User:Csell/ema6136

The molar specific heat of pure C, as Graphite, at constant volume may be fit reasonably well with Einstein's quantum model of a simple harmonic oscillator (SHO) crystal, if the material's characteristic Einstein temperature is selected as θE = 900 K.

1) Use a convenient computer math package to develop a plot of the molar specific heat, Cv [J/mol-K], of graphite, from 0 K to 500 K. Has the specific heat of graphite reached the Dulong and Petit classical limit of about 25 J/mol-K at 500 K?  Explain briefly.

2) Using Einstein's formula for Cv, calculate and then plot the constant volume entropy function, S(T) [J/mol-K], for graphite versus temperature. The standard molar entropy for graphite at 298 K is listed in the CRC Handbook of Chemistry and Physics as S298 = 5.7 J/mole-K. Compare your calculated entropy answer at 298 K, based on the quantum SHO crystal, to the Handbook's tabulated experimental datum for C as graphite, and provide a reason explaining any discrepancy.

3) Again apply the quantum SHO model and compute the change in the Helmholtz free energy, ΔF(T,V) of C upon: a) slowly warming one g-atom of graphite at constant volume from 0 K to 250 K. b) Compute the isochoric (constant volume) change in Helmholtz free energy upon further heating graphite from 250 K to 500 K.

4) Explain any differences found for ΔF in answers 3(a) and 3(b), given that you are changing the temperature of the graphite crystals in both examples by the same amount, i.e., 250 K.