Page:Zur Thermodynamik bewegter Systeme (Fortsetzung).djvu/4



9. Application to cavity radiation.

We base our calculation on the relative ray path. We consider radiation that encloses angles between $$\phi$$ and $$\phi+d\phi$$ with the direction of motion; it carries – in unit volume through the unit surface of a perpendicular (co-moving) plane – the energy amount:

$2\pi J\ \sin\phi\ \cos\phi\ d\phi.$

We call $$J$$ the intensity of the total (relative) radiation. If this radiation is incident upon an absorbing surface, it performs the pressure work:

$q\cdot\frac{2\pi J\sin\phi\cos\phi\ d\phi}{c}\cdot \cos\varphi=2\pi J\sin\phi\cos\phi\ d\phi\ \beta\cos\varphi,$

where $$\varphi$$ is the angle between the absolute radiation direction and the direction of motion. The difference:

$2\pi J\ \sin\phi\ \cos\phi\ d\phi(1-\beta\ \cos\varphi) = 2\pi i\ \sin\phi\ \cos\phi\ d\phi$

we call the true (relative) radiation. The true radiation intensity

is crucial for the heat transport between bodies of equal velocity.

We employ the standpoint of 's contraction hypothesis and introduce the angle $$\phi'$$ by the equation