The Ideal and Real Gas Heat Capacity of Cesium Atoms at High Temperatures

The Ideal Gas Heat Capacity, Cp, of Cesium Atoms is Calculated to High Temperatures using Statistical Mechanics. There Are a Large Number of Electronic States in the State Sum that Determines the Partition Function: 174 Known Levels for Cesium Atoms Below the First Ionization Potential. Thus, at High Temperatures, Cp Becomes Very Large Unless the Number of Contributing States is Constrained. Two Arguments Are Used to Do This. First, at High Temperatures, the Increased Size of the Atoms Constrains the Sum (Bethe Method). Second, the Existence of Interacting Charged Species at Higher Temperatures, Which Lowers the Ionization Potential, Constrains the Sum (Ionization Potential Lowering Method). If Atoms Constitute a Real Gas Obeying the Virial Equation of State, the Lowest Non-Ideal Contribution to Cp Depends on the Second Derivative of the Second Virial Coefficient, B″(T), Which Depends on the Interaction Potential Energy Curves between Two Atoms. When Two Ground-State (2S) Cesium Atoms Interact, They Follow Either of Two Potential Energy Curves. When a 2S Cesium Atom Interacts with a Cesium Atom in the First Electronically Excited (2P) State, They Follow Any of Eight Potential Energy Curves. the Values of B″(T) for the Ten States Are Determined, Then Averaged, and Used to Calculate the Lowest Order Non-Ideal Contribution to Cp

The Ideal and Real Gas Heat Capacity of Potassium Atoms at High Temperatures

The Ideal Gas Heat Capacity, Cp, of Potassium Atoms is Calculated to High Temperatures using Statistical Mechanics. Since There Are a Large Number of Electronic Energy Levels in the Partition Function (Boltzmann Sum) Below the First Ionization Potential, the Partition Function and Cp will become very large as the Temperature Increases Unless the Number of Energy Levels Contributing to the Partition Function is Constrained. Two Primary Categories of Arguments Are Used to Do This. First, at High Temperatures, the Increased Size of the Atoms Constrains the Sum (Bethe Method). Second, an Argument based on the Existence of Interacting Charged Species at Higher Temperatures is Used to Constrain the Sum (Ionization Potential Lowering Method). When Potassium Atoms Are Assumed to Constitute a Real Gas that Obeys the Virial Equation of State, the Lowest Non-Ideal Contribution to Cp Depends on the Second Derivative of the Second Virial Coefficient, B(T), Which Depends on the Interaction Potential Energy Curves between Two Potassium Atoms. When Two Ground-State (2S) Atoms Interact, They Can Follow Either of the Two Potential Energy Curves. When a 2S Atom Interacts with an Atom in the First Electronically Excited (2P) State, They Can Follow Any of the Eight Potential Energy Curves. the Values of B(T) for the Ten States Are Determined, Then Averaged, and Used to Calculate the Nonideal Contribution to Cp

Inelastic Cross Sections for Molecules Interacting Through Dipole And/or Quadrupole Potentials

Formal expressions for the lowest order inelastic contribution to the degeneracy averaged total cross section for both distinguishable and indistinguishable rigid diatomic molecules are obtained for molecules interacting through a multiple potential. Explicit expressions for the inleastic cross section are obtained for molecules interacting through permanent dipole-dipole, dipole-quadrupole, or quadrupole-quadrupole potentials. These results require the summation over only a single quantum number; the relative angular momentum quantum number. Thus, they are useful for analytic or numerical calculations

Restrictions on the Potential and Cross Section for Collisions Between Rigid Rotors

A restricted distorted-wave treatment of the total cross section when two rigid diatomic molecules with orbital and nuclear spin angular momenta collide is examined. There are certain restrictions on the intermolecular potential and on the possible combinations of the various quantum numbers. These restictions are examined for the lowest order nonspherical elastic and the lowest order inelastic contributions to the total cross section. The effects of degeneracy averaging and of collisions between indistinguishable molecules are also briefly examined

Effect of Angular Momentum on the Relaxation Time in a Multicomponent Gas Mixture

