2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185437The finite temperature Casimir free energy is calculated for a dielectric ball of radius $a$ embedded in an infinite medium. The condition $εμ=1$ is assumed for the inside/outside regions. Both the Green function method and the mode summation method are considered, and found to be equivalent. For a dilute medium we find, assuming a simple "square" dispersion relation with an abrupt cutoff at imaginary frequency $\hat ω= ω_0$, the high temperature Casimir free energy to be negative and proportional to $x_0 \equiv ω_0 a$. Also, a physically more realistic dispersion relation involving spatial dispersion is considered, and is shown to lead to comparable results.18 pages, 5 eps figures; minor extensions of the discussion in sect. 3; 5 new references. To appear in J. Phys. A: Math. GenHigh Energy Physics - TheoryQuantum Physicstext