Statistical Aspects of Second and Third Law Heats

The effects of random errors and of nonconstant heat of vaporization upon the estimation of the second and third law heats of vaporization are examined. The most important conclusion is that the often noticed marked improvement in precision of the third law heat over that for the second law heat is real and is a natural consequence of the difference between the two estimators. The effects of systematic errors upon the two heats are not investigated here. Other results of interest, but of less importance because of the small magnitude of the effects, include: (1) the two heats are negatively correlated, (2) the second law heat is generally biased, (3) the third law heat is not the minimum variance unbiased estimator of the heat of vaporization, and (4) the standard deviation obtained from least squares fitting consistently overestimates the true standard deviation, but by a negligible amount. Any reversible process for which the equilibrium constant, is treated by a similar procedure is governed by the same considerations. The results apply approximately at any temperature although the stimulus for these considerations comes from high temperature chemistry.