### 8.1.3. Quantities of Interest

The spectral radiative heat flux, , passing through a surface at some location r with a unit vector normal n is:

| (8–13)

Integrating the equation of transfer over solid angles, the divergence of the spectral radiative heat flux is given by:

| (8–14)

where G v is the spectral incident radiation, given by:

| (8–15)

The total radiative flux is obtained by integrating Equation 8–14 over the spectrum:

| (8–16)

In the case of pure scattering, . Therefore , as it should because in this case no energy is lost from the radiation field; clearly this is also true in thermodynamic equilibrium.

#### 8.1.3.1. Optical Thickness

Optical thickness is a dimensionless quantity that represents the ability of a given path length of gas to attenuate radiation of a given wavelength. Optical thickness is given by:

| (8–17)

where is the optical thickness (or opacity) of the layer of thickness and is a function of all the values of between 0 and . A large value of means large absorption of radiation. Note that this definition of optical thickness is different from that traditionally found in the optics literature where the optical thickness is a property of the material.

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