# Confidence intervals for thermodynamic constants

## Abstract

Phase equilibrium experiments using the same reactants and run at different temperatures and pressures give rise to linear constraints on thermodynamic variables, such as entropies, enthalpies, and volume changes of reaction. Linear programming has been applied to this problem to determine maxima and minima for these parameters separately. Since these temperatures and pressures are measured or set with uncertainty, their nominal values as reported by the experimenter need not define the same feasible region as that defined by their true values. Clearly, then, the ranges resulting from the linear programming procedure will not represent the reasonable ranges of parameter values. This paper explores the problem of inference on these parameters when a normal error distribution is postulated for temperature and pressure. Current methodologies and their relation to the field of statistical inference are discussed. Two algorithms for generating bounds on the entropies and enthalpies are presented. The first uses a normal approximation to the location of feasible region vertices and makes allowances for variations in the constraints contributing to this vertex to construct confidence intervals for the extrema in random linear programs in order to generate bounds holding for one parameter at a time. The second generates bounds holding simultaneously for all parameters. A comparison of these confidence intervals with those generated by conventional methods demonstrates that estimates of thermodynamic variables have far less variability than commonly believed. © 1991.