Isochoric conditions

Tab. 4.15 Computed (EXPL05) gun propellant parameters for a single, double and triple base propellant in comparison with a new high-nitrogen formulation (isochoric conditions).

In what follows we distinguish again between mechanical and nonmechanical work by setting W = di Wm + dWn and ds = de + dsn- In the Exercises the reader is asked to show that dsm and ds must separately be nonnegative. If, in addition to T, the volume V is held fixed (isothermal-isochoric conditions, for which no mechanical work is possible) then the above expressions reduce to... 

A special case arises if the volume is also held fixed under such isentropic-isochoric conditions... 

Electromagnetic Effects Under Isothermal-Isochoric Conditions... 

In eqs Al-1—Al-3, k is the Boltzmann constant, T is the absolute temperature, Np is the number of particles of species / in the volume v, is the chemical potential per molecule of species a, Va is the partial molar volume per molecule of species a, kf is the isothermal compressibility, and Ca is the bulk molecular concentration of component a (ca = Na/v). The derivative (dfiJdNp)T,v y f is taken rmder isothermal—isochoric conditions and with Ny = constant for any y B o/3 represents the cofactor... 

The development thus far has implicitly assumed constant-volume (isochoric) conditions. Constant-pressure (isobaric) conditions are also... 

Nevertheless we determine Ta in the same marmer as for salol. Although ta is more than four times larger than for salol, it is again constant for isobaric conditions at any P or isochoric conditions at any V(Table 1). 

Diamond cell experiments were performed between -40° and 60°C, and at pressures up to 900 MPa. To prepare samples, synthetic methane hydrate [11, 12] was loaded in the sample chamber of the cell. After the sample chamber is sealed, the total mass of the sample remains constant. The bulk density (and sample pressure) is then adjusted by changing the volume of the sample chamber, which is achieved by adjusting the distance between the two diamond-anvil faces. Once the volume of the sample chamber is fixed, the sample remains under isochoric conditions [6]. Thermal expansion of various parts of the cell, within the small temperature range of this study, has a negligible effect on the sample volume under these experimental conditions. Occasionally, samples were prepared by sealing AI4C3 and distilled water in the sample chamber, and CH4 was generated at temperatures above 200 °C by the reaction... 

The mechanical properties of a gel are influenced by the degree of swelling. The volume phase transition and therefore the switching between two temperatures (above and below the temperature for volume phase transition) can be performed as a process under isobar or under isochoric conditions. For PNIPAAm, the bulk modulus shows a strong increase at 33 °C during heating. The abmpt change in the... 

In general, an attempt is made to achieve an isochoric condition (K = 0) by temperature control in liquid solution. Such isochoric behaviour is taken for granted in the subsequent discussions. Therefore the change in concentration of each reactant can be expressed by... 

Under isothermal-isobaric-isochoric conditions, M is solely a function of and E. The dependence on E at constant defines a (normal) physical part whereas the dependence of M on at constant E may be referred to as the chemical contribution to a change in M. The field dependence of the total moment may then be expressed as... 

Historically, the first experimental determinations of the vapor densities and pressures approaching the critical region of a metal were made for mercury. Bender (1915, 1918) carried out pioneering measurements of vapor densities up to about 1400 °C. The samples in these studies were enclosed in strong fused quartz capillaries. In 1932, Birch made the first measurements of the vapor pressure of mercury and obtained realistic values for the critical temperature and pressure. Birch found values = 1460 °C and = 1610 bar, results that are remarkably close to the most accurate values available today (Table 1.1). A number of groups in various countries have contributed subsequently to the pool of pVT data currently available (Hensel and Franck, 1966, 1968 Kikoin and Senchenkov, 1967 Postill et al., 1968 Schonherr et al., 1979 Yao and Endo, 1982 Hubbard and Ross, 1983 Gotzlaff, 1988). The result is that the density data for mercury are now the most extensive and detailed available for any liquid metal. Data have been obtained by means of isothermal, isobaric, or isochoric measurements, but as we have noted in Sec. 3.5, those obtained under constant volume (isochoric conditions) tend to be preferable. In Fig. 4.10 we present a selection of equation-of-state data that we believe to be the most reliable now available for fluid... 

This method operates at isochoric condition (constant volume). A P-T cycle method is illustrated in Fig. 10.4. The crystallizer content is mixed after pressurizing with the gas. 

HS-GC) because of the high volatihty of n- C4, and studied the segregation of a second liquid phase for the solutions of 1,4-PB under isochoric conditions (instead of the usual isobaric procedure). Figure 11 shows the thus-obtained phase diagram together with the miscibility gap calculated from the measured vapor pressures. Here, it is worth mentioning that the Sanchez-Lacombe theory [4, 51] models the vapor/liquid equilibria for the present systems very well but fails totally when the parameters obtained from such measurements are applied for the calculation of liquid/liquid equilibria. 

The simple physical picture presented above has two consequences. In the first place it suggests a very simple way to include a temperature dependence in t/. Since the radius of the cavity, R, is one of the standard parameters used in implementing the cell theory, one simply needs to replace R with (T), where R(T) could be identified with the inner extremity of lattice vibrations at a given temperature. The second consequence is that the magnitude of this effect is likely to be exaggerated by the isochoral conditions used in the simulations. Under the more common isobaric conditions, the entire lattice will also expand as temperature increases. Consequently the effective size of a cavity will depend on a competition between expansion of the lattice and larger amplitude vibrations within the lattice. 

Last, in view of Eq. (1.12.1a), fluctuations in composition under adiabatic and isochoric conditions (arising, for example, through fluctuations in equilibrated chemical equations, triggered by temperature fluctuations) are subject to the constraint that at equilibrium is at a minimum ... 

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