Compression entropies

Structural Entropy A molar structural entropy of ions in solution, A 5, is obtained from the standard molar entropy of solvation of the ion, when certain irrelevant quantities are subtracted from the latter. These include the compression entropy (change of available volume) on transfer from the gas to the solution and contributions from the formation of the ionic solvation shell and possible limitation of the ionic rotation of a polyatomic ion in the solution compared with the gas. The terms kosmottopes for water structure-making ions and chaotropes for water structure-breaking ions were introduced by Collins [48] (Section 5.1) according to whether A S < or respectively. This view sfressed the competition... 

This expression took care of the compression entropy and the numerical coefficients pertain to ion hydration. The entropy change corresponding to the formation of the solvation shell was obtained from the temperature derivative of the Bom expression for the Gibbs energy of solvation (Section 2.3.1.4) ... 

Given saturated-liquid enthalpies and entropies, the calculation of these properties for pure compressed hquids is accomplished by integration at constant temperature of Eqs. (4-34) and (4-35) ... 

The Carnot refrigeratiou cycle is reversible and consists of adiabatic (iseutropic due to reversible character) compression (1-2), isothermal rejection of heat (2-3), adiabatic expansion (3-4) and isothermal addition of heat (4-1). The temperature-entropy diagram is shown in Fig. 11-70. The Carnot cycle is an unattainable ideal which serves as a standard of comparison and it provides a convenient guide to the temperatures that should be maintained to achieve maximum effectiveness. 

For elastic compression the entropy increase is small and can come only from effects of thermal conduction. Thus, to a very good approximation at low compressions in most materials,... 

The effect of compressibility is important in high mach number machines. Mach number is the ratio of velocity to the acoustic speed of a gas at a given temperature M = Vja. Acoustic speed is defined as the ratio change in pressure of the gas with respect to its density if the entropy is held constant ... 

The transition from a ferromagnetic to a paramagnetic state is normally considered to be a classic second-order phase transition that is, there are no discontinuous changes in volume V or entropy S, but there are discontinuous changes in the volumetric thermal expansion compressibility k, and specific heat Cp. The relation among the variables changing at the transition is given by the Ehrenfest relations. 

In adiabatic compression or expansion, no release or gain of heat by the gas occurs, and no change occurs in entropy. This condition is also known as isentropic and is typical of most compression steps. Actual conditions often cause a realistic deviation, but usually these are not sufficiently great to make the calculations in error. Table 12-4 gives representative average k values for a few common gases and vapors. 

Follow the constant entropy (isentropic compression) line from the suction point until it intersects the discharge pressure line at 250 psia. 

For points 2-3, there is constant entropy (S) compression for a one pound of air from Pg to P3. From points 3-5 the air cools at constant pressure, and gives up heat, Q, to the intercooler. From points 5-6 the air is compressed at constant S to the final pressure Pg. Note that point Tj = point Tg for constant temperature. For minimum work Tg = T3. Then the heat, Q, equals the Work, Wl of Figure 12-36B. Figure 12-38 is convenient for estimating the moisture condensed from an airstream, as well as establishing the remaining water vapor in the gas-air. 

Adiabatic compression (termed adiabatic isentropic or constant entropy) of a gas in a centrifugal machine has the same characteristics as in any other compressor. That is, no heat is transferred to or from the gas during the compression operation. The characteristic equation... 

Polytropic compression is characterized by being neither adiabatic nor isothermal but is a variable entropy process. Its relation is expressed... 

Figure 12-70. Entropy-temperature diagrams help to solve compression work problems. Data for ammonia provided. (Used by permission Corrigan, T. E. and A. F. Johnson. Chemical Engineering, V. 61, No. 1, 1954. McGraw-Hill, Inc. All rights reserved.)...

To analyze compressible flow through chokes it is assumed that the entropy of the fluid remains constant. The equation of isentropic flow is... 

If the system is not isolated, its entropy may either increase or decrease. Thus, if a mass of gas is compressed in a cylinder impervious to heat, its entropy increases, but if heat is allowed to pass out into a medium, the entropy of the gas may decrease. By including the"gas and medium in a larger isolated system, we can apply (10) of 45, and hence show Jhat the medium gains more entropy than the gas loses. An extended assimilation of this kind shows that, if every body affected in a change is taken into account, the entropy of the whole must increase by reason of irreversible changes occurring in it. This is evidently what Clausius (1854) had in mind in the formulation of his famous aphorism The entropy of the universe strives towards a maximum. The word universe is to be understood in the sense of an ultimately isolated system. 

A three-stage compressor is required to compress air from 140 kN/m2 and 283 K to 4000 kN/m2. Calculate fee ideal intermediate pressures, the work required per kilogram of gas, and fee isothermal efficiency of fee process. Assume the compression to be adiabatic and the interstage cooling to cool the air to the initial temperature. Show qualitatively, by means of temperature-entropy diagrams, fee effect of unequal work distribution and imperfect intercooling, on the performance of the compressor. 

Calculate the ideal intermediate pressures and the work required per kilogram of gas. Assume compression to be isentropic and the gas to behave as an ideal gas. Indicate on a temperature-entropy diagram the effect of imperfect imercooling on the work done at each stage. 

Self-Test 7.3A Calculate the change in molar entropy of an ideal gas when it is compressed isothermally to one-third its initial volume. 

The entropy change accompanying the isothermal compression or expansion of an ideal gas can be expressed in terms of its initial and final pressures. To do so, we use the ideal gas law—specifically, Boyle s law—to express the ratio of volumes in Eq. 3 in terms of the ratio of the initial and final pressures. Because pressure is inversely proportional to volume (Boyle s law), we know that at constant temperature V2/Vj = E /E2 where l is the initial pressure and P2 is the final pressure. Therefore,... 

The entropy decreases, as expected for a sample that has been compressed into a smaller volume at constant temperature. 

Note that the change in entropy due to the five-fold compression is much greater than that due to the small rise in temperature. 

Calculate the entropy change associated with the isothermal compression of 6.32 mol of ideal gas atoms from 6.72 atm to 13.44 atm. 

Salts of fatty acids are classic objects of LB technique. Being placed at the air/water interface, these molecules arrange themselves in such a way that its hydrophilic part (COOH) penetrates water due to its electrostatic interactions with water molecnles, which can be considered electric dipoles. The hydrophobic part (aliphatic chain) orients itself to air, because it cannot penetrate water for entropy reasons. Therefore, if a few molecnles of snch type were placed at the water surface, they would form a two-dimensional system at the air/water interface. A compression isotherm of the stearic acid monolayer is presented in Figure 1. This curve shows the dependence of surface pressure upon area per molecnle, obtained at constant temperature. Usually, this dependence is called a rr-A isotherm. 

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