Residual entropy associated with proton disorder

Residual entropy associated with proton disorder 

The Bernal-Fowler-Pauling statistical model for the proton arrangements in ice presents a very subtle problem in the actual evaluation of the number of possible configurations in a macroscopic crystal. This is not just an academic exercise for, if we suppose there are configurations, all of which are equally likely, then the entropy of the system due to this cause is k In Further, if these configurations become frozen at some temperature where the disordering is still essentially complete, the measured entropy of the ice crystal will still have the residual value In at o °K, entropy from all other sources having vanished. 

Experimental determination of this residual entropy is straightforward in principle, though it requires careful technique. The entropy of a mole of ice under pressure p and at temperature T can be found experimentally from the integral 

This approach was used by Giaque Stout (1936), who measured the specific heat of ice down to 15 °K, extrapolating to lower 

5o(expt.) = 0-82 0-05 cal mole i deg. (2.2) It is this value which must be explained in terms of proton disorder in the crystal. 

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Residual entropy associated with proton disorder... 

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