Abstract

A study was made of the total absorption of five water vapor bands between 1μ and 7μ, using a multiple-reflection absorption cell in which optical path length, water vapor density, and total pressure could be varied independently. Absorption was determined as a function of these parameters. For the range of concentrations studied it was found that the fractional absorption of an entire band can be represented by an error-function formula

A=erf(t)=2/π120t-x2dx,

where t=12β(πw)12(PT+PP/760)14. Here w is the water vapor concentration, PT the total pressure, and PP the partial pressure of the water vapor. The quantity t in this formula is very nearly proportional to the fourth root of the pressure. Values of the “generalized absorption coefficient” β are determined for the five bands.

© 1952 Optical Society of America

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References

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  1. F. Ladenberg and F. Reiche, Ann. Physik 42, 181 (1911).
  2. Matossi, Mayer, and Rauscher, private communication; see also Naturwiss. 33, 219 (1946).
  3. F. Matossi and E. Rauscher, Z. Phys. 125, 418 (1949).
    [Crossref]
  4. W. Elsasser, “Heat Transfer by Infrared Radiation in the Atmosphere,” Harvard Meteorological Study No. 6 (1942).
  5. M. Summerfield and J. Strong, Phys. Rev. 60, 162 (1941).
  6. T. G. Cowling, Rept. Prog. Phys. 9, 29 (1942).
    [Crossref]
  7. J. U. White, J. Opt. Soc. Am. 32, 285 (1942).
    [Crossref]

1949 (1)

F. Matossi and E. Rauscher, Z. Phys. 125, 418 (1949).
[Crossref]

1942 (3)

W. Elsasser, “Heat Transfer by Infrared Radiation in the Atmosphere,” Harvard Meteorological Study No. 6 (1942).

T. G. Cowling, Rept. Prog. Phys. 9, 29 (1942).
[Crossref]

J. U. White, J. Opt. Soc. Am. 32, 285 (1942).
[Crossref]

1941 (1)

M. Summerfield and J. Strong, Phys. Rev. 60, 162 (1941).

1911 (1)

F. Ladenberg and F. Reiche, Ann. Physik 42, 181 (1911).

Cowling, T. G.

T. G. Cowling, Rept. Prog. Phys. 9, 29 (1942).
[Crossref]

Elsasser, W.

W. Elsasser, “Heat Transfer by Infrared Radiation in the Atmosphere,” Harvard Meteorological Study No. 6 (1942).

Ladenberg, F.

F. Ladenberg and F. Reiche, Ann. Physik 42, 181 (1911).

Matossi,

Matossi, Mayer, and Rauscher, private communication; see also Naturwiss. 33, 219 (1946).

Matossi, F.

F. Matossi and E. Rauscher, Z. Phys. 125, 418 (1949).
[Crossref]

Mayer,

Matossi, Mayer, and Rauscher, private communication; see also Naturwiss. 33, 219 (1946).

Rauscher,

Matossi, Mayer, and Rauscher, private communication; see also Naturwiss. 33, 219 (1946).

Rauscher, E.

F. Matossi and E. Rauscher, Z. Phys. 125, 418 (1949).
[Crossref]

Reiche, F.

F. Ladenberg and F. Reiche, Ann. Physik 42, 181 (1911).

Strong, J.

M. Summerfield and J. Strong, Phys. Rev. 60, 162 (1941).

Summerfield, M.

M. Summerfield and J. Strong, Phys. Rev. 60, 162 (1941).

White, J. U.

Ann. Physik (1)

F. Ladenberg and F. Reiche, Ann. Physik 42, 181 (1911).

Harvard Meteorological Study No. 6 (1)

W. Elsasser, “Heat Transfer by Infrared Radiation in the Atmosphere,” Harvard Meteorological Study No. 6 (1942).

J. Opt. Soc. Am. (1)

Phys. Rev. (1)

M. Summerfield and J. Strong, Phys. Rev. 60, 162 (1941).

Rept. Prog. Phys. (1)

T. G. Cowling, Rept. Prog. Phys. 9, 29 (1942).
[Crossref]

Z. Phys. (1)

F. Matossi and E. Rauscher, Z. Phys. 125, 418 (1949).
[Crossref]

Other (1)

Matossi, Mayer, and Rauscher, private communication; see also Naturwiss. 33, 219 (1946).

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of apparatus. A, Nernst filament and chopper assembly; B, absorption cell; C, spectrometer; D, optical path length control; E, sample port.

Fig. 2
Fig. 2

A typical set of traces, at constant water vapor density, of the 1.87μ water vapor band. Water vapor density: 22.7 g/m3. Optical path length: I, 8 meters; II, 16 meters; III, 32 meters; IV, 48 meters. Total pressure: A, 27.5 mm Hg; B, 50 mm Hg; C, 100 mm Hg; D, 200 mm Hg; E, 400 mm Hg; F, 740 mm Hg.

Fig. 3
Fig. 3

Plots of t w - 1 2 against (PT+PP)/760 for five water vapor bands: A, 6.27μ; B, 2.70μ; C, 1.87μ; D, 1.35μ; E, 3.17μ.

Fig. 4
Fig. 4

The application of Eq. (3) to the observed data of the 1.87μ water vapor band.

Tables (2)

Tables Icon

Table I Effective slit width of the spectrometer in the present study.

Tables Icon

Table II Values of the generalized absorption coefficient β and the effective width Δν for the water vapor bands studied.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

A = e r f ( t ) = 2 / π 1 2 0 t - x 2 d x ,
a = 1 2 δ ω 0 - δ ω 0 + δ ( 1 - - k z ) d ω ,
A = e r f ( t ) = 2 / π 1 2 0 t - x 2 d x ,
A = e r f ( t )             where             t = 1 2 β ( π w ) 1 2 ( P T + P P / 760 ) 1 4 .