Isentropic volume changes

In Equation 2.10 B is a constant and the A/s represent the relaxation amplitudes that are proportional to the square of the isentropic volume change 0/° given by Equation 2.9 and that contains both 07 and AH°. Indeed, the propagation of ultrasonic waves in fluids gives rise to harmonic changes of p and T. The investigated equilibria are shifted periodically by these two perturbations, thus the ultrasonic relaxation amplitude dependence on... 

Fig. 8.2. Schematic cartoons illustrating various types of adiabatic volume changes. In each case the points on the PV diagram correspond to those in Figure 8.1. (a) Reversible, Isentropic. (b) Joule Expansion, (c) Joule-Thompson Expansion.

Thus, the isentropic temperature change of a van der Waals gas on the volume V is dependent solely on the van der Waals parameter b. For example, this relation is relevant for diesel engines or for the impact sensitivity of explosives. 

AV and are the isentropic and isothermal volume changes associated with the reaction 6, d, and Cp are the coefficient of thermal expansion, the density and the specific heat at constant pressure of the solution. ... 

Figure C-1 Steam values of isentropic exponent, k (for small changes in pressure (or volume) along an isentrope, pVk = constant).

In Example 14.3 and Problem 14.6 use has been made of entropy — enthalpy diagrams. The change in enthalpy due to isentropic compression or expansion may also be calculated, however, using equations 8.30 and 8.32 in Volume 1. 

From studies of the concentration dependence of density and isentropic compressibility coefficients, the apparent molar volume and the isentropic apparent molar compressibility may be obtained above and below the CMC. Such studies have recently been performed for several systems by Brun, Holland and Vikingstad32,39-41 who deduced the change in partial molar volume and compressibility on micelle formation. This gives information on the counterion hydration and the packing of the hydrocarbon chains in the micelles. 

Equation (6.54) accounts for the change of state in the isentropic processes of a gas-solid mixture in which the effect of a finite particle volume is considered. An example using this equation to obtain the speed of sound in a gas-solid mixture is introduced in the next section. 

Isentropic-isopiestic systems are of no great practical importance, and the chief value of the function H lies in its relationship to the heat of reaction at constant pressure, Qp, Suppose that we allow a chemical system to react at the atmospheric pressure, in such a manner that the only work don-e is that due to the change in the volume of the system. 

If the change of pressure with distaiKe, dp/dx, is gradual, then little energy will be lost to friction and the expansion will be close to isentropic. We will take this as a reasonable starting assumption, applicable to at least some pipe expansions, and correct any deficiencies later through the choice of the bo function. Hence we may write the specific volume at a downstream point as ... 

We have divided both numerator and denominator by the mol number to introduce now the molar quantities. Here we observe a mysterious and miraculous effect of the energy law. It is interesting to note that the isentropic application of pressure itself is not directly associated with a change of volume, however, with a change of temperature. The change of temperature effects a change in volume. So the change of volume under pressure and consequently the compression work is done in an indirect way. 

This is an extremely useful relationship, as we no longer need to measure the change in volume with respect to entropy at constant pressure It equals the isentropic change in temperature with respect to pressure. Notice that we have lost any direct relationship to any energy. 

For 9502 the heat of formation needs to be changed to 4-4.0 kcal/100 grams (from -12.48) to achieve an infinite medium C-J pressure of 300 kbar. The infinite medium 9502 isentrope from 1 mbar to 1 atmosphere is run through the C-J state of 300 kbar, 2422 K (detonation velocity of 7884 m/sec and C-J gamma of 2.867). The isentrope pressure as a function of volume is shown in Figure 6.42 for this isentrope and the gamma law isentrope. 

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