Conditions isobar-isothermal

The IsoSiv process is an isobaric, isothermal adsorption technique used to separate n-paraffins from gas oils. The operation conditions are approximately 370°C and 100 psi. Desorption is achieved using n-pentane or n-hexane. The solvent is easily distilled from the heavier n-paraffins and then recycled. 

We may treat this system two ways Hold temperature constant (isothermal conditions) and vary pressure and concentration, or hold pressure constant (isobaric conditions) and vary concentration and temperature. Both situations are shown in Figure 2.3. The plots in Figures 2.3a and 2.3b represent conditions for isothermal and isobaric treatments, respectively. 

Equation (49) must be substituted for V in eqn. (46) and dV/dt is to be expressed through reaction rates using equations of states under given conditions. For isobaric isothermal conditions and in the case of the applicability of the ideal gas model... 

The most stable compound of a multiphase binary system is often assumed to be the first to occur and grow at the A-B interface. The change, ArG , of the isobaric-isothermal potential (Gibbs free energy) in the reaction of formation of any compound from the elements under given conditions is usually considered to be a measure of its thermodynamic stability. The more negative the value of AfG°, the more stable the compound is. 

Under equilibrium conditions the change in isobaric-isothermal potential Gj- p) of the exchange reaction ... 

The successive Legendre transformations of E yield a state function, G, for which the natural variables p and T, are both intensive properties (independent of the size of the system). Furthermore, for dp = 0 and dT = 0 (isobaric, isothermal system), the state of the system is characterized by dG. This is clearly convenient for chemical applications under atmospheric pressure, constant-temperature conditions (or at any other isobaric, isothermal conditions). Then, in place of equation (21) for internal energy variation, we state the conditions for irreversible or reversible processes in terms of the Gibbs energy as... 

A straightforward, but tedious, route to obtain information of vapor-liquid and liquid-liquid coexistence lines for polymeric fluids is to perform multiple simulations in either the canonical or the isobaric-isothermal ensemble and to measure the chemical potential of all species. The simulation volumes or external pressures (and for multicomponent systems also the compositions) are then systematically changed to find the conditions that satisfy Gibbs phase coexistence rule. Since calculations of the chemical potentials are required, these techniques are often referred to as NVT- or NPT- methods. For the special case of polymeric fluids, these methods can be used very advantageously in combination with the incremental potential algorithm. Thus, phase equilibria can be obtained under conditions and for chain lengths where chemical potentials cannot be reliably obtained with unbiased or biased insertion methods, but can still be estimated using the incremental chemical potential ansatz [47-50]. 

And at last, if we assume dP = 0 and dT= 0, we will get isobar-isothermal conditions, under which maximum useful work is equal... 

The sum U + PV - TS = F + PV = H - TS = Z characterizes extensive property called isobar-isothermal potential. It was introduced in 1874 by Josiah Willard Gibbs (1839-1903) and initially also called by him free energy, which caused confusion. To put things in order, this potential was renamed Gibbs free energy. In its content it is enthalpy without kinetic energy of motion. For this reason isobaric-isothermal potential is often called also free enthalpy. It follows from this that under the isobaric-isothermal conditions the measure of maximum useful work is free enthalpy... 

We considered energies of simple departure of Pt from the surface as cation by means of semiempirical method PM6. Activation energies are included into Table 5 in several possible species of complexes. These surface complexes are formed and stabilized by Pt cation interaction with molecules and ions from the environment. Our calculation confirmed existence of prevailing compound [Pt(OH) (Up) (under the condition of exclusion of other harmful ions), while it is accompanied by the largest changes of Gibbse isobar-isotherm potential, whereas the activation energy of its departure is the lowest. 

The steady-state conditions permit equations (3) to be used and to be applied only to the balance of the species, as the conditions are isothermal and isobaric ... 

This computer program calculates a batch reactor working under different conditions (adiabatic, isothermal, isobaric, isochoric) and carries out a sensitivity analysis of the reaction mechanisms. It is part of the CHEMKIN system. 

This amount of heat is to be removed (negative sign) on condensation and needs to be supplied (positive sign) on melting if isobaric isothermal conditions are intended. The following expression is called differential solution enthalpy or differential heat of solution of the constituent b ... 

For isobaric-isothermal conditions the characteristic Gibbs function reduces to... 

In Chapter 3, the states of a system were specified by p, V, and other variables. It was shown that information in the statistical sense was low in most cases and indeed bordered on zero. The reason is that fluctuations wield only tiny impacts for large volume, multiparticle systems under equilibrium conditions. Matters are different when structured programs are applied. All the programmed pathways of Chapters 4 and 5 featured extended collections of states. For a given collection, there was appreciable information allied with the variables in query-and-measurement exercises. The exceptions were n for closed systems, and p, T, S, and so forth for isobaric, isothermal, and adiabatic—the special transformations of thermodynamics. 

Liquid-in-glass thermometers 200-500 K To lO- K Isobaric, isothermal conditions Large heat capacity and sluggishness, numerous error sources... 

In isobaric isothermal conditions, being confronted with the intervention of the two processes of nucleation and growth, two types of kinetic curves (Figure 13.1) have been reported ... 

In general the experimental data presented and easily accessible are the variations of the mass of solids with time under isobaric-isothermal conditions... 

A reaction heat is called the largest possible amount of heat generated or absorbed during the reaction, assuming that the transformation takes place in isothermal conditions, and that also a constant value is kept for one of the parameters pressure or volume. Therefore, a distinction is made between heat of reaction for an isochoric-isothermal Q ) or isobaric-isothermal Qp) reaction. They differ from each other, but are referred to as 1 kmol or 1 kg. 

However, it is common practice to sample an isothermal isobaric ensemble NPT, constant pressure and constant temperature), which normally reflects standard laboratory conditions well. Similarly to temperature control, the system is coupled to an external bath with the desired target pressure Pq. By rescaling the dimensions of the periodic box and the atomic coordinates by the factor // at each integration step At according to Eq. (46), the volume of the box and the forces of the solvent molecules acting on the box walls are adjusted. 

Just as one may wish to specify the temperature in a molecular dynamics simulation, so may be desired to maintain the system at a constant pressure. This enables the behavior of the system to be explored as a function of the pressure, enabling one to study phenomer such as the onset of pressure-induced phase transitions. Many experimental measuremen are made under conditions of constant temperature and pressure, and so simulations in tl isothermal-isobaric ensemble are most directly relevant to experimental data. Certai structural rearrangements may be achieved more easily in an isobaric simulation than i a simulation at constant volume. Constant pressure conditions may also be importai when the number of particles in the system changes (as in some of the test particle methoc for calculating free energies and chemical potentials see Section 8.9). 

For a process carried out under isothermal and isobaric conditions... 

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