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Partition functions
Published in Nils O. Petersen, Foundations for Nanoscience and Nanotechnology, 2017
The partition functions are particularly useful since they can be used to derive thermodynamic properties of materials from the molecular properties of the system. Calculation of the partition functions is then important. We saw that the grand canonical partition function (for open systems) depends linearly on the canonical partition function (for closed systems) (Equation 11.8 which in turn depends on the Nth power of the microcanonical partition function (for isolated systems) (Equations 11.5 and 11.6). The general problem then depends on calculating the molecular partition function, q.
Z-Partition Function
Published in Mihai V. Putz, New Frontiers in Nanochemistry, 2020
From a physical point of view, partition function (Z) characterizes the statistical properties of a system in thermodynamic equilibrium. Partition functions are functions of the thermodynamic state variables, such as the temperature and volume. Vibrational contribution to various thermodynamic functions is expressed in terms of a partition function and its first two derivatives (internal energy and respectively, heat capacity), seeAndrews, Frank C. (1963).
The thermodynamic potentials and the Maxwell relations
Published in C.B.P. Finn, Thermal Physics, 2017
In general, the partition function is an invaluable tool in the calculation of the bulk thermodynamic properties of a system using statistical mechanics, especially when more complicated systems are considered than the one here.
Reparametrised Pöschl–Teller oscillator and analytical molar entropy equation for diatomic molecules
Published in Molecular Physics, 2022
The partition function (Q) is a very useful thermodynamic expression because other thermodynamic relations are easily expressible in terms of it. In the case of gaseous substances, the partition function is the product of the rotational (Qrot), translational (Qtra) and vibrational (Qvib) partition functions expressed as [39] If a diatomic molecule is considered a rigid rotor and interaction between any two molecules in a spatial volume V is neglected, then Qrot and Qtran are expressed as [12,13] where Θr = h2 / (8 π2µ re2kB) is the rotational characteristic temperature, kB and m are the Boltzmann constant and molecular mass respectively, δ = 1, 2 for heteronuclear and homonuclear diatomic molecules, respectively.
The magnetocaloric effect, thermo-magnetic and transport properties of LiH diatomic molecule
Published in Molecular Physics, 2022
C. O. Edet, P. O. Amadi, E. B. Ettah, Norshamsuri Ali, Muhammad Asjad, A. N. Ikot
This research article is concerned with studying the thermomagnetic and transport properties and MCE of Lithium Hydride (LiH). To this end, the Schrödinger equation with the Varshni potential is solved in the presence of magnetic and Aharanov-Bohm (AB) fields are solved using the functional analysis approach to obtain the energy and wave function. The obtained energy is then utilised to calculate the partition function by summing over all accessible energy levels using the Boltzmann-Gibbs statistics. This partition function is then used to obtain the thermal, magnetic and transport properties and MCE for the LiH. The impacts of the magnetic and AB fields on the aforementioned properties have been scrutinised over a wide temperature region. It is concluded here that the susceptibility has only positive values in different scenarios analysed. The temperature dependence of the magnetic entropy changes shows a decreasing trend. This research can be applied in molecular physics and will provoke conversations and studies on MCE for several molecules.
Eigenvalues and thermal properties of the A1Σ u + state of sodium dimers
Published in Molecular Physics, 2022
Ridha Horchani, Nidhal Sulaiman, Safa Al Shafii
Using the energy eigenvalue of a particular molecular system, the vibrational partition function can be calculated using any convenient method. With the partition function, numerous microscopic models have been developed for different chemical reactions and rate processes. The information about the vibrational partition function is also useful in several chemical-physics challenges involving gases at different temperatures. Furthermore, the zero-temperature limit of the vibrational partition function is helpful in the evaluation of quantum-mechanical ground-state energy. The partition function can obtain various thermodynamic properties for any system under study, such as the entropy, the enthalpy and the Gibbs free energy.