As far as I understand, Wien defines entropy, which he uses in his derivation, as S=v∫0∞φ(ρ,ν)dν, S = \text{v} \int\limits_0^{\infty} \varphi(\rho, \nu) d \nu, where v\text{v} is the volume occupied by the radiation, ν\nu is the frequency of that radiation, ρ(ν)\rho(\nu) is the radiation density and φ\varphi is a function of the variables ρ\rho and ν\nu. Unfortunately, I can't find an English translation of his seminal paper Wien, W., "Temperatur und Entropie der Strahlung", Ann. Phys. Chem., 52, 132-165 (1894), where he has developed his ideas on the matter. I would appreciate it if someone who has dealt with this problem could shed some light on this important derivation and/or possibly give a link to an English translation or perhaps a translation in Russian of the paper. ANSWER: One can at once see how this integral can be entropy by considering φ=ρ(ν)T\varphi = \frac{\rho(\nu)}{T}, where ρ(ν)\rho(\nu) is radiation density. So, then, we will have v∫0∞φ(ρ,ν)dν=vT∫0∞ρ(ν)dν=UT=QT=S \text{v} \int\limits_0^{\infty} \varphi(\rho, \nu) d\nu = \frac{\text{v}}{T} \int\limits_0^{\infty} \rho(\nu) d\nu = \frac{U}{T} = \frac{Q}{T} = S because the process is isochoric. Unfortunately the above formula for SS cannot be used to recover the II law for an isochoric process dSdU=1T,\frac{dS}{dU} = \frac{1}{T}, so SνS_\nu must be used, expressing the entropy for a given frequency and not over all frequencies as in the integral shown in the OP, which I don't believe Wien used in any of his works (unless, someone can show otherwise).