The effect of pressure P and temperature T on the properties of mixing of helium-hydrogen (He-H2 ) fluid mixture is studied based on statistical mechanical perturbation theory. The constituent species are considered to be interacting via a pair potential consisting of short range repulsion and a long range attraction which has been included through a double Yukawa (DY) potential. He and H2 are the lightest elements; therefore, the quantum effect is included via first-order quantum correction in the framework of Wigner-Kirkwood expansion. The dimerization of the H2 molecule is treated as a hard convex body fluid for which the equation of state (EOS) can be derived from hard sphere system based on scaled particle theory. An advanced and most recent EOS has been used for our investigation. The use of the DY potential, which can readily be simulated to empirical potentials, has enabled us to obtain analytical expressions for attractive and quantum energy contributions in terms of Laplace transforms. With a view to ensure internal consistency of the various thermodynamic functions to extract information on segregation and order in the mixture, different functions, such as compressibility factor, Gibbs free energy of mixing, entropy of mixing, and concentration fluctuations in the long wavelength limit, have been calculated as functions of composition of the mixture over an extended region of P and T. The results suggest that segregation, heterocoordination, or both may occur in the He-H2 mixture depending upon its composition, pressure, and temperature.

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By employing the extended Nikiforov–Uvarov (ENU) method, we solved the radial Schrodinger equation with the shifted screened Kratzer potential model. The analytical expression of the energy eigenvalues and numerical results were determined for some selected diatomic molecule systems. Variations of the energy eigenvalues obtained with potential parameters and quantum numbers were discussed graphically. Also, variations of different thermodynamic properties with temperature and maximum vibration quantum numbers were discussed extensively. Our results correspond to the results obtained in the literatures. The shifting parameters contribute a great effect to the energy results obtained. It has also been established that there exists a critical temperature at specific entropy values for the selected diatomic molecule systems.

Enhancing science education in developing countries has been a focal point of many studies and efforts, but reform has mainly been driven by top-down approaches that often face impediments. A shift to active learning pedagogies can potentially address these challenges, but it has thus far been predominantly implemented and understood in developed countries. Thanks to the growing accessibility of open education resources and ubiquitous technologies, education reform can now be carried out from the bottom up. Here, we present the results of a two-year implementation of active learning in five core physics and astronomy courses comprising 2,145 students from the Middle East and North Africa (MENA) region. Simultaneous improvements are observed in both students’ performance and their perception of the quality of learning; means improved by 9% (0.5 SD) and 25% (1.5 SD), respectively. The performance gap between students in the bottom quartile and those in the top quartiles was narrowed by 17%. The failure rate was reduced to a third of that in traditional classes; this is 36% better than the results in developed countries, indicating a greater need for active pedagogies by MENA students. Our findings reveal a multidimensional positive influence of active learning, the viability of its grassroots implementation with open resources, and its sustainability and reproducibility. We suggest that wider implementation can boost education-driven economic growth by 1% in per capita gross domestic product [GDP], substantially cut costs of repeating courses, and produce a more competent STEM workforce—all of which are urgently needed to stimulate development and growth.

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