An analytical equation of state is applied to calculate the thermodynamic properties for argon. Theequation of state is that of Song and Mason. It is based on a statistical-mechanical perturbation theory ofhard convex bodies and can be written as fifth-order polynomial in the density. There exist three temperaturedependentparameters: the second virial coefficient, an effective molecular volume,...

In this work we have used a closed system model to derive an analytical equation for the osmotic pressure of two component electrolyte and non-electrolyte solutions. In order to do so, we have used an equation of state, known as the dense system equation of state (DSEOS), for the model system. Based on the model, a new definition is given for the osmotic pressure of a closed system. Good ag...

A semi-empirical equation of state has been studied for modelling vapour-liquid data of pure substances. The specific molecular based equation of state is employed here as basis because of its mathematical simplicity. The semi-empirical extension has been accomplished to real fluids by correlating the density dependence of the attraction term to vapour liquid data of a reference fluid. The resu...

In order to obtain a solution to an optimal control problem‎, ‎a numerical technique based on state-control parameterization method is presented‎. ‎This method can be facilitated by the computation of performance index and state equation via approximating the control and state variable as a function of time‎. ‎Several numerical examples are presented to confirm the analytical findings and illus...

In this paper, we state some results on product of operators with closed ranges and we solve the operator equation $TXS^*-SX^*T^*= A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $TS = 1$. Furthermore, by using some block operator matrix techniques, we nd explicit solution of the operator equation $TXS^*-SX^*T^*= A$.

We have used a variational approach to calculate some thermodynamic properties of the quasi-one dimensional liquid 3He such as the energy, entropy, free energy, equation of state and heat capacity at finite temperature. We have employed the Lennard-Jones potential as the inter-atomic interaction. We have seen that the total energy increases by increasing both temperature and density....