Zero point energy from Heat Capacity vs Temperature Curve

[alberrace]

A table gives the values of heat capacity at constant volume of pure germanium estimate its vibrational zero point energy.



The vibrational zero point energy is just the missing 'area' in the plot of Cv vs T. I have plotted heat capacity versus T and calculated the zero point energy. What I want to do is show mathematically that this area corresponds to the zero point energy.

i know that internal energy is given as U=0.5*hbar*w + hbar*w/(exp(hbar*w/kb*T) - 1)

The first term is the zero point energy contribution and the the integral of heat capacity gives the second term in the above eqn (this is the area under the heat capacity curve).

 

[NateD]

So, integrating the heat capacity vs T curve would give us the total energy. Subtracting the first term (zero point energy) from the total energy will give us the energy contribution due to thermal vibrations. Therefore, the vibrational zero point energy of pure germanium can be estimated by subtracting the zero point energy term from the total energy obtained from the integral of the heat capacity vs T curve.