Page:Zur Dynamik bewegter Systeme.djvu/7

 Furthermore, the momentum

$$G=\frac{4q\epsilon V}{3c^{2}+q^{2}}$$.

Substituting these values into the expression of A, and the values of A and E into the equation for dS, the latter is as follows:

$$dS=\frac{d(\epsilon V)-qd\left(\frac{4q\epsilon V}{3c^{2}+q^{2}}\right)+\frac{c^{2}-q^{2}}{3c^{2}+q^{2}}\epsilon dV}{T}$$.

The condition that this expression forms a complete differential of the three independent variables q, V and T (bearing in mind that ε only depends on q and T, not on V) gives as a necessary consequence the relations:

and

where the constant a is determined by the fact that ε goes over to aT4 for q = 0, which is in accordance with the radiation law.

With these values we obtain for the energy E, the pressure p and the momentum G of the moving cavity radiation as functions of the independent variables q, V and T, the following expressions:

So, for example, if we impart some acceleration to the cavity radiation, while its volume V is kept constant and no heat is supplied from outside so that also the entropy S remains constant, the temperature T of the radiation is decreased by (2) in the ratio