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Published in Splinter Robert, Illustrated Encyclopedia of Applied and Engineering Physics, 2017
[thermodynamics] Entropic thermodynamic potential defined as Φ = S − (1/T)U, where S=(U/T)+(PV/T)+∑i=1n(−μi(Ni/T)) represents the entropy of a system, T the temperature, U the internal energy, P pressure, V the volume of the system, μi the chemical potential chemical constituent i and Ni the quantity of items (particles, atoms, ions, etc. expressed in mole) of chemical component i. The concept of free entropy as introduced by François Massieu (1832–1896) in 1869. The Massieu potential and free energy predate the Gibbs’s free energy, which was introduced in 1875 by Josiah Willard Gibbs (1839–1903). It was shown that the free entropy follows from the Legendre transform of the true entropy of a system or process. The Massieu potential is based on the fact that the state of a body is completely defined when two of the three parameters that represent the volume of the system, the temperature of the system, as well as the pressure on its surface are known. Also known as Helmholtz free entropy.
Comparison of ion-exchange resins for efficient cobalt(II) removal from acidic streams
Published in Chemical Engineering Communications, 2018
Anna Wołowicz, Zbigniew Hubicki
The effect of temperature on cobalt(II) sorption process was performed using 273, 313, and 333 K to obtain the thermodynamic parameters such as Gibbs free energy (ΔG°), enthalpy (ΔH°), and entropy (ΔS°). The plot of ln Kd vs. 1/T was obtained (Figure 7) and the changes of enthalpy and entropy were calculated from the slope (−ΔH°/R) and intercept (ΔS°/R) of the plot, whereas the change of the free energy (ΔG°) was calculated using the following equations: where ΔG° is the change of free energy of the system (kJ mol−1), R is the gaseous constant (8.314 J mol−1 K−1), T is temperature (K), Kd is the equilibrium constant (L mg−1), ΔH° is the change of free enthalpy of the system (kJ mol−1), ΔS° is the change of the free entropy (kJ mol−1 K−1) (Hamed et al., 2016; Kowsari et al., 2016).
Using zeolite and Fe3O4@zeolite composites in removal of Reactive Red 120 from wastewater: Isotherm, kinetic, thermodynamic and adsorption behaviors
Published in Journal of Dispersion Science and Technology, 2023
Thermodynamic parameters of the adsorption of RR120 onto zeolite and Fe3O4@Z, standard free energy change (ΔGo), free enthalpy change (ΔHo) and free entropy change (ΔSo), were determined using the following equations;