Critical Specific Volume Research Articles

Heat engine efficiency for four-dimensional charged AdS black holes in Rastall gravity

In this paper, we analyze the [Formula: see text] criticality and the heat engine efficiency of two black holes, one is the four-dimensional charged AdS black hole in Rastall gravity and the other is the four-dimensional charged AdS black hole surrounded by quintessence in Rastall gravity. For the four-dimensional charged AdS black hole in Rastall gravity, the ratio [Formula: see text] is related to the Rastall parameter [Formula: see text]. When [Formula: see text] the ratio becomes [Formula: see text], which is same as the van der Waals liquid-gas system. Additionally, as the Rastall parameter [Formula: see text] increases, the heat engine efficiency [Formula: see text] of the black hole will increase. Moreover, the efficiency [Formula: see text] decreases rapidly at first and then increases with the entropy [Formula: see text]. But the efficiency ratio [Formula: see text] decreases with the Rastall parameter [Formula: see text]. For the four-dimensional charged AdS black hole surrounded by quintessence in Rastall gravity, as the charge q increases, the critical specific volume [Formula: see text] and the efficiency ratio [Formula: see text] also increase, however, the critical temperature [Formula: see text] and the critical pressure [Formula: see text] gradually decrease. Moreover, the heat engine efficiency [Formula: see text] and the efficiency ratio [Formula: see text] of the black hole are similar to the four-dimensional charged AdS black hole in Rastall gravity.

Einstein–AdS gravity coupled to modified arctan-electrodynamics, magnetic black hole thermodynamics and Joule–Thomson expansion

The metric and mass functions of Einstein–AdS gravity coupled to modified arctan- electrodynamics (proposed here) are obtained. We find corrections to the Reissner–Nordström solution. It is demonstrated that if the Schwarzschild mass is zero and as r→0 the asymptotic has the de Sitter core. Thermodynamics of magnetically charged black holes in Anti-de Sitter spacetime in an extended phase space, where the cosmological constant is treated as a pressure and the black hole mass is considered as the chemical enthalpy, is studied. It is shown that the black hole thermodynamics mimics the Van der Waals liquid–gas thermodynamics. The magnetic potential and vacuum polarization are calculated. We formulate the first law of black hole thermodynamics and proof that the generalized Smarr relation holds. The critical specific volume, temperature and pressure are evaluated and the critical behaviour of black holes is investigated. We calculate and study the Gibbs free energy and show that phase transitions take place. The local stability are studied by calculating the heat capacity. The black hole Joule–Thomson adiabatic expansion, cooling and heating phase transitions are investigated. We evaluate the Joule–Thomson coefficient and the inversion temperature.

Prediction of the critical properties: A simple accurate strategy applied to environmentally friendly substances HFOs

This paper aims to propose a modified Joback method to predict the critical temperature, critical pressure, and critical specific volume of substances accurately based on their molecular structures. The Joback and the modified Joback methods have been applied to various environmentally friendly substances as R-1225ye(Z), R-1233zd(E), R-1234yf, R-1234ze(E), R-1234ze(Z), R-1243zf, and R-1336mzz(Z) to verify their accuracy. The average absolute percentage errors (AAPE) of the predicted critical temperatures from the Joback method using the predicted normal boiling temperatures for all the studied substances is 6.03%. If the experimental normal boiling temperature is used in the prediction of the critical temperature with the Joback method, the AAPE of the predicted critical temperatures is 1.73%. When the modified Joback method is applied, the AAPE of the predicted critical temperatures is 0.63%, smaller than half of that from the Joback method. In the prediction of the critical pressure, the AAPE of the predicted critical pressures with the Joback method and the modified Joback method are 8.01% and 3.10%, respectively. The AAPE of the predicted critical specific volumes with the Joback method and the modified Joback method are 1.93% and 1.49%, respectively. The study also shows the advantages of the modified Joback method, especially in the prediction of the critical temperature compared to some other available methods.

The change in the phase diagram of a simple substance at decreasing of the nano-system size

