Page:Zur Theorie der Strahlung in bewegten Körpern.djvu/23

has to be changed in accordance with the previous equation, and by that also the temperature of the radiation must change.

The apparent radiation gained from the work, now (after changing the velocity) has the density $\epsilon _{0,1}\tau _{1}$, thus the work

$h(\epsilon _{0,1}\tau _{1}-\epsilon _{0}\tau )\,$

has to be performed for this change. (In this case, also our apparent mass introduced earlier would have another value; though no real meaning can be applied to it, as we will see in the next section.)

In the same way as before, the sign of $\delta w$ plays no role here, and our considerations can be applied to finite velocity changes as well, when they are performed sufficiently slow.

In particular, if the motion of our system is completely suspended, then the gained work is equal to $h\epsilon _{0}\tau$, since the final value of $\tau$ (for $\beta =0$) is zero. This work is thus equal to the surplus of the total radiation energy over the true one. The amount of the latter is thus not changing; its density remains unchanged and equal to $\epsilon _{0}\varkappa$. On the other hand, this radiation has now evidently a temperature, which is higher than that of the heat reservoir, with which the cavity was initially (at velocity $w$) connected. Because the emission capacity of the latter was (see eq. 20) $e={\tfrac {c}{4}}\epsilon _{0}$; however, now we have to connect the (resting) cavity with a black body of emission capacity $e_{1}={\tfrac {c}{4}}\varkappa \epsilon _{0}$, so that no heat transfer takes place. Since $\varkappa >1$, thus also $e_{1}>e$, thus the temperature of radiation is increased. (According to the Stefan-Boltzmann law in the ratio $1:\varkappa ^{1/4})$).

§ 6.

Now it is near at hand, to use this increase of temperature, in order to construct a cyclic process, which transports heat from a body of lower temperature to a body of higher temperature.

If we again imagine a system, consisting of a