Energy Levels and Thermodynamic Properties of the Internal Rotator

Abstract

To facilitate the calculation of the thermodynamic properties of internal rotators lying outside the limits of available tabulations, methods of determining the energy levels are studied for the purpose of finding the most expeditious route to accurate results. It proves to be unnecessary in any case to calculate many levels from the wave mechanics. A partition function is set up in terms of the correct ground state and a series of approximate levels derived from the old quantum theory, and this is corrected to constancy by the successive substitution of correct levels, starting with the first excited state. A set of levels obtained in this way which gives the correct partition function always leads to correct values of all the thermodynamic properties. To obtain accurate energy levels, the continued fractions of Koehler and Dennison are recommended as most convenient.

Experimental Study and Correlation Models of the Density and Viscosity of 1-Hexene and 1-Heptene at Temperatures from (298 to 473) K and Pressures up to 245 MPa

“…The present data for 1-hexene and 1-heptene extend the pressure range of measurements by other authors (see Tables and ), provide a set of densities over a wide range of experimental conditions, and can be used to develop accurate reference EOS. Figures to demonstrate the satisfactory consistency of the temperature and pressure dependences of the density of 1-hexene and 1-heptene measured in the present work and reported data, ,,− ,,− except for the old data reported in 1892 by Landolt and Jahn . Various isobars for 1-hexene and 1-heptene densities are plotted against temperature in Figure .…”

“…The present density measurements for 1-hexene and 1-heptene at high pressures were compared with the data reported by other authors (see Figures to ). Figure shows the comparison between the present and reported data for the density of 1-hexene and the values calculated from correlation (eq ) derived from the speed sound measurements. , The deviation plots for the present measured densities and previously reported density data − and the values calculated from the Tait EOS are given below (detailed discussion of agreement between the present results and various reported data sources is given below).…”

“…Left: ●, this work; ○, Wright; ▲, Kireev (saturated liquid density); △, Landolt and Jahn; □, Kerimov and Apaev; ■, Forziati et al; ▽, Letcher and Marsicano; ◇, Guseinov et al; ▼, Burkat and Richard; ×, Abas-zade et al; ◆, Camin . Right: ●, this work; △, Treszczanowicz et al; □, Domanska; ○, Guseinov et al; ▲, Kireev (saturated liquid density); ▽, Halford . Solid lines are calculated from eq…”

“…Existing data cover only a limiting range of temperature and pressure, and contain large uncertainties and inconsistencies. Tables and summarize, to the best of our knowledge, the experimental measurements of the density − and viscosity − of liquid 1-hexene and 1-heptene reported in the literature. The literature search was based on the TRC/NIST archive .…”

“…The uncertainty for most reported density data is within 0.05 % (at low temperatures and low pressures, basically at atmospheric pressure) and 0.1 % to 0.3 % at high temperatures and high pressures, while the uncertainty of the reported viscosity data is within 2 % to 3 %. Most reported density data (see Table ) were performed in the very limited temperature range, from (293 to 323) K, and at atmospheric pressure. − ,,− , High-temperature, from (293 to 533) K, and high-pressure (up to 70 MPa) density measurements were performed in the works. ,, Also for viscosity of liquid 1-heptene one reported data source was measured at atmospheric pressure and at temperatures between (293 and 313) K using the capillary tube method. Measurements in the works , were performed at temperatures from (298 to 473) K, while Guseinov , reported low temperature measurements of the viscosity (from mp to 293 K) and at pressures up to 50 MPa.…”