imagine a device which is able to measure the thermal radiation power $S(\nu)$ at a given frequency $\nu$. would it be possible to determine unambiguously the temperature of a blackbody by carrying out measurements at two frequencies $\nu_1$ and $\nu_2$?

At first glance one would assume that this is possible because S depends on nu and T (and known natural constants) so that you can resolve the equation if S is given for a special nu and get T. So it should even suffice knowing it for only one frequency. Also when looking at the graphs for different parameters T this seems to be true since they should not have a common point (except for nu = 0). Maybe there's a trick in the question in referring to two frequencies?

ReplyDeleteI agree with the above. Planck curves for different temperatures do not cross. Either it's a trick question or there is too much information (or the too much information is part of the trick).

DeleteRadio astronomers sometimes speak of the "brightness temperature" of an object, which is just a conversion from

S(ν)to temperature based on the Planck formula. (Of course, this can be done for any body, not just a black body; only in the case of a black body, however, does it correspond to a temperature. However, the point is that this would make no sense at all if there weren't a one-to-one relationship for black bodies.)