Article pubs.acs.org/JPCA
Uncertainty Analysis in the Use of Chemical Thermometry: A Case Study with Cyclohexene Joshua S. Heyne* and Frederick L. Dryer Mechanical & Aerospace Engineering Department, Princeton University, Princeton, New Jersey 08540, United States S Supporting Information *
ABSTRACT: A general method to evaluate the absolute uncertainties in temperatures derived using chemical thermometry is developed and applied to the retro Diels−Alder reaction of cyclohexene. Experiments from previous studies of this reaction are reanalyzed to establish the minimum absolute uncertainty limit. Chemical thermometry results are compared with thermocouple measurements in experiments performed in a flow reactor at 6.1 atm pressure and at temperatures from 957 to 978 K . Using conservative uncertainty estimates, our analysis yields absolute (1σ) uncertainties of temperature through chemical thermometry using this reaction greater than ±20 at 1000 K. Neither more refined experimental techniques nor computational theory is likely to refine rate correlation parameters sufficiently to reach the absolute temperature uncertainties often reported in the literature for chemical thermometry using the retro Diels−Alder reaction of cyclohexene. Published chemical thermometry uncertainty estimates typically have not quantitatively considered the absolute uncertainties of the original data from which the reference rate correlations were based.
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INTRODUCTION
case study, though the methods that we apply are more generally applicable. The retro Diels−Alder reaction of cyclohexene in the gas phase is one of the most studied and well characterized reactions in gas kinetics7−9 and references therein. The assumed veracity of the data have led to the use of this reaction as an “internal”4,5 standard in the characterization of decompositions and as an “external” standard3 in other kinetic studies primarily in shock tube experiments. Typically, reaction temperatures in reflected shock experiments are determined from experimental measurements of shock speed at reflection. Advancements in spectroscopic methods for determining temperatures in reflected shock experiments have further strengthened and confirmed the uncertainty estimates associated with shock speed methods.10 On the other hand, the incentive for using chemical thermometry has been born out of the efforts to circumvent nonideal gas effects3 and more generally in response to other nonidealities in single pulse shock tube experiments.11 The uncertainty typically prescribed in the literature to chemical thermometry is