On the basis of proposed earlier the three-phase model of simple matter and the RP(vac)-model of a nanocrystal, the equation for the free Helmholtz energy of a nanocrystal, in which take into account both lattice vacancies and delocalized (diffusing) atoms was obtained. A model of the Gibbs surface is proposed, on which a part of the cells is vacant, and some of the atoms are in a delocalized state. It is taken into account that some of the delocalized atoms are delocalized according to the “bulk” manner and some by the “surface” way. The state equation was calculated for argon, the atoms of which interacted by the Mie-Lennard-Jones pairwise potential. Calculations for the macro-system showed that at middle temperatures the state equation has two S-loops on isotherms that correspond to phase transitions (PT) crystal-liquid (C-L) and liquid-gas (L-G). At high temperatures, the S-loop for PT L-G decreases to a critical point. At low temperatures, two S-loops of the PT C-L and L-G merge into one large S-loop corresponding to the PT crystal-gas. When the number of atoms (N) in nano-system decreases the S-loops for PT C-L and L-G on the isotherm decreases, and for a certain value of the number of atoms (N0), the S-loop for PT C-L disappears. It is shown that the value of N0 increases both with increasing temperature on the isotherm and when the shape of the nano-system deviates from the most energetically optimal shape (for a RP(vac)-model, this is a cube). In a cluster of N < N0 atoms, the PT C-L are no longer present. Such a cluster at an isothermal increase in the specific volume smoothly passes into the liquid phase. At a decrease in the number of atoms, the S-loop for the PT of L-G also decreases. The parameters of the critical point for the L-G phase transition at a decrease in the number of atoms also change: the critical temperature and pressure decrease, and the critical specific volume increases.

P–V criticality in the extended phase–space of charged accelerating AdS black holes

In this paper, we investigate the P–V criticality and phase transition of charged accelerating AdS black holes in the extended thermodynamic phase–space in analogy between black hole system and van der Waals liquid–gas system, where the cosmological constant [Formula: see text] is treated as a thermodynamical variable interpreted as dynamic pressure and its conjugate quantity is the thermodynamic volume of the black holes. When the electric charge vanishes, we find that no P–V criticality will appear but the Hawking–Page-like phase transition will be present, just as what Schwarzschild-AdS black holes behave like. For the charged case, the P–V criticality appears and the accelerating black holes will undergo a small black hole/large phase transition under the condition that the acceleration parameter A and the horizon radius rh meet a certain simple relation Arh = a, where a is a constant in our discussion. To make P–V criticality appear, there exists an upper bounds for constant a. When P–V criticality appears, we calculate the critical pressure P[Formula: see text], critical temperature T[Formula: see text] and critical specific volume r[Formula: see text], and we find that [Formula: see text] is an universal number.

Combined effects of f(R) gravity and conformally invariant Maxwell field on the extended phase space thermodynamics of higher-dimensional black holes

In this paper, we investigate the thermodynamics of higher-dimensional $f(R)$ black holes in the extended phase space. Both the analytic expressions and numerical results for the possible critical physical quantities are obtained. It is proved that meaningful critical specific volume only exists when $p$ is odd. This unique phenomenon may be attributed to the combined effect of $f(R)$ gravity and conformally invariant Maxwell field. It is also shown that the ratio $P_cv_c/T_c$ differs from that of higher dimensional charged AdS black holes in Einstein gravity. However, the ratio for four-dimensional $f(R)$ black holes is the same as that of four-dimensional RN-AdS black holes, implying that $f(R)$ gravity does not influence the ratio. So the ratio may be related to conformally invariant Maxwell field. To probe the phase transition, we derive the explicit expression of the Gibbs free energy with its graph plotted. Phase transition analogous to the van der Waals liquid-gas system take place between the small black hole and the large black hole. Classical swallow tail behavior, characteristic of first order phase transition, can also be observed in the Gibbs free energy graph. Critical exponents are also calculated. It is shown that these exponents are exactly the same as those of other AdS black holes, implying that neither $f(R)$ gravity nor conformally invariant Maxwell field influence the critical exponents. Since the investigated black hole solution depends on the form of the function $f(R)$, we discuss in detail how our results put constraint on the form of the function $f(R)$ and we also present a simple example.

Computation of liquid-vapor critical points for multi-component mixtures

Liquid-vapor critical point for a thermodynamic mixture is an important parameter for the design of mixture transportation and processing. The classical critical points model for the multicomponent mixture is based on the tangent plane distance in terms of the Helmholtz energy. In this work, we have applied the damped Newton-Raphson scheme to solve the model using the critical temperature, critical specific volume and change in mole fraction of each component as independent variables. According to numerical experiments, the convergence criteria, initial guesses of variables and damped factor formulation were determined. The method was tested on twenty five mixtures containing two to eleven components using the SRK and PR equation of state. Comparisons between the calculated critical parameters and experimental values illustrated the overall accuracy of the solution method is satisfactory. This method can solve all the variables simultaneously using the whole iteration, which is more reliable than the nested two-singe variable loops method proposed by Heidemann and Khalil. Thus it can be used for practical purposes of locating the liquid-vapor critical points of multi-component mixtures.

