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- TL;DR Summary
- Standard theory on radiation says that pressure in isotropic radiation is given by ##P_\nu=\frac 1 3 U_\nu##. However, why is there any pressure at all, since isotropic means that no direction is preferred? What is actually the definition of pressure inside radiation field?

It is a standard result that in a blackbody radiation there is a pressure (at a certain frequency), given by

$$P_\nu=\frac 1 3 U_\nu$$

However, I am quite confused by this result.

Firstly, how do we even define pressure in radiation gas? I would think that this would be the pressure on a small hypothetical surface ##dA##. However, since blackbody radiation is isotropic and no direction is preferred, why do we expect the imaginary surface to be blown away by the pressure? Certainly my definition of pressure cannot be correct.

The reason I think that pressure is defined as described above, is that in a book "Astrophysics for Physicists" the author says that "The pressure of the radiation field over a surface is given by the flux of momentum perpendicular to that surface". However, if radiation is isotropic, how can there be any flux of momentum?

Any insight would be greatly appreciated.

$$P_\nu=\frac 1 3 U_\nu$$

However, I am quite confused by this result.

Firstly, how do we even define pressure in radiation gas? I would think that this would be the pressure on a small hypothetical surface ##dA##. However, since blackbody radiation is isotropic and no direction is preferred, why do we expect the imaginary surface to be blown away by the pressure? Certainly my definition of pressure cannot be correct.

The reason I think that pressure is defined as described above, is that in a book "Astrophysics for Physicists" the author says that "The pressure of the radiation field over a surface is given by the flux of momentum perpendicular to that surface". However, if radiation is isotropic, how can there be any flux of momentum?

Any insight would be greatly appreciated.