Planck function

Consider continuous radiation with specific intensity I incident normally on a uniform slab with a source function 5 = Bv(Tex) unit volume per unit solid angle to the volume absorption coefficient Kp and is equal to the Planck function Bv of an excitation temperature Tcx obtained by force-fitting the ratio of upper to lower state atomic level populations to the Boltzmann formula, Eq. (3.4). For the interstellar medium at optical and UV wavelengths, effectively S = 0. 

A form of the curve of growth more relevant to stellar (as opposed to interstellar) absorption lines is derived from work by E. A. Milne, A. S. Eddington, M. Min-naert, D. H. Menzel and A. Unsold. In the Milne-Eddington model of a stellar photosphere, the continuum source function (equated to the Planck function in the LTE approximation) increases linearly with continuum optical depth rA and there is a selective absorption i]K, in the line, where rj(Av), the ratio of selective to continuous absorption, is a constant independent of depth given by... 

The function G 4- T occurs so often in thermodynamics that we call it the Planck function. 

The letter F previously has been associated with the Gibbs function, particularly in the United States. Some older tabulations of chemical thermodynamic data use F for the function of Equation (7.17). The term free energy is most commonly assigned to G, but we have adopted the name Gibbs function to be consistent with Helmholtz function for A and Planck function for Y. 

Thus, the Planck function is a temperamre-normalized Gibbs function. 

PROPERTIES OF THE GIBBS, HELMHOLTZ, AND PLANCK FUNCTIONS For y as a function of the natural variables T and P, the results are... 

In the preceding sections, we estabhshed the properties of the Gibbs, Helmholtz, and Planck functions as criteria for equihbrium and spontaneity of transformations. Thus, from the sign of AG, AA, or AT, it is possible to predict whether a given chemical transformation can proceed spontaneously under the respective appropriate conditions. 

TABLE 7.1. Standard States for Gibbs Function and Planck Function... 

Thus far we have observed that the Gibbs and Planck functions provide the criteria of spontaneity and equilibrium in isothermal changes of state at constant pressure. If we extend our analysis to systems in which other constraints are placed on the system, and therefore work other than mechanical work can be performed, we find that the Gibbs and Helmholtz functions also supply a means for calculating the maximum magnitude of work obtainable from an isothermal change. 

APPLICATION OF THE GIBBS FUNCTION AND THE PLANCK FUNCTION TO SOME PHASE CHANGES... 

Compute the change in the Gibbs function and the change in the Planck function for this allotropic transition at 25°C. 

Equilibrium Constant and Change in Gibbs Functions and Planck Functions for Reactions of Real Gases... 

We will adopt this statement as the working form of the third law of thermodynamics. This statement is the most convenient formulation for making calculations of changes in the Gibbs function or the Planck function. Nevertheless, more elegant formulations have been suggested based on statistical thermodynamic theory [5]. 

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