Pressure effects specific volume

It should be noted that the acceleration component is dominant in the last part of the pipe, where, because of the rapid pressure drop and the low absolute pressure, the specific volume of the gas increases sharply. This effect is more pronounced at high mass flow rates with large values of mass flow ratio, 3 (= mjm,). As shown in Figures 3.44a and 3.446, the average friction coefficient is affected by the mixture mass flow rate m, the mass flow ratio 3, and the diameter of the pipe D. The Re is defined as... 

The systems of interest in chemical technology are usually comprised of fluids not appreciably influenced by surface, gravitational, electrical, or magnetic effects. For such homogeneous fluids, molar or specific volume, V, is observed to be a function of temperature, T, pressure, P, and composition. This observation leads to the basic postulate that macroscopic properties of homogeneous PPIT systems at internal equiUbrium can be expressed as functions of temperature, pressure, and composition only. Thus the internal energy and the entropy are functions of temperature, pressure, and composition. These molar or unit mass properties, represented by the symbols U, and S, are independent of system size and are intensive. Total system properties, J and S do depend on system size and are extensive. Thus, if the system contains n moles of fluid, = nAf, where Af is a molar property. Temperature... 

Refrigerant Evapo- rator Pressure, psia Con- denser Pressure, psia Com- pression Ratio Net Refrig- erating Effect, Btu/lb , Refrigerant Circulated, 1b /min Specific Volume of Suction Gas, ftVlb Com- pressor Displace- ment, cfm Power Consump- tion, hp... 

The PETN Detonation Pressure, P (also called the CJ Pressure), is shown as a function of packing density in Table 7 and in Fig 4. Note that the measured P values in Fig 4 lie quite close to the theoretical curve developed by Lee Homig (Ref 72), which is based on a Wilkin s type equation of state (see Vol 4, D294-L) with a Grueneisen ratio, r, for the detonation products, that is solely a function of specific volume. Shea et al obtained an effective T = 8.077 p-12.288 (Ref 74)... 

In the flow of a gas through a nozzle, the pressure falls from its initial value Pi to a value P2 at some point along the nozzle at first the velocity rises more rapidly than the specific volume and therefore the area required for flow decreases. For low values of the pressure ratio P2/P1, however, the velocity changes much less rapidly than the specific volume so that the area for flow must increase again. The effective area for flow presented by the nozzle must therefore pass through a minimum. It is shown that this occurs if the pressure ratio P2/P1 is less than the critical pressure ratio (usually approximately 0.5) and that the velocity at the throat is then equal to the velocity of sound. For expansion... 

Jenner investigated the kinetic pressure effect on some specific Michael and Henry reactions and found that the observed activation volumes of the Michael reaction between nitromethane and methyl vinyl ketone are largely dependent on the magnitude of the electrostriction effect, which is highest in the lanthanide-catalyzed reaction and lowest in the base-catalyzed version. In the latter case, the reverse reaction is insensitive to pressure.52 Recently, Kobayashi and co-workers reported a highly efficient Lewis-acid-catalyzed asymmetric Michael addition in water.53 A variety of unsaturated carbonyl derivatives gave selective Michael additions with a-nitrocycloalkanones in water, at room temperature without any added catalyst or in a very dilute aqueous solution of potassium carbonate (Eq. 10.24).54... 

For liquids stored at their saturation vapor pressure, P = Ps, and Equation 4-91 is no longer valid. A much more detailed approach is required. Consider a fluid that is initially quiescent and is accelerated through the leak. Assume that kinetic energy is dominant and that potential energy effects are negligible. Then, from a mechanical energy balance (Equation 4-1), and realizing that the specific volume (with units of volume/mass) v = 1/p, we can write... 

Calculation of the pressure drop and flooding rate is particularly important for vacuum columns, in which the pressure may increase severalfold from the top to the bottom of the column. When a heat-sensitive liquid is distilled, the maximum temperature, and hence the pressure, at the bottom of the column is limited and hence the vapour rate must not exceed a certain value. In a vacuum column, the throughput is very low because of the high specific volume of the vapour, and the liquid reflux rate is generally so low that the liquid flow has little effect on the pressure drop. The pressure drop can be calculated by applying equation 4.15 over a differential height and integrating. Thus ... 

Any characteristic of a system is called a property. The essential feature of a property is that it has a unique value when a system is in a particular state. Properties are considered to be either intensive or extensive. Intensive properties are those that are independent of the size of a system, such as temperature T and pressure p. Extensive properties are those that are dependent on the size of a system, such as volume V, internal energy U, and entropy S. Extensive properties per unit mass are called specific properties such as specific volume v, specific internal energy u, and specific entropy. s. Properties can be either measurable such as temperature T, volume V, pressure p, specific heat at constant pressure process Cp, and specific heat at constant volume process c, or non-measurable such as internal energy U and entropy S. A relatively small number of independent properties suffice to fix all other properties and thus the state of the system. If the system is composed of a single phase, free from magnetic, electrical, chemical, and surface effects, the state is fixed when any two independent intensive properties are fixed. 

