Heat and Thermodynamics

12.17 Einstein's Theory of Specific Heat

Einstein's derivation of specific heat formula is based upon the following assumptions:

1. All atoms of a monatomic solid vibrate with the same frequency v.
2. The frequency depends on the mass of the atom and the restoring force.
3. These atoms, like Planck's oscillators, are in equilibrium with ether vibrations of the same frequency.
4. Instead of classical law of equipartition, that is ½KT for each degree of freedom, Einstein uses the mean energy of Planck's oscillator for each degree of freedom, that is,

    

   

    

For one gram-atom of a monatomic solid, consisting of N atoms each with 3 degrees of freedom, the total ...