The virial equation of state p = ρRT[ 1 + B(T) ρ + C(T) ρ2 + · · ·] for high pressure and density gases is used for computing chemical equilibrium properties and mixture compositions of strong shock and detonation waves. The second and third temperature-dependent virial coefficients B(T) and C(T) are included in tabular form in computer codes, and they are evaluated by polynomial interpolation. A very accurate numerical integration method is presented for computing B(T) and its derivatives for tables, and a sophisticated method is introduced for interpolating B(T) more accurately and efficiently than previously possible. Tabulated B(T) values are non-uniformly distributed using an adaptive grid, to minimize the size and storage of the tables and to control the maximum relative error of interpolated values. The methods introduced for evaluating B(T) apply equally well to the intermolecular potentials of Lennard-Jones in 1924, Buckingham and Corner in 1947, and Rice and Hirschfelder in 1954.

The virial equation of state p = ρRT[ 1 + B(T) ρ + C(T) ρ2 + · · ·] for high pressure and density gases is used for computing chemical equilibrium properties and mixture compositions of strong shock and detonation waves. The second and third temperature-dependent virial coefficients B(T) and C(T) are included in tabular form in computer codes, and they are evaluated by polynomial interpolation. A very accurate numerical integration method is presented for computing B(T) and its derivatives for tables, and a sophisticated method is introduced for interpolating B(T) more accurately and efficiently than previously possible. Tabulated B(T) values are non-uniformly distributed using an adaptive grid, to minimize the size and storage of the tables and to control the maximum relative error of interpolated values. The methods introduced for evaluating B(T) apply equally well to the intermolecular potentials of Lennard-Jones in 1924, Buckingham and Corner in 1947, and Rice and Hirschfelder in 1954.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-06-07T19:46:54Z No. of bitstreams: 1 sebastiaomaurofilho.pdf: 422464 bytes, checksum: 2d72827356c924e509ef415cf17ff6bc (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-06-26T17:47:29Z (GMT) No. of bitstreams: 1 sebastiaomaurofilho.pdf: 422464 bytes, checksum: 2d72827356c924e509ef415cf17ff6bc (MD5) / Made available in DSpace on 2017-06-26T17:47:29Z (GMT). No. of bitstreams: 1 sebastiaomaurofilho.pdf: 422464 bytes, checksum: 2d72827356c924e509ef415cf17ff6bc (MD5) Previous issue date: 2012-02-29 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Recentemente foi demonstrado [17] que correções quânticas para o potencial gravitacional de Newton explica as curvas de rotação em galáxias espirais sem introduzir o halo de matéria escura. O único parâmetro fenomenológico aѵ da teoria cresce com a massa da galáxia. A fim de melhor investigar a dependência de aѵ com a massa é preciso verificar o limite superior para aѵ em uma escala menor. Aqui nós realizamos o cálculo correspondente por meio da análise da dinâmica do vetor de Laplace-Runge-Lenz e da condição de equilíbrio de anãs-brancas. A limitação resultante sobre correções quânticas sugerem uma dependência de aѵ com a massa. / Recently it was shown that quantum corrections to the Newton potential can explain the rotation curves in spiral galaxies without introducing the Dark Matter halo. The unique phenomenological parameter aѵ of the theory grows with the mass of the galaxy. In order to better investigate the mass-dependence of aѵ one needs to check the upper bound for aѵ at a smaller scale. Here we perform the corresponding calculation by analyzing the dynamics of the Laplace-Runge-Lenz vector and the equilibrium condition of white-dwarf. The resulting limitation on quantum corrections is suggesting a mass-dependence of aѵ.