Abstract: In general，for a thermodynamic system each thermodynamic function has only one expression. However，solid has two chemical potentials，one for solid atoms and another for phonons，which have finite and vanishing value，respectively. Einstein utilized the Boltzmann statistics to discuss the heat capacity of the solid especially at low temperature，in which the partition function for single oscillating degree of freedom of the solid atoms can as well be intepreted on the base of phonon gas. It is evident that the chemical potential for the solid atoms can not be taken to be that of the phonon gas. How to simultaneouly determine the values of both chemical potentials is explicitly illustrated with microcanonical ensemble.

Key words: phonon, solid atom, oscillator, chemical potential, microcanonical ensemble