The effects of molecular angular momentum (spin polarization) on the bulk viscosity and relaxation time in a multicomponent gas mixture are considered. Formal theoretical results are obtained, using the Wang Chang-Uhlenbeck approach to the kinetic theory of gases with internal states. The results are given in terms of integrals over the weighted quantum mechanical degeneracy averaged cross section

Calculation of the Thermophysical Properties of Ground State Sodium Atoms

Transport properties of dilute monatomic gases depend on the two body interaction potentials between the atoms. When two ground state sodium atoms interact, they can follow either of two potential energy curves corresponding to the Na2 molecule in the X1Σ+g or the 3Σ+u. Transport collision integrals and second virial coefficients of monatomic sodium have been calculated by accurately representing quantum mechanical potential energy curves with the Hulburt-Hirschfelder potential. The generally good agreement of calculated viscosities and second virial coefficients with the available experimental viscosities and with previously calculated virial coefficients provides further evidence that this approach can be used for accurate estimates of thermophysical properties under conditions where experimental data are sparse or unavailable. © 1987 American Institute of Physics

Transport Properties of Ground State Nitrogen Atoms

Transport properties of dilute monatomic gases depend on the two body atom-atom interaction potential. When two ground state (4S) nitrogen atoms interact, they can follow any of four potential energy curves corresponding to the N2 molecule; the X 1Σ+g, A3Σ+u, 5Σ+g, and 7Σ+u curves. Transport collision integrals for the 1Σ+g and 3Σ+u states have been calculated by representing the potentials for these states with the Hulburt-Hirschfelder potential. The5Σ+g state has a large local maximum which requires changes in the computational procedure used previously; a modified Hulburt-Hirschfelder potential has been used to represent the potential for this state. Collision integrals for the 7Σ+u state have been obtained by direct use of a recent theoretical potential for this state. The collision integrals are compared with results obtained in previous studies

Effect of Molecular Angular Momentum on the Thermal Conductivity of a Multicomponent Gas Mixture

The effects of molecular angular momentum (spin polarization) on the thermal conductivity of a multicomponent gas mixture are considered. The Wang Chang-Uhlenbeck approach to the kinetic theory of gases with internal states is used. Formal results are obtained for the thermal conductivity of a gas mixture of uniform composition. These results are given in terms of the quantum mechanical degeneracy-averaged cross section

Transport Properties of Ground State Oxygen Atoms

The transport properties of dilute monatomic gases depend on the two body interactions between like atoms. When two ground state oxygen atoms interact, they can follow any of 18 potential energy curves corresponding to O2, all of which contribute to the transport properties of the ground state atoms. Transport collision integrals have been calculated for those interactions with an attractive minimum in the potential by accurately representingab initio quantum mechanical potential energy curves with the Hulburt-Hirschfelder potential. Repulsive ab initio potential energy curves have been accurately represented either with the exponential repulsive potential or with an exponential repulsive potential with an additional Gaussian term to model a shoulder-like feature on the repulsive wall. Results are given for viscosity, thermal conductivity, and diffusion and they are compared with previous theoretical calculations

Binary Collision Dynamics and Numerical Evaluation of Dilute Gas Transport Properties for Potentials with Multiple Extrema

Prediction of gaseous transport properties requires calculation of Chapman-Enskog collision integrals which depend on all possible binary collision trajectories. The interparticle potential is required as input, and for a variety of applications involving monatomic gases the Hulburt-Hirschfelder potential is useful since it is determined entirely from spectroscopic information and can accomodate the long-range maxima and minima found in many systems. Hulburt-Hirschfelder potentials are classified into five distinct types according to their qualitative binary collision dynamics, which in general can be quite complex and can exhibit “double orbiting”, i.e., a pair of orbiting impact parameters for a single energy of collision. The collision integral program of O\u27Hara and Smith has been revised extensively to accomodate all physical cases of the Hulburt-Hirschfelder potential, and the required numerical methods are described and justified. The revised program substantially extends the range of potentials for which collision integrals can be calculated