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I was reading the black body radiation and there the total energy of the black body radiation is $E=\sigma T^4$ and so specific heat is $C_v = 4 \sigma T^3$ so it is proportional to $T^3$.

I read that specific heat actually depends on degree of freedom of the system and also depends on the number of ways in which flow of heat can occur. So is in this case degree of freedom $3$? And is that where the $3$ in $T^3$ comes from?

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There is a simple relation between specific heat and the number of degrees of freedom for some classes of classical systems (https://en.wikipedia.org/wiki/Equipartition_theorem). Black body radiation is a quantum system, so there is no such simple relation, and the number of degrees of freedom is infinite for black body radiation.

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  • $\begingroup$ No. Of degree of freedom for blackbody is infinite ? How? $\endgroup$
    – user101134
    Commented May 23, 2018 at 4:48
  • $\begingroup$ @user101134 : There are photon modes corresponding to arbitrarily short/long wavelengths. $\endgroup$
    – akhmeteli
    Commented May 23, 2018 at 4:58

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