The spectral function θ(t)=m=1exp(tλm), t>0 where {λm}m=1 are the eigenvalues of the Laplacian in Rn, n=2 or 3, is studied for a variety of domains. Particular attention is given to circular and spherical domains with the impedance boundary conditions ur+γju=0 on Γj (or Sj), j=1,,J where Γj and Sj, j=1,,J are parts of the boundaries of these domains respectively, while γj, j=1,,J are positive constants.