For the forced convective region, only limited data are available on the effects of the different variables involved, since the existence of this region has only been recognized recently. As previously mentioned, the velocity required for the suppression of nucleate boiling increases with pressure further, an increase in pressure reduced the specific volume of the vapour and hence the linear velocity of the two phase mixture at a given quality will be reduced. Thus higher velocities and steam qualities would be required for the forced convective region to be entered at the same heat flux. The effect of diameter is, as far as can be seen from the work of previous experiments and from these experiments, that to be expected with convective heat transfer, namely, that the coefficient is proportional to the diameter or the equivalent diameter to the power —02. 

The distance between chemically bound atoms in many molecules is shorter than the sum of the radii of the same atoms when free, and the specific volume of the compound may be actually smaller than the total covolume of its gaseous products. If, as seems plausible, the drastic compression within the detonation front ruptures chemical bonds, many atoms suddenly expand, exerting forces like those by which solids resist compression. Such forces could result in a spike pressure much higher than the peak pressure of the non-reactive shock front, exert a brisant effect on the surroundings, and expedite the progress of the detonation wave. This view accords with observations of cases in which... 

Before studying the properties of gases and liquids, we need to understand the relationship between the two phases. The starting point will be a study of vapor pressure and the development of the definition of the critical point. Then we will look in detail at the effects of pressure and temperature on one of the intensive properties of particular interest to petroleum engineers specific volume. 

As there exists a phase equilibrium both phases must have reached in the internal thermodynamic equilibrium with respect to the arrangement and distribution of the molecules the measuring time. Therefore, no time effects or path dependencies of the thermodynamic properties in the liquid crystalline phase should be expected. To check this point for the l.c. polymer, a cut through the measured V(P) curves at 2000 bar has been made (Fig. 6) and the volume values are inserted at different temperatures in Fig. 7, which represents the measured isobaric volume-temperature curve at 2000 bar 38). It can be seen from Fig. 7 that all specific volumes obtained by the cut through the isotherms in Fig. 6 he on the directly measured isobar. No path dependence can be detected in the l.c. phase. From these observations we can conclude that the volume as well as other properties of the polymers depend only on temperature and pressure. The liquid crystalline phase of the polymer is a homogeneous phase, which is in its internal thermodynamic equilibrium within the normal measuring time. 

The specific volume was slightly lower for a sample of very high molecular weight and was reflected by an increase in c to 156° C. This effect was attributed to the very high melt elasticity of this polymer. One consequence of the finite value of c is that the internal pressure is not constant as it is for melted polyethylene but decreases with increasing volume. 

Lupton, J. M. Effect of pressure on the specific volume of polymer melts. Meeting of the American Chemical Society, Chicago, September 1958. 

Abstract. Walter Kauzmann stated in a review of protein thermodynamics that volume and enthalpy changes are equally fundamental properties of the unfolding process, and no model can be considered acceptable unless it accounts for the entire thermodynamic behaviour (Nature 325 763-764, 1987). While the thermodynamic basis for pressure effects has been known for some time, the molecular mechanisms have remained rather mysterious. We, and others in the rather small field of pressure effects on protein structure and stability, have attempted since that time to clarify the molecular and physical basis for the changes in volume that accompany protein conformational transitions, and hence to explain pressure effects on proteins. The combination of many years of work on a model system, staphylococcal nuclease and its large numbers of site-specific mutants, and the rather new pressure perturbation calorimetry approach has provided for the first time a fundamental qualitative understanding of AV of unfolding, the quantitative basis of which remains the goal of current work. 

The volume changes on mixing non-aqueous liquids, the densities of mixed liquids, of solutions of non-polar solutes in non-polar solvents, and the changes of total volume on the solution of solid salts in water, noticed at an early period and much investigated, can only be mentioned here some aspects of these will be dealt with later. Hyde found the densities of solutions of jp-nitrotoluene in carbon disulphide smaller than the density of either component, but the anomaly disappears if the p-nitrotoluene is supposed to be in the liquid state. Biron found that the volume change on mixing two liquids was Av=kx( —x where x , (1— ) are the mol fractions, and he investigated the effect of pressure on the value of Av. The apparent specific volume of alcohol in aqueous mixtures was determined by Brown, lo... 

The number of formulae representing the effect of temperature on latent heat, and empirical formulae for latent heats, is large, and latent heat is a quantity which is peculiarly adaptable to representation by empirical formulae, some of which agree with experiment for one group of liquids and fail for others. In the following, 4 and 4/ are the total and internal ( l.VIIIL) latent heats in g.cal. per g., L =M1 and Qg the densities in g./ml. of liquid and vapour, vt, Vg the specific volumes of liquid and vapour in ml. /g., p the vapour pressure, T the abs. temp., Tb the b.p. abs., Tc the critical temperattire, pc the critical pressure, Vc the critical volume, Qc the critical density, d —TjTc r=TdT, c or Cp is the specific heat, M=mol. wt., a=coefiicient of expansion of liquid, =compressibility of liquid, k, K, ki, k2, Aq, B, m, , /q, s are constants. 

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