Entropy thermal disorder

We can expect disorder to increase when a system is heated because the supply of energy increases the thermal motion of the molecules. Heating increases the thermal disorder, the disorder arising from the thermal motion of the molecules. We can also expect the entropy to increase when a given amount of matter spreads into a greater volume or is mixed with another substance. These processes disperse the molecules of the substance over a greater volume and increase the positional disorder, the disorder related to the locations of the molecules. 

STRATEGY We expect a positive entropy change because the thermal disorder in a system increases as the temperature is raised. We use Eq. 2, with the heat capacity at constant volume, Cv = nCV m. Find the amount (in moles) of gas molecules by using the ideal gas law, PV = nRT, and the initial conditions remember to express temperature in kelvins. Because the data are liters and kilopascals, use R expressed in those units. As always, avoid rounding errors by delaying the numerical calculation to the last possible stage. 

That is, S —> 0 as T - 0. The perfect crystal part of this statement of the third law refers to a substance in which all the atoms are in a perfectly orderly array, and so there is no positional disorder. The T— 0 part of the statement implies the absence of thermal motion-—thermal disorder vanishes as the temperature approaches zero. As the temperature of a substance is raised from zero, more orientations become available to the molecules and their thermal disorder increases. Thus we can expect the entropy of any substance to he greater than zero above T = 0. 

Potassium nitrate dissolves readily in water, and its enthalpy of solution is +34.9 kj-niol. (a) Does the enthalpy of solution favor the dissolving process (b) Is the entropy change of the system likely to be positive or negative when the salt dissolves (c) Is the entropy change of the system primarily a result of changes in positional disorder or thermal disorder ... 

The thermal data on possible condis crystals are collected in Table 8. Substantial entropy gains are observed at the disordering transition, but variations are large, depending on the amount of conformational mobility gained. When compared to the total entropy of fusion, