Corresponding States Equation Research Articles

Efficient Multi‐walled Carbon Nanotubes/Iron Oxide Nanocomposite for the Removal of the Drug Ketoprofen for Wastewater Treatment Applications

AbstractCurrent environmental restrictions, such as the zero liquid discharge policy, require developing new methods to completely remove micropollutants from wastewater. Non‐steroidal anti‐inflammatory drugs (NSAID) are major component of such pollutants. The adsorptive removal of ketoprofen (KP), a widely prescribed NSAID, was studied using a newly synthesized magnetic adsorbent. The maximum adsorption capacity was determined to be 39.2 mg/g with almost 98 % removal for 50 mg/L KP at neutral pH. The adsorption of KP was found to be pH dependent and more efficient in acidic media. The isothermal behavior of the adsorbent followed a sigmoidal behavior and was best fitted to the corresponding‐states equation (CSE). The adsorption was found to follow second‐order kinetics with a half‐life of 4.4 min. The adsorption was also found to be exothermic and therefore it is favorable at low temperatures. The study also showed that the adsorbent can be regenerated for several adsorption‐desorption cycles. The adsorption mechanism was also explored by state‐of‐the‐art periodic quantum theoretical calculations.

Measurements of isobaric specific heat capacity (cp) for pure trans-1,3,3,3-tetrafluoropropene and (trans-1,3,3,3-Tetrafluoropropene + 1,1,1,2-tetrafluoroethane) binary mixtures at temperatures from (231.84 to 338.68) K and pressures up to 8.2 MPa

Due to the increasingly serious greenhouse effect, R134a with high global warming potential (GWP) will be phased out gradually. Pure trans-1,3,3,3-Tetrafluoropropene (R1234ze(E)) and (R1234ze(E) + 1,1,1,2-tetrafluoroethane (R134a)) mixtures have become one of the most potential alternative refrigerants owing to lower GWP. The isobaric specific heat capacity (cp) is one of the most important thermophysical properties for the design of heat exchangers and the verification of the accuracy of the equation of state (EoS). In this paper, the cp of pure R1234ze(E) and (R1234ze(E) + R134a) mixtures at temperatures from (231.84 to 338.68) K was measured by a self-design flow calorimeter, and the pressures up to 8.2 MPa. A total of 160 liquid cp data are reported, including 57 data points for pure substance and 103 data points for mixtures. Uncertainties for temperature, pressure and cp were estimated to be less than 11 mK, 0.02 MPa and 1.0 %. In addition, the experimental data were compared with the pieces of literature data and the predictions of three models (Helmholtz energy EoS, Peng-Robinson (PR) EoS and corresponding states equation (CSE)). Among the three models, the Helmholtz energy EoS gives the best description, while the prediction performance of the PR EoS is the worst, especially in the low-temperature region and the near-critical region. Then, a brief investigation was performed to understand the reasons behind these discrepancies and found that the specific volume data have a significant impact on the cp prediction for PR EoS. When using the high-precision specific volume data in the cp calculation, the prediction performance of PR EoS will be significantly improved.

A new prediction equation of compressed liquid isochoric heat capacity for pure fluids and mixtures

In this paper, a new prediction equation for compressed liquid isochoric heat capacity (cv) was developed based on the corresponding states principle (CSP). By knowing acentric factor (ω), critical parameters (Tc, pc and vc) and ideal gas isochoric heat capacity (cv,0), the new equation could predict cv for pure fluids and mixtures (including polar and nonpolar fluids) at 0.25 < Tr < 1 and 0.5 < pr < 10. The overall average absolute relative deviation (AARD) of the new equation for 25 pure fluids and 10 mixtures are 2.21% and 1.62%, respectively. A comparison was conducted between the new equation and other models (PR EoS, Helmholtz energy EoSs, generalized equation (GE) of Zhong et al. [1] and corresponding states equation (CSE) of Sheng et al. [2]). The new equation significantly improves the prediction performance for the heat capacity of important fluids, such as halogenated hydrocarbons, carbon dioxide, water and so on, compared with the existing models. Although the prediction performance of the new equation is slightly worse than that of the Helmholtz energy EoS, the new equation has a simpler form and more powerful prediction performance than the Helmholtz energy EoS for mixtures.

A new generalized corresponding-states equation of state for the extension of the Lee–Kesler equation to fluids consisting of polar and larger nonpolar molecules

The Lee–Kesler equation of state for the thermodynamic properties of small nonpolar fluids is extended to all fluids consisting of polar and larger nonpolar molecules, based on the general corresponding-states theory for highly nonspherical fluids. The thermodynamic functions are represented by an analytical equation of state. The results for polar fluids are substantially better than those obtainable from other currently available methods, while the results for nonpolar fluids are equivalent to and mostly better than those obtained by the Lee–Kesler method. The input data required are the critical temperature, the critical volume, the acentric factor and the aspherical factor, which is related to the critical compression factor; the critical volume is therefore required in the present method. The method developed in this work shows good accuracy for 15 representative nonpolar, polar, hydrogen bonding and associating fluids and provides a simple method for industrial applications. Average deviations for the compressibility factor, the heat capacity and the speed of sound for six nonpolar and nine polar fluids from the new equation of state are 0.74%, 2.1% and 2.3%, which are about 8 times smaller than those obtained from the Lee–Kesler equation (about 5.6%, 17% and 29%, respectively).

A corresponding states equation and compensation effects in crystal growth rates

AbstractInterpretation of grain size measurements in terms of the kinetics of grain growth depends on the ability to define the temperature variation of mineral growth rates. An outline is presented of the application to mineral growth rates of a corresponding states equation (CSE), which provides a relationship of growth rate to a reduced temperature function. Additionally, growth rates exhibit a 'compensation effect' between the pre-exponential constant and the activation energy in the standard Arrhenius equation, analogous to that shown by diffusion data. The general systematics of activation energy, equilibrium temperature and growth rate maxima are controlled by the relationships of the CSE, the standard Arrhenius equation and the compensation effect, and on this basis the temperature variation of growth rate between the equilibrium and the glass temperature may he estimated.

Thermodynamics of tetramethyl + tetramethyl: comparison with theory

Thermodynamic excess functions calculated from various equations of state are compared with the experimental results for tetramethyl + tetramethyl at 283.15 K. The Carnahan and Starling form of the generalized van der Waals equation of state is very successful, particularly when an adjustable energy parameter is included for the mixtures, but there is little justification for an adjustable distance parameter. The behaviour of the pure fluids is well described by an empirical corresponding-states equation and by a form of the generalized van der Waals equation for tetrahedral particles, but in each case the predictions for mixtures are disappointing.

Note on a Corresponding-States Equation of Practical Interest for General Physico-chemical Computations

Note on a Corresponding-States Equation of Practical Interest for General Physico-chemical Computations