Pressure volume related

Thus, from the form of (4.7), shock pressure is given as the sum of a linear and quadratic term in particle velocity, based on the data of Table 4.1. A pressure volume relation can be obtained by combining (4.6) with (4.1) to yield... 

The effect of such a transformation on a pressure-volume relation and on wave profiles is shown in Fig. 2.12. Above the transformation, its characteristics dominate the wave profile. At sufficiently high pressure, the peak pressure wave will move at higher speeds and a strong shock regime can be encountered. 

Fig. 2.22. At very high pressures the observed pressure-volume relations of porous samples show expansions due to the very high temperatures produced in collapsing the voids. The figure shows representative behavior at porous sample densities of 25% to 100% of solid density.

It has been a persistent characteristic of shock-compression science that the first-order picture of the processes yields readily to solution whereas second-order descriptions fail to confirm material models. For example, the high-pressure, pressure-volume relations and equation-of-state data yield pressure values close to that expected at a given volume compression. Mechanical yielding behavior is observed to follow behaviors that can be modeled on concepts developed to describe solids under less severe loadings. Phase transformations are observed to occur at pressures reasonably close to those obtained in static compression. 

Note that the total static pressure curve of Figure 12-145 is limited by the lowest output pressure of the multifan system. The limit curve is established using the fan curve (No. 1 in this example) having the smallest volume increment to the system resistance curve. In this situation fen No. 2 cannot add to the system until its pressure-volume relation reaches the peak point on its curve. 

The value of the integral depends on the pressure-volume relation. 

The velocity uw = fkP2v2 is shown to be the velocity of a small pressure wave if the pressure-volume relation is given by Pifi = constant. If the expansion approximates to a reversible adiabatic (isentropic) process k y, the ratio of the specific heats of the gases, as indicated in equation 2.30. 

Similarly, when the pressure-volume relation is Pvk — constant, equation 4.30 replaces equation 6.26 ... 

Thermodynamic equilibrium is found by balancing chemical potentials, where the chemical potentials of condensed species are functions of only pressure and temperature, whereas the potentials of gaseous species also depend on concentrations. To solve for the chemical potentials, it is necessary to know the pressure-volume relations for species that are important products in detonation. It is also necessary to know these relations at the high pressures and temperatures that typically characterize the C-J state. Thus, there is a need for improved high-pressure equations of state for fluids, particularly for molecular fluid mixtures. 

If the products of explosion behave as ideal gases with a constant ratio of specific heats y and are further assumed to undergo adiabatic changes, the pressure-volume relation is P(V/W)Y= k, where W is the mass of explosive products in grams and k is a constant. The internal energy E(a) is then given by... 

This procedure is called flash vaporization, flash liberation, pressure-volume relations, constant composition expansion, or flash expansion. 

Under isentropic conditions and with constant heat capacities, the pressure-volume relation is... 

BOYLE S LAW. This law, attributed to Robert Boyle (1662) but also known as Mariottc s law, expresses the isothermal pressure-volume relation for abody of ideal gas. That is, if the gas is kept at constant temperature, the pressure and volume are in inverse proportion, or have a constant product. The law is only approximately true, even for such gases as hydrogen and helium nevertheless it is very useful. Graphically, it is represented by an equilateral hyperbola (see Fig. I). If the temperature is not constant, the behavior of die ideal gas must be expressed by die Boyle-Charles law. 

The thermodynamic functions for the gas phase are more easily developed than for the liquid or solid phases, because the temperature-pressure-volume relations can be expressed, at least for low pressures, by an algebraic equation of state. For this reason the thermodynamic functions for the gas phase are developed in this chapter before discussing those for the liquid and solid phases in Chapter 8. First the equation of state for pure ideal gases and for mixtures of ideal gases is discussed. Then various equations of state for real gases, both pure and mixed, are outlined. Finally, the more general thermodynamic functions for the gas phase are developed in terms of the experimentally observable quantities the pressure, the volume, the temperature, and the mole numbers. Emphasis is placed on the virial equation of state accurate to the second virial coefficient. However, the methods used are applicable to any equation of state, and the development of the thermodynamic functions for any given equation of state should present no difficulty. 

