh, J. Quant. Spectry. Radiative Transfer 4, 559 (1964).
[Crossref]

L. D. Gray and S. S. Penner, J. Quant. Spectry. Radiative Transfer 5, 611 (1965).
[Crossref]

J. Res. Natl. Bur. Std. (U. S.) (1)

E. K. Plyler, J. Res. Natl. Bur. Std. (U. S.) 64A, 201 (1960).
[Crossref]

Proc. Roy. Soc. (London) (1)

D. R. J. Boyd, H. W. Thompson, and R. L. Williams, Proc. Roy. Soc. (London) A213, 42 (1952).

Other (2)

G. Herzberg, Molecular Spectra and Molecular Structure II (D. Van Nostrand Co., Inc., New York, 1945).

R. M. Goody, Atmospheric Radiation, Vol. I: Theoretical Basis (Oxford University Press, Oxford, 1964).

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Figures (12)

Fig. 1
Fig. 1

Curves of growth at various frequencies observed for the 3.3-μ band of CH4 at 24°C, together with their asymptotes for the linear and square-root regions. The ordinate is in atm−1 at 24°C.

Fig. 2
Fig. 2

Curves of growth at various frequencies observed for the 3.3-μ band of CH4 at 400°C, together with their asymptotes for the linear and square-root regions. The ordinate is in atm−1 at 400°C.

Fig. 3
Fig. 3

Curves of growth at various frequencies observed for the 3.3-μ band of CH4 at 650°C, together with their asymptotes for the linear and square-root regions. The ordinate is in atm−1 at 650°C.

Fig. 4
Fig. 4

Frequency dependence of the parameter αν = x/L (cm−1) for the 3.3-μ band of CH4 at 297, 673, and 923 K.

Fig. 5
Fig. 5

Frequency dependence of the parameter βν = 2πγ0/d (atm−1 at indicated temperatures) for the 3.3-μ band of CH4 at 297, 673, and 923 K.

Fig. 6
Fig. 6

Frequency dependence of the absorption coefficient kν for the 3.3-μ band of CH4 at several temperatures. Values of kν are not reduced to STP.

Fig. 7
Fig. 7

Comparison of Burch’s results with the present curves of growth at the peak of the P branch (top curve: ν = 2959 cm−1) and the R branch (bottom curve: ν = 3092 cm−1). Circles indicate Burch’s results, triangles indicate present results.

Fig. 8
Fig. 8

The integrated absorption ∫Aν = ∫(1 − Tν) of the 3.3-μ band of CH4 at 400°C for various pressures, as obtained by Vanderwerf12 and by the present study. Triangles: Vanderwerf’s results for L = 30.6 cm. Circles: present results for L = 30.0 cm.

Fig. 9
Fig. 9

Comparison between Gray’s formula for kν (full line) and present experimental results at 297 and 923 K (kν is not normalized to STP.). Triangles: present results at 297 K. Circles: present results at 923 K.

Fig. 10
Fig. 10

Comparison of calculated values of (S0/d)ν with the present measured values for T = 297 K. Circles: present results. Full line: calculated results for Δν = 40 cm−1. Dotted line: calculated results for Δν = 30 cm−1.

Fig. 11
Fig. 11

Comparison of calculated values of (S0/d)ν with the present measured values for T = 673 K. Circles connected by smooth curve indicate present results. Full line: calculated results for Δν = 40 cm−1.

Fig. 12
Fig. 12

Comparison of calculated values of (S0/d)ν with the present measured values for T = 923 K. Circles connected by smooth curve indicate present results. Full line: calculated results for Δν = 40 cm−1.

Tables (1)

Tables Icon

Table I Normalized band intensity of ν3 fundamental of CH4 at various temperatures.

Equations (26)

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T ν = exp [ - α ν β ν L / ( 1 + 2 α ν L ) 1 2 ] .
α ν = x ν / L = S ν 0 / 2 π γ ν 0 , β ν = 2 π γ ν 0 p / d = β ν 0 p .
L e = ( p a / p e ) L             and             p e = p t + ( B - 1 ) p a ,
B = γ a 0 / γ m 0 ,
γ m = γ m 0 p e = γ a 0 p e / B .
α ν , m = B α ν , a
β ν , m 0 = β ν , a 0 / B ,
T ν = exp [ - α ν , m β ν , m 0 p e L e ( 1 + 2 α ν , m L e ) 1 2 ] .
lim p L 0 T ν = ( exp - α ν β ν 0 p L ) = exp [ - ( S ν 0 / d ν ) p L ] .
T ν = exp [ - k ν p L ] ,
k ν = α ν β ν 0 .
L e = L / B - ( ln T ) / p e = B - 1 [ - ( ln T ) / p ] .
S 0 / d = ( J 2 3 2 S b / π 1 2 B ) exp ( - J 2 ) ,
S b = band k ν d ν .
( S 0 / d ) ν = i S i 0 / Δ ν .
T ν = exp { - ( β ν 0 p / 4 ) [ ( 1 + 8 α ν L ) 1 2 - 1 ] } ,
y j = - [ ln T ν ( L j ) / p ] av ,
f ( α ν , β ν 0 , L j ) = α ν β ν 0 L j / ( 1 + 2 α ν L j ) 1 2 .
f 1 = f ( α ν , β ν 0 , L ) / α ν , f 2 = f ( α ν , β ν 0 , L ) / β ν 0 ,
Z i j = f i ( L j , α ν , β ν 0 ) ,
i = 1 , 2 j = 1 , 2 n .
Δ y j y j = y j - f ( α ν , β ν 0 , L j ) y j = Z 1 j y j Δ α + Z 2 j y j Δ β .
F ( Δ α , Δ β ) = j ( Δ y j y j - Z 1 j y j Δ α - Z 2 j y j Δ β ) 2 = min .
F / ( Δ α ) = F / ( Δ β ) = 0.
α ν , i + 1 = α ν , i + Δ α β ν , i + 1 0 = β ν , i 0 + Δ β
Δ α / α + Δ β / β < 0.0002.