Heats of mixing of nonelectrolytes

1979 ◽  
Vol 44 (2) ◽  
pp. 313-318
Author(s):  
Jiří Rameš ◽  
Petr Kyselka ◽  
Karel Procházka
Keyword(s):  
Hard Sphere ◽  
Helmholtz Free Energy ◽  
Contact Point ◽  
Perturbation Expansion ◽  
Liquid Mixtures ◽  
Good Qualitative Agreement ◽  
First Order ◽  
Binary Liquid ◽  
Heats Of Mixing ◽  
First Order Perturbation

The first-order perturbation method is applied to a rapid estimation of heats of mixing of binary liquid mixtures containing molecules with a negligible polarity and approximately spherical symmetry. The calculation is based on the approximate perturbation expansion of the Helmholtz free energy up to first order and requires the knowledge of the radial distribution function of the hard-sphere reference system at the contact point. Generalized relations are used for estimating the molecular parameters. The calculated values are compared with experimental data on six mixtures. Good qualitative agreement was achieved in all cases investigated.

Thermodynamic properties of binary liquid mixtures

1976 ◽  
Vol 54 (14) ◽  
pp. 2280-2282 ◽  
Author(s):  
Murari Venkata Prabhakara Rao ◽  
Puligundla Ramachandra Naidu
Keyword(s):  
Statistical Theory ◽  
Thermodynamic Properties ◽  
Binary Mixtures ◽  
Binary Systems ◽  
Liquid Mixtures ◽  
Excess Volumes ◽  
Diethyl Ketone ◽  
Binary Liquid ◽  
The Third ◽  
Heats Of Mixing

Excess volumes of the three binary mixtures: (1) cyclohexane – diethyl ketone, (2) cyclohexane–benzonitrile, and (3) toluene–benzonitrile have been measured at 303.15 K using a dilatometer. Excess volumes of the first two systems are positive over the whole range of composition and are negative for the third system. The measured excess volumes and the excess heats of mixing reported in the literature for the three binary systems have been analysed in the light of the statistical theory of liquid mixtures developed by Flory. The analysis has shown that the theory in its modified form is approximately applicable to the mixtures cyclohexane–diethylketone and cyclohexane–benzonitrile.

A simple perturbation method for electrolyte solutions

1989 ◽  
Vol 54 (11) ◽  
pp. 2872-2878
Author(s):  
Jan Sýs ◽  
Anatol Malijevský ◽  
Stanislav Labík
Keyword(s):  
Helmholtz Free Energy ◽  
Osmotic Coefficients ◽  
Perturbation Expansion ◽  
Electrolyte Solutions ◽  
Simple Expression ◽  
Monte Carlo Data ◽  
First Order ◽  
Restricted Primitive Model ◽  
Heats Of Dilution ◽  
Perturbation Potential

The first order perturbation expansion of the Helmholtz free energy was used to calculate the thermodynamic properties of aqueous electrolytes. The restricted primitive model was used as the reference system. Its properties were determined using semiempirical formulae consistent with simulated Monte Carlo data. A simple expression with two adjustable parameters was chosen for the perturbation potential. Integral heats of dilution and osmotic coefficients of alkaline halides and tetraalkylamonium bromides were calculated. An excellent agreement with the tabulated data was found up to the concentrations of 2-3mol/dm3.

Hard‐Sphere Model of Binary Liquid Mixtures

1967 ◽  
Vol 47 (7) ◽  
pp. 2248-2255 ◽  
Author(s):  
Neil S. Snider ◽  
Thelma M. Herrington
Keyword(s):  
Hard Sphere ◽  
Liquid Mixtures ◽  
Binary Liquid Mixtures ◽  
Hard Sphere Model ◽  
Sphere Model ◽  
Binary Liquid

STOCHASTIC POST-BUCKLING OF FRAMES USING KOITER'S METHOD

2006 ◽  
Vol 06 (03) ◽  
pp. 333-358 ◽  
Author(s):  
B. W. SCHAFER ◽  
L. GRAHAM-BRADY
Keyword(s):  
Monte Carlo ◽  
Perturbation Method ◽  
Perturbation Expansion ◽  
Random Variable ◽  
Order Perturbation ◽  
Initial Slope ◽  
First Order ◽  
Post Buckling ◽  
The Impact ◽  
First Order Perturbation

The objective of this paper is to explore the impact of stochastic inputs on the buckling and post-buckling response of structural frames. In particular, we examine the impact of random member stiffness on the buckling load, and the initial slope and curvature of the post-buckling response of three example frames. A finite element implementation of Koiter's perturbation method is employed to efficiently examine the post-buckling response. Monte Carlo simulations where the member stiffness is treated as a random variable, as well as correlated and uncorrelated random fields, are completed. The efficiency of Koiter's perturbation method is the key to the feasibility of applying Monte Carlo simulation techniques, which typically requires a large number of sample simulations. In an attempt to curtail the need for multiple sample calculations, an alternative first-order perturbation expansion is proposed for approximating the mean and variance of the post-buckling behavior. However, the limitations of this first-order perturbation approximation are demonstrated to be significant. The simulations indicate that deterministic characteristics of the post-buckling response can be inadequate in the face of input randomness. In one case, a frame that is stable symmetric in the deterministic case is found to be asymmetric when randomness in the input is incorporated; therefore, this frame has real potential for imperfection sensitivity. The importance of random field models for the member stiffness as opposed to random variable models is highlighted. The simulations indicate that the post-buckling response can magnify input randomness, as variability in the post-buckling parameters can be greater than the variability in the input parameters.

scholarly journals Strongly coupled overdamped pendulums

2008 ◽  
Vol 30 (4) ◽  
pp. 4304.1-4304.4
Author(s):  
R. De Luca
Keyword(s):  
Dynamical Equation ◽  
Second Harmonic ◽  
Perturbation Expansion ◽  
Order Perturbation ◽  
Dynamical Equations ◽  
Strongly Coupled ◽  
First Order ◽  
The One ◽  
First Order Perturbation

It is shown, by a first-order perturbation expansion, that the dimensionality of the dynamical equations for the angular variables of two strongly coupled identical overdamped pendulums can be reduced from two to one. The resulting dynamical equation is seen to be similar to the one of a single pendulum with an additional fictitious torque characterized by a second harmonic contribution.

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