Finite-size corrections to the blackbody radiation laws

We investigate the radiation of a blackbody in a cavity of finite size. For a given geometry, we use semiclassical techniques to obtain explicit expressions of the modified Planck and Stefan-Boltzmann blackbody radiation laws as a function of the size and shape of the cavity. We determine the range of parameters (temperature and size and shape of the cavity) for which these effects are accessible to experimental verification. Finally we discuss potential applications of our findings in the physics of the cosmic microwave background and sonoluminescence.

Figure 1

(Color online) Density of energy $u\left(\nu \right)$ in ${\text{J/m}}^{\text{3}}$ of a blackbody versus frequency. The solid line is Planck’s law. The dashed line is the analytical prediction for a spherical blackbody [Eqs. (3, 9)]. Finite-size effects are clearly visible. The parameters chosen $\left(r_0=2\text{cm},T=5\text{K}\right)$ fall within the region accessible to experiments (see text). In order to reproduce FIRAS resolution only rays shorter than $l_{\text{cut}}=2\times {10}^{2}c/\nu$ are included in Eq. (3). In the inset we plot $R_{\text{sca}}\left(x\right)=R\left(T\right)/\sigma T^4$ with $x=T{r}_0{k}_B/\hslash c$.