view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Thermodynamics of the Gray Atmosphere. Wildt, Rupert Abstract The classical problem in radiative transfer is to find the source function sustaining strict radiative equilibrium in a gray atmosphere. That restriction, owing to the linearity of the monochromatic transfer equation, has made it possible to detach study of the conservation of radiant energy from inquiry into its spectral composition. The latter commences with an appeal to Planck's generalization, for nonequilibrium radiation, of Wien's displacement law. For every pencil of radiation inside a gray atmosphere in strict radiative equilibrium, energy spectra characteristic of different effective temperatures (net fluxes) are linked by a certain similarity transformation, provided that the source function, which need not be Plauckian, undergoes the identical transformation; and vice versa. Analogous displacement laws hold for the concomitant changes in spectral distribution of radiant entropy and of the entropy source function. The physical correlate these similarity laws have in common are quasistatical processes that convey, by a finite change of the net flux, the radiation field of the gray atmosphere, i.e., a nonequilibrium system, from one steady state to another. Because they satisfy all appropriate criteria, it is well within the bounds of accepted usage to call them reversible adiabatic processes, a term reserved in classical thermodynamics for passage through a sequency of equilibrium states. The complete distribution, throughout a gray atmosphere, of the spectrum of the source function accrues from a tentative extremum principle replacing arguments from thermostatics. Minimization of the global entropy deficit of the source function (a quantity identically nought in LTE), under the constraints that strict radiative equilibrium is preserved at all levels and that the photon flux escaping at the surface remains invariant, yields the Kothari-Singh function. It differs from the Plauck function by an additive parameter related to the nonvanishing free enthalpy of nonequilibrium radiation. Since the new parameter varies proportional to the second exponential integral of the optical depth, LTE is reached asymptotically. This event dispos&s of a conjecture (Wildt, R., Astrophys. J. 123,115, 1956) which had left the march of the parameter undetermined. Publication: The Astronomical Journal Pub Date: September 1963 DOI: 10.1086/109071 Bibcode: 1963AJ.....68Q.547W full text sources ADS |