## Thermodynamic Derivation of Wien's Law?

Can someone tell me how I can derive Wien's law, i.e.,

$\lambda_{max} T = constant$

where $\lambda_{max}$ is the peak wavelength and $T$ is the absolute temperature of the black body, using the equation,

$P=\frac{U^{*}}{3}$

where $U^{*}$ is the energy density.

Note: I'm not looking for the derivation using Plank's formula. I'm looking for a purely thermodynamic derivation.

$P$ is the Radiation Pressure. It relates to the first law of termodynamics definition of work, $PdV$. Basically, I'm looking to derive Wien's law from the first law.