Constant pressure system

When we transfer energy to a constant-pressure system as hear, the enthalpy of the system increases by that amount. When energy leaves a constant-pressure system as heat, the enthalpy of the system decreases by that amount. For example, the formation of zinc iodide from its elements is an exothermic reaction that (at constant pressure) releases 208 kj of heat to the surroundings for each mole of Znl2 formed ... 

Two types of instruments are employed to determine the specific surface area by permea-metry. Those of the first type are called constant pressure systems, and the Fisher subsieve sizer is a typical example that belongs to such systems. Instruments of the second type are known as constant volume permeameters, and the apparatus devised by Blain is an example. 

Equations 3.1.47 and 3.1.50 express the relation between system concentrations and the fraction conversion for variable-volume systems that satisfy the linearity assumption of equation 3.1.40. This assumption is a reasonably unre-strictive one that is valid for all practical purposes in isothermal constant pressure systems in... 

Hence, for a constant pressure system, an infinitesimal change in temperature gives an infinitesimal change in enthalpy and the constant of proportionality is the heat capacity at constant pressure. 

For an adiabatic constant pressure system the first law reduces to... 

By following the change in volume of a constant-pressure system. 

While Eqs. (9)-(16) provide a recipe for evaluating Sc T) for constant volume (V) systems (i.e., constant cj)), they can easily be applied to constant pressure systems by computing cj) for a given pressure P and temperature T from the equation of state. For internal consistency, this equation of state must be derived from the free energy T expression appropriate to the /-ensemble. 

Substituting these definitions and the species continuity equation, the energy equation for the constant-pressure system becomes... 

The stop-flow technique is the simplest and least expensive method of injection. The flow of the mobile phase is first stopped, either by turning an on—off valve in the line before the column (with constant-pressure systems), or by stopping the pump (with constant-flow systems). The column then returns rapidly to atmospheric pressure, and the sample can be injected directly on to the column with a normal low-pressure syringe. 

In our consideration of phase equilibria at constant pressure, we imagined the overall system confined by a piston. However, when we talk about constant-pressure systems, we usually mean that the pressure is maintained by an inert gas (e.g., the atmosphere).2 In some situations, much higher constant pressures of inert gases are applied to systems. If we take a gas-condensed phase equilibrium and apply an inert gas pressure to both phases, we get, from Eqs. (31) and (33),... 

Equation (1.210) means that dP dx] = 0, and at a specified temperature and the total vapor pressure of a binary liquid mixture is a minimum or a maximum at the composition of the azeotropic mixture. A similar analysis of constant pressure systems indicates that, at a specified pressure and temperature of a binary liquid, mixture is a minimum or a maximum at the composition of the azeotropic mixture. If we simultaneously vary the temperature and pressure for an azeotropic mixture, we have the Clapeyron relation... 

Use tii instead of 0, for a closed constant-pressure system, since Q - H for such systems. 

The internal energy, or the thermodynamic energy as it is often called, arises in the statement of the first law. It is not the most convenient thermodynamic function for chemical applications. There are other, more useful, state functions available to describe systems of chemical interest, in particular, constant-temperature, constant-pressure systems undergoing chemical reactions. 

Equivalently (Figure 2.2), dS nw = 0 at equilibrium. The Gibbs function thus expresses the second law as dG < 0 for all possible processes in constant-temperature, constant-pressure systems. (Similarly, the Helmholtz free energy function. A, expresses the second law for isochoric, isothermal systems as dA < 0 for all possible processes.)... 

This form of the mass based dusty gas model equation, which corresponds with the mole based formulation (2.342), is restricted to constant pressure systems. 

Thus, in a constant-pressure system, placing a particle at a fixed position causes a change in the volume of the system V. Relation (G.26) shows that the average change in the number of particles in VCor in a T,V,N system is the same as the average number of particles occupying V (i.e., pV ) in a T, P, N system. 

The first generalization of the analysis given here is to the case of multiple chemical reactions in a closed, single-phase, constant-temperature and constant-pressure system. Using the notation of Sec. 8.3, the number of mples of species i present at any time is... 

Volume change EGD (40) Constant pressure system employed... 

Txy diagrams have entirely analogous rules, but just be aware that the graph is "reversed" somewhat in shape. It s somewhat harder to calculate even in an ideal case, requiring an iterative solution, but is more useful for isobaric (constant-pressure) systems and is worth the effort. The extreme ends of the txy diagram are the boiling temperatures of pure toluene (xb = 0) and benzene (xb = 1) at 760 mmHg. 

Enthalpy is an extensive property. The magnitude of AH is proportional to the amount of reactant consumed in the process. For example, 890 kj of heat is produced when 1 mol of CH4 is burned in a constant-pressure system ... 

The effect of different lubricant supply methods on hydrostatic bearing static stiffness is shown in Fig. 4. Hydrostatic bearing stiffness for constant pressure systems strongly depends on the type of flow restrictor (Bassani andPiccigallo 1992). The most popular flow restrictors are the capillary and oriflce types. An orifice restriction can provide a higher stiffness than a capillary restriction. The constant flow supply system gives a higher stiffness than the orifice restriction but requires expensive peripheral equipment such as a... 

As expected in a binary constant-pressure system, fixing the composition fixes the temperature. So the temperatures at the top and at the bottom do not change. In theory. 

For a system with n species, the relevant Stefan Maxwell equations for describing this constant pressure system are ... 

For constant pressure systems, the above equation becomes ... 

S. Lashkari, A. Tran, B. Krnczek, Effect of back diffusion and back permeation of air on membrane characterization in constant pressure system, J. Membr. ScL, 324, 162 (2008). 

For ideal gases, the driving force on the left side of these equations reduces to (l/P)dp/dz, which for constant pressure systems is equivalent to dy/dz, and Eqs. f 15-541 sinplify to Eqs. fl5-52a.bl. For nonideal systems, the chemical potential can be written in terms of the activity coefficients Ya nd Yb liquids or the fugacity coefficients for gases. The results for conponent A for liquids are... 

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