The upper limits for the reverberation time and Q factor of acoustic reverberation chambers with perfectly rigid walls with a smooth surface are determined. The reflection factor for a rigid wall of arbitrary thermal conductivity is determined from a consideration of the viscosity and heat conductivity-boundary layer. The cases of isothermal and adiabatic boundary conditions are discussed. At very low frequencies the boundary absorption and at very high frequencies the volume absorption are the important factors in determining the losses. The analogous problem of the electric reverberation chamber is compared with the acoustic case. For some conditions the electric and acoustic equations are identical in form, if the electric skin depth is replaced by the thickness of the acoustic viscosity boundary layer. At comparable wavelengths and room sizes the electric Q factors are approximately factor of 50 higher than the acoustic upper limiting values.