Energy of an EM Wave and its temperature and amplitude I'm trying to understand why classical physics fails to explain black body radiation.
I'm confused.
According to Boltzmann, energy calculation for em wave is based on temperature. 
According to Maxwell, energy calculation for em wave is based on amplitude.
Are those different kinds of energies? How can we determine the energy of an em wave just taking temperature as a parameter, but not amplitude or frequency??
 A: Maxwell is talking about a single wave.  Boltzmann is talking about an ensemble of many many many many many such waves.  Boltzmann finds that the average energy of an ensemble of waves depends on the temperature of whatever the waves contact, assuming that we've let enough time go by that the measurable properties of the system no longer change with time (equilibrium, temperature the same everywhere).
Same goes for any other property you want to consider, for example, the distribution of energy with wavelength (black body curve).   
A: M. Planck started to explain black-body radiation by the relation predicted with classical statistical mechanics (with continous energy equi-partition to every degree of freedom of the system). This was Wien's Law which indeed was accurate for high frequencies but divergent for low frequencies.
Then Planck decided to account for a quantized energy (or treat as a series of harmonic oscillators), which by the then statistical arguments was not justified, and managed to find a relation (Planck's Law) which correctly described the black-body radiation and was in accord to the original Wien Law in the area the latter was correct.
Now the whole point is why did the then statistical mechanics thought this was not a justifiable argument (in fact if one takes into account that a finitely bounded system can have such a propety the rest follows, since it is a physical argument of bounded energy of a bounded system). This was a start of what was to become Quantum Mechanics.
