Entropy evaporation

For the evaporation process we mentioned above, the thermodynamic probability of the gas phase is given by the number of places a molecule can occupy in the vapor. This, in turn, is proportional to the volume of the gas (subscript g) 12- oc V In the last chapter we discussed the free volume in a liquid. The total free volume in a liquid is a measure of places for molecules to occupy in the liquid. The thermodynamic probability of a liquid (subscript 1) is thus V, oc V, frgg. Based on these ideas, the entropy of the evaporation process can be written as... 

A great many liquids have entropies of vaporization at the normal boiling point in the vicinity of this value (see benzene above), a generalization known as Trouton s rule. Our interest is clearly not in evaporation, but in the elongation of elastomers. In the next section we shall apply Eq. (3.21) to the stretching process for a statistical—and therefore molecular—picture of elasticity. 

Molecular Nature of Steam. The molecular stmcture of steam is not as weU known as that of ice or water. During the water—steam phase change, rotation of molecules and vibration of atoms within the water molecules do not change considerably, but translation movement increases, accounting for the volume increase when water is evaporated at subcritical pressures. There are indications that even in the steam phase some H2O molecules are associated in small clusters of two or more molecules (4). Values for the dimerization enthalpy and entropy of water have been deterrnined from measurements of the pressure dependence of the thermal conductivity of water vapor at 358—386 K (85—112°C) and 13.3—133.3 kPa (100—1000 torr). These measurements yield the estimated upper limits of equiUbrium constants, for cluster formation in steam, where n is the number of molecules in a cluster. 

With motion along the connodal curve towards the plait point the magnitudes Ui and U2, Si and S2, and ri and r2, approach limits which may be called the energy, entropy, and volume in the critical state. The temperature and pressure similarly tend to limits which may be called the critical temperature and the critical pressure. Hence, in evaporation, the change of volume, the change of. entropy, the external work, and the heat of evaporation per unit mass, all tend to zero as the system approaches the critical state ... 

For convenience and in accordance with a familiar formulation of the third law of thermodynamics, let us take our starting point for entropy measurements such that the entropy of the crystal is zero at the extremely low temperature involved. Starting with the crystal let us then form by reversible evaporation one mole of vapor at the vapor pressure. The entropy of the gas thus formed will evidently be... 

These two examples show that regular patterns can evolve but, by definition, dissipative structures disappear once the thermodynamic equilibrium has been reached. When one wants to use dissipative structures for patterning of materials, the dissipative structure has to be fixed. Then, even though the thermodynamic instability that led to and supported the pattern has ceased, the structure would remain. Here, polymers play an important role. Since many polymers are amorphous, there is the possibility to freeze temporal patterns. Furthermore, polymer solutions are nonlinear with respect to viscosity and thus strong effects are expected to be seen in evaporating polymer solutions. Since a macromolecule is a nanoscale object, conformational entropy will also play a role in nanoscale ordered structures of polymers. 

The evaporation of B is causing a significant increase in the reaction entropy. As we stated before is this necessary to reach a high energy density within the storage. 

Even if one of the processes is not chemical but is categorized as a phase change, for example, evaporation, the extended De Donder s equation (Equation 13.17), is known to be valid. Any large magnitude of entropy production rate (diS/dt) due to evaporation might give a correlation such as... 

Remember that the phase diagram s y-axis is the applied pressure. At room temperature and pressure, liquid water evaporates as a consequence of entropy (e.g. see p. 134). For this reason, both liquid and vapour are apparent even at s.t.p. The pressure of the vapour is known as the saturated vapour pressure (s.v.p.), and can be quite high. 

The symbol for entropy is S, so a change in entropy is shown as AS. The values in the preceding chart allow calculations of the entropy change when water evaporates at 25° C. 

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