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This paper studies the influence of a finite container on an ideal gas. Thetrace of the heat kernelΘ (t) = ∑∞μ=1 exp(-tλμ), where {λμ}μ=1 are the eigenvalues of thenegative Laplacian -△n = - ∑np (a/axp)2 in Rn(n = 2 or 3), is studied for a general multi-c