The resulting chart record contains a point by point representation of each dose cycle. The apparatus has usually been programmed to deliver four or five consecutive doses, and then wait for equilibration. Only the equilibration points are read from the chart. The points on the chart record represent a pressure-volume relation which has not been corrected for the amount of vapor not adsorbed by the sample, the so-called dead space correction/ ... 

It has been found that the C70FX transforms from a crystalline to an amorphous phase at about 5.5 GPa [58]. Figure 16 shows the change in XRD pattern of C70FV with pressure. It indicates a discontinuous loss in the diffracted X-ray intensity between 3.8 and 5.5 GPa. The pressure-volume relation of C7(,FY was also investigated and the bulk modulus and its pressure derivative were determined to be 26.6 GPa and 3.0, respectively (see Table 3). 

Both volumetric and gravimetric techniques have been used for the determination of adsorption isotherms of gases on solids. The volumetric technique is one of the widely used methods for the adsorption isotherm determination and is based on the measurement of the pressure-volume relation to determine the... 

Pressure volume relation of three main group elements. Aluminium and sodium exhibit continuous compression behaviour in the selected pres sure range. The discontinuous volume changes of silicon are caused by structural phase transitions. 

After introducing a function for the force and using Hook s law, application of a scaling procedure results in a universal function that can be simplified into a pressure-volume relation ... 

Fig. 1. Hemodynamic effects of anandamide in anesthetized mice. Representative recordings ofthe effects of anandamide [20 mg/kg i.v., W-arachidonoyl-ethanolamine (/1 4)] on mean arterial pressure (iW/iP, top panel, cardiac contractility (left ventricular systolic pressure LVSP and dP/df (dPdt) middle panel and pressure-volume relations (bottom panel in a pentobarbital-anesthetized C57BL6 mouse. The five parts of the and bottom panels represent baseline conditions (BI, phase I (/), phase II (//), and phase III (III ofthe anandamide response, and recovery 10 min following the injection. The arrow indicates the injection ofthe drug. The decrease ofthe amplitude of PV loops and shift to the right indicate decrease of cardiac contractile performance...

Park RC, Little WC, O Rourke RA. Effect of alternation of left ventricular activation sequence on the left ventricular end-systolic pressure-volume relation in closed-chest dogs. Circ Res 1985 57(5) 706—17. 

Fig. 6. Pressure-volume relations for NO NOs and other molecular systems. NO NOs determined from the present energy-dispersive x-ray diffraction ( ) and that from previous angle-dispersive x-ray diffraction with refined cell parameters ( ), and that from C.S. Yoo et al. ( ) (Ref. [81]), compared with a third-order Birch-Mumaghan (—) and Vinet et al. EOS fits For O2 ( ) data, below 5.5 GPa are for fluid O2 (Ref. [123]) above 5.5 GPa for the solid (Ref. [124]). Experimental data for O2 (o) at several pressures performed from Ref. [125] are also plotted. For N2 ( ), experimentally determined EOS is from Ref [126], for N2O ( ) from Ref. [127]. Volumes for N2O4 ( ) determined in the present study is fitted by the Birch-Mumaghan equation of state (—) tentatively. Also shown are the corresponding volumes of stoichometrically equivalent assemblages of N2 + 2O2 (—) and N2O+ 3/2 O2 (—).

Smith, E. R., Smiseth, O. A., and Kingma, I. (1984). Mechanisms of action of nitrates. Role of changes in venous capacitance and in left ventricular diastolic pressure-volume relation. Am.J. Med. 76, 14-19. 

In Fig. 9 the pressure-volume relations of a gas-liquid system are represented. A corresponds to a dilute unsaturated vapour. On compression at constant temperature the pressure and volume change more or less in accordance with Boyle s law and the curve AB is followed. Imagine the vapour to be tested at various points by being placed in contact with a continuous surface of its liquid. Up to B, the saturation point, it would take up liquid which would evaporate into it. At B there would be equilibrium, and if in presence of the liquid the pressure were infinitesimally raised, complete condensation would occur at constant pressure the line BC would be followed to the point C. If pressure were raised further, the compression curve of the liquid, CD, would be traversed. The only variable... 

Maughan W.L., Sunagawa K., Burkhoff D., et al. 1984. Effect of arterial impedance changes on the end-systolic pressure-volume relation. Circ. Res. 54 595. 

Ventricular Hemodynamics Ventricular Pressure-Volume Relations and Energetics... 

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