Consistent Application of the Boltzmann Distribution to Residual Entropy in Crystals

“Residual” entropy (3–12 J mol 1 K 1) is present near 0 K in some crystals composed of nonsymmetric molecules, for example, CO, N2O, FClO3, and H2O. It is detected only by the difference between spectroscopic calculations of the absolute entropy of the gaseous chemical and calorimetric measurements of its heat capacity (and phase changes) from 0 K to the temperature of the gas. Calorimetry, like any thermodynamic measurement, yields a difference, and thus gives ∆S rather than absolute entropy values. Unlike the corresponding energy or enthalpy, entropy is normally set equal to zero at 0 K in accord with the third law of thermodynamics thereby allowing for the calculation of its absolute values at any given temperature. I shall show that residual entropy can be estimated by four different approaches to entropy (methods 1–4). Because they are applied to the same system, they should yield the same result and they do; therefore, confirming the utility of the informational, thermodynamic, stochastic, and statistical–probabilistic aspects of entropy. The assumptions, limitations, and constraints of this thesis will be stated.