Synthetic fluid inclusions: IX. Critical PVTX properties of NaCl-H2O solutions

Critical PVTX properties of NaCl-H2O fluids having compositions of 0–30 wt% NaCl have been determined using the synthetic fluid inclusion technique. Critical temperatures and pressures increase from 374.1°C and 220 bars for pure H2O, to 820°C and 1574 bars for 30.0 wt% NaCl. Critical specific volumes decrease from 3.11 to 1.44 cm3/g over this same salinity range. Critical temperatures of NaCl-H2O fluids over the range 0–30 wt% NaCl are described by the equation T = 374.1 + 8.800φ + 0.1771φ2 − 0.02113φ3 + 7.334·10−4φ4 where T is the critical temperature in degrees Celsius (±4.0°C) and φ is fluid composition in weight percent NaCl. The critical pressure, determined from the intersection of the critical isochore with the critical temperature in P-T space, is expressed as a function of the critical temperature according to the relationship P = 2094 − 20.56T + 0.06896T2 − 8.903 × 10−5T3 + 4.214·10−8T4 where P is the critical pressure in bars (±21 bars) and T is the critical temperature in degrees Celsius. The critical specific volume is given as SV = 3.106 − 0.5967ψ − 0.01066ψ2 + 0.01267ψ3 where SV is the critical specific volume in cm3/g (± 0.02 cm3/g) and ψ is related to the salinity as ψ = ln (wt% NaCl + 1) The slopes (ΔPΔT) of P−T projections of the critical isochores increase regularly with increasing salinity, from ~2.8 bars/°C for pure H2O to ~6.8 bars/°C for a 30 wt% NaCl solution.

Heat transfer in a two-phase thermosyphon operating with a fluid in the near critical state

The heat transfer in the heating and cooling zones of a closed thermosyphon tube has been studied experimentally. Fluid pressure (0.8 ⩽ p/ p c < 1.0), heat flow rate (175 ⩽ ⩽ 1975 W) and inclination angle (0 ⩽ φ ⩽ 60°) of the tube were varied. Refrigerant R115 was used as a working fluid. According to the critical specific volume, the quantity of the fluid was determined. Boiling occurs in the heating zone and condensation appears in the cooling zone. Depending on pressure, there are three regimes of boiling : nucleate boiling, nucleate boiling in a transition regime and film boiling. In the thermosyphon, there exist laminar and turbulent film condensation, respectively. Combined heat transfer in the heating and cooling zones renders an overall performance with optimal conditions at an inclination angle of about φ = 40°, a small heat flow rate and pressures 0.9 < p/ p c < 1.0 as long as no film boiling occurs.

Experimental Study of P-V-T Properties of Fluorocarbon Refrigerant R 13 (CC1F&lt;SUB&gt;3&lt;/SUB&gt;) : Second Report : Experimental Results of the Saturation Pressure and Determination of the Critical Parameters

Measurements of the saturation pressure of fluorocarbon refrigerant R 13 (CC1F3) were conducted about 29 points using the P-V-T equipment described in the first report in the range of temperatures from -40°C to 28.7°C. An equation of the saturation pressure was formulated using these observed results and those by Riedel and by Albright et al. in the range of temperature above -140°C with a mean absolute deviation of ±0.040% concerning the present observed saturation pressure. Critical temperature was also determined with direct observation of the meniscuc using three different methods. Critical pressure was calculated from the equation of the saturation pressure at critical temperature. And also the critical specific volume was determined with Cailletet-Mathias law analyzing the P-V-T data described in the first report.

Der kritische Punkt reiner fluider Stoffe

From a study of the equation of the saturation densities and of the thermal equation of state at the critical point the critical specific volume ν kr and the derivations of the thermal equation of state at the critical point (∂ 3 p/∂ν 3) kr , (∂ 4 p/∂ν 4) kr and (∂ 3 p/∂ν 2∂ T) kr are obtained.

Heat Transfer to Sulfur Hexafluoride Near the Thermodynamic Critical Region in a Natural-Circulation Loop

Heat transfer near the thermodynamic critical region to sulfur hexafluoride was investigated in two closed natural circulation loops. The vertical distance between the test section and the heat exchanger was the primary difference between two loop configurations. Local and average heat transfer coefficients along the test section were calculated from the experimental data. Test results were correlated by the equation. (Nu)(Grf)(Pr)=0.00982(Re)11/4 The range of variables included: System pressure, 535–896 psia, mean fluid bulk temperature, 111–193 deg F; specific volume, 0.016–0.043 cu ft/lbm; heat flux, 1900–9040 Btu/hr sq ft. The highest heat transfer coefficients were obtained at system pressures and mean fluid bulk temperatures slightly greater than the critical values with mean specific volumes in the loop slightly less than the critical specific volume of the system fluid. The heat transfer coefficients were increased by expanding the vertical distance between the test section and heat exchanger.