absolute entropy using partition functions

Absolute entropy using partition functions full#

Owing to the importance of Q tot( T), a number of studies were conducted throughout the past several decades to obtain more accurate values and present them in a convenient way. Together with other thermodynamic quantities, partition functions are used in many astrophysical problems, including equation of state, radiative transfer, dissociation equilibrium, evaluating line intensities from spectra, and correction of line intensities to temperatures other than given in standard atlases. If the particle is not isolated, there is an occupation probability between 0 and 1 for each level depending on interactions with its neighbours. It is the statistical sum over all the Boltzmann factors for all the bound levels. The total internal partition function, Q tot( T), is used to determine how atoms and molecules in thermodynamic equilibrium are distributed among the various energy states at particular temperatures.

Absolute entropy using partition functions full#

The full datasets in 1 K temperature steps are only available at the CDS via anonymous ftp to ( 130.79.128.5) or via Reported internal partition functions and thermodynamic quantities in the present work are shown to be more accurate than previously available data. For most of the relevant astrophysical cases it is strongly advised to avoid using simplifications, such as a harmonic oscillator and rigid rotor or ad hoc summation limits of the eigenstates to estimate accurate partition functions and to be particularly careful when using polynomial fits to the computed values. Dunham coefficients of these states of H 2 are also reported.Ĭonclusions. The calculations are not limited to the ground electronic state, but include all bound and quasi-bound levels of excited electronic states. Our results are compared to previous estimates in the literature. New partition functions for equilibrium, normal, and ortho and para hydrogen are calculated and thermodynamic quantities are reported for the temperature range 1–20 000 K. Various shortcomings in existing calculations are demonstrated, and the reasons for them are explained. Both equilibrium and normal hydrogen was taken into consideration. Dunham coefficients were determined from experimental and theoretical energy levels of a number of electronically excited states of H 2. These were compared to what we consider the most accurate and most complete treatment (case 8). Seven possible simplifications of various complexity are described, together with advantages and disadvantages of direct summation of experimental values. Therefore a more complicated approach has to be taken. These errors carry on to calculations of thermodynamic quantities. These shortcomings can lead to errors of up to 40 percent or more in the estimated partition function. We here rigorously show the shortcomings of various simplifications that are used to calculate the total internal partition function. Therefore thermodynamic data for molecular hydrogen have to be as accurate as possible in a wide temperature range.Īims. It is also of high interest in plasma physics. Its thermodynamic quantities dominate the physical conditions in molecular clouds, protoplanetary disks, etc.

Hydrogen is the most abundant molecule in the Universe. Niels Bohr Institute & Centre for Star and Planet Formation, University of Copenhagen, Øster Voldgade 5–7, 1350 Copenhagen K, DenmarkĬontext.

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