The role of the critical compressibility factor in the equation of state for the critical fluid

Based on the literature data of PVT measurements, the amplitudes of the equations of the critical isotherm D0(Zk), the critical isochore Г0(Zk), the phase boundaries В0(Zk) are expressed in terms of the critical factor of compressibility of the substance Zk=PkVk/RTk in the entire fluctuation region near the critical point. By doing so, a phenomenological method has been used for calculating the values of the critical exponents of the fluctuation theory of phase transitions based on the introduction of small parameters into the equations of the fluctuation theory. It has been shown that, within the limits of the PVT measurement errors, these dependences D0(Zk) and В0(Zk) on the compressibility factor are linear, and Г0 practically does not depend on the compressibility factor Zk. The relationship of these amplitudes with the amplitudes a and k of the linear model of the system of parametric scale equations of state of substance near the critical point has been established. It has been shown that the dependences k(Zk) and а(Zk) are also linear in the entire fluctuation region near the critical point. The obtained dependences k(Zk) and а(Zk) agree with the known relationship between the amplitudes of the critical isotherm D0(Zk), critical isochore Г0(Zk), phase boundaries В0(Zk) Aerospace Institute of the National Academy of Sciences of Ukrainewithin the framework of the system of parametric scaling equations. The relations а(Zk), k(Zk) make it possible, on the basis of a linear model of the system of parametric scale equations of state of substance, to determine such important characteristics of the critical fluid as the temperature and field dependences of the correlation length Rc(T,m) and the fluctuation part of the thermodynamic potential Ф(T,m) in the entire fluctuation region near the critical point. Then, based on the form of the fluctuation part of the thermodynamic potential Ф(T,m)~Rc(T,m)-3, the results obtained allow one to calculate the field and temperature dependences of the thermodynamic quantities for a wide class of molecular liquids in the close vicinity of the critical point (DP<10-3, Dr<10-2, t<10-4), where precision experiments are significantly complicated, and its can also be used when choosing the conditions for the most effective practical application of the unique properties of the critical fluid in the newest technologies.

Electrocaloric Effect of (110) Oriented KNbO3 Film

The room temperature electrocaloric effect is researched for (110) oriented KNbO3 film based on Landau-Devonshire theory. The phase map with different ferroelectric states is built at room temperature with the considerations of thermodynamic equilibrium conditions and minimum of thermodynamic potential. Five ferroelectric structural phases are obtained theoretically. The negative in-plane misfit strains are conducive to form the tetragonal c phase and the positive strains are in favor of the stability of tetragonal a1 and a2 phases. The electrocaloric effect relies on both misfit strain and electric field. Moreover, large electrocaloric effect is achieved in the orthorhombic phases.

Fishing with Scissors: A Mnemonic for Thermodynamic Formula

Most of the branches of engineering and basic science require,to a different extent,the use of basic thermodynamic formulas relating state variables (temperature, T; pressure, P; volume, V; entropy, S) and thermodynamic potentials (internal energy, U; Helmholtz free energy, A; enthalpy, H; Gibbs free energy, G). The different interrelations among variables, their constrains, and dependencies make them particularly difficult to remember and understand. For students learning and for chemists and engineers needing to rapidly recall these thermodynamic relationships for problem solving and practical applications, a quick method to easily remember them would be most welcome. Herein, Fishing with scissors mnemonic is presented. The mnemonic is seen as Sun with rays. Thermodynamic potential terms (A, G, H, U) as alphabetic doubles are aligned in sun rays regions where as state variables (T, P, S, V) are at sun body. Following a simple set of rules in this mnemonic, a large range of thermodynamic equations can be easily recalled without direction or sign difficulties present in previously reported methods.

Thermodynamic equilibrium theory revealing increased hysteresis in ferroelectric field-effect transistors with free charge accumulation

At the core of the theoretical framework of the ferroelectric field-effect transistor (FeFET) is the thermodynamic principle that one can determine the equilibrium behavior of ferroelectric (FERRO) systems using the appropriate thermodynamic potential. In literature, it is often implicitly assumed, without formal justification, that the Gibbs free energy is the appropriate potential and that the impact of free charge accumulation can be neglected. In this Article, we first formally demonstrate that the Grand Potential is the appropriate thermodynamic potential to analyze the equilibrium behavior of perfectly coherent and uniform FERRO-systems. We demonstrate that the Grand Potential only reduces to the Gibbs free energy for perfectly non-conductive FERRO-systems. Consequently, the Grand Potential is always required for free charge-conducting FERRO-systems. We demonstrate that free charge accumulation at the FERRO interface increases the hysteretic device characteristics. Lastly, a theoretical best-case upper limit for the interface defect density DFI is identified.

Quasilocal Smarr relation for an asymptotically flat spacetime

We investigate the thermodynamics of Einstein–Maxwell (-dilaton) theory for an asymptotically flat spacetime in a quasilocal frame. We firstly define a quasilocal thermodynamic potential via the Euclidean on-shell action and formulate a quasilocal Smarr relation from Euler’s theorem. Then we calculate the quasilocal energy and surface pressure by employing a Brown–York quasilocal method along with Mann–Marolf counterterm and find entropy from the quasilocal thermodynamic potential. These quasilocal variables are consistent with the Tolman temperature and the entropy in a quasilocal frame turns out to be same as the Bekenstein–Hawking entropy. As a result, we found that a surface pressure term and its conjugate variable, a quasilocal area, do not participate in a quasilocal thermodynamic potential, but should be present in a quasilocal Smarr relation and the quasilocal first law of black hole thermodynamics. For dyonic black hole solutions having dynamic dilaton field, a non-trivial dilaton contribution should occur in the quasilocal first law but not in the quasilocal Smarr relation.

Cosmological solutions, a new wick-rotation, and the first law of thermodynamics

We present a modified implementation of the Euclidean action formalism suitable for studying the thermodynamics of a class of cosmological solutions containing Killing horizons. To obtain a real metric of definite signature, we perform a “triple Wick-rotation” by analytically continuing all spacelike directions. The resulting Euclidean geometry is used to calculate the Euclidean on-shell action, which defines a thermodynamic potential. We show that for the vacuum de Sitter solution, planar solutions of Einstein-Maxwell theory and a previously found class of cosmological solutions of $$ \mathcal{N} $$ N = 2 supergravity, this thermodynamic potential can be used to define an internal energy which obeys the first law of thermodynamics. Our approach is complementary to, but consistent with the isolated horizon formalism. For planar Einstein-Maxwell solutions, we find dual solutions in Einstein-anti-Maxwell theory where the sign of the Maxwell term is reversed. These solutions are planar black holes, rather than cosmological solutions, but give rise, upon a standard Wick-rotation to the same Euclidean action and thermodynamic relations.

An Operator-theoretical Study on the BCS-Bogoliubov Model of Superconductivity Near Absolute Zero Temperature

In the BCS-Bogoliubov model of superconductivity, no one gave a proof of the statement that the solution to the BCS-Bogoliubov gap equation is differentiable with respect to the temperature. But, without such a proof, one differentiates the solution and the thermodynamic potential with respect to the temperature twice, and one obtains the entropy and the specific heat at constant volume of a superconductor. In the preceding papers, the present author showed that the solution is indeed differentiable with respect to the temperature twice. Thanks to these results, we in this paper differentiate the thermodynamic potential with respect to the temperature twice so as to obtain the entropy and the specific heat at constant volume from the viewpoint of operator theory. Here, the potential in the BCS-Bogoliubov gap equation is a function and need not be a constant. We then show the behavior near absolute zero temperature of the entropy, the specific heat, the solution and the critical magnetic field. Mathematics Subject Classification 2020. 45G10, 47H10, 47N50, 82D55.

Proposal of a Methodology for the Estimation of Slope, Water Depth and Cross-sectional Area by Using the State Function, Ф (T): Testing With the Measurements Made by H. Fischer in M. Keck Channel Laboratory of Caltech University

A basic topic in river studies, whether in hydrodynamics or water quality, is the accurate estimation of both geomorphological and geometric characteristics in cross sections in streams or channels. Many measurements or methodologies that are within the state of the art, are not direct or easy by several aspects. For this reason, this article analyses the application of a state function, Ф (t), which, acting as a thermodynamic potential, allows the magnitudes of the cross sections, depth of the water sheet, slope and longitudinal dispersion coefficient to be obtained directly, using NaCl as a tracer. In order to apply and validate this new method properly, an experiment conducted in 1966 by H.B. Fischer in the W.M. Keck Laboratory of Caltech in USA was studied on two points of the canal. It found average differences of 0.016 m2 (with reference) in the area of the canal, 0.015 m of the height of the water sheet and an average difference of -0.00015 in the slope of the canal

Hybrid stars from a three-flavor NJL model with two kinds of tensor condensates

To obtain the equation of state of quark matter and construct hybrid stars, we calculate the thermodynamic potential in the three-flavor Nambu–Jona-Lasinio model including the tensor-type four-point interaction and the Kobayashi–Maskawa–’t Hooft interaction. To construct the hybrid stars, it is necessary to impose the [Formula: see text] equilibrium and charge neutrality conditions on the system. It is shown that tensor condensed phases appear at large chemical potential. Under the possibility of the existence of the tensor condensates, the relationship between the radius and mass of hybrid stars is estimated.