27.

Since ${ϵ}_{\nu }$ and ${\alpha }_{\nu }$ depend only on the nature of the medium, the temperature, and the frequency $\nu$, the intensity of radiation of a definite color in the state of thermodynamic equilibrium is completely defined by the nature of the medium and the temperature.

An exceptional case is when ${\alpha }_{\nu }=0$, that is, when the medium does not at all absorb the color in question. Since ${𝖪}_{\nu }$ cannot become infinitely large, a first consequence of this is that in that case ${ϵ}_{\nu }=0$ also, that is, a medium does not emit any color which it does not absorb. A second consequence is that if ${ϵ}_{\nu }$ and ${\alpha }_{\nu }$ both vanish, equation [eqn:(26)] (26) is satisfied by every value of ${𝖪}_{\nu }$.

In a medium which is diathermanous for a certain color thermodynamic equilibrium can exist for any intensity of radiation whatever of that color.

This supplies an immediate illustration of the cases spoken of before ([sect:24.] Sec. 24), where, for a given value of the total energy of a system enclosed by a rigid cover impermeable to heat, several states of equilibrium can exist, corresponding to several relative maxima of the entropy.

That is to say, since the intensity of radiation of the particular color in the state of thermodynamic equilibrium is quite independent of the temperature of a medium which is diathermanous for this color, the given total energy may be arbitrarily distributed between radiation of that color and the heat of the body, without making thermodynamic equilibrium impossible.

Among all these distributions there is one particular one, corresponding to the absolute maximum of entropy, which represents absolutely stable equilibrium. This one, unlike all the others, which are in a certain sense unstable, has the property of not being appreciably affected by a small disturbance.

Indeed we shall see later ([sect:48.] Sec. 48) that among the infinite number of values, which the quotient ${\displaystyle \frac{{ϵ}_{\nu }}{{\alpha }_{\nu }}}$ can have, if numerator and denominator both vanish, there exists one particular one which depends in a definite way on the nature of the medium, the frequency $\nu$, and the temperature.

This distinct value of the fraction is accordingly called the stable intensity of radiation ${𝖪}_{\nu }$, in the medium, which at the temperature in question is diathermanous for rays of the frequency $\nu$.

Everything that has just been said of a medium which is diathermanous for a certain kind of rays holds true for an absolute vacuum, which is a medium diathermanous for rays of all kinds, the only difference being that one cannot speak of the heat and the temperature of an absolute vacuum in any definite sense.

For the present we again shall put the special case of diathermancy aside and assume that all the media considered have a finite coefficient of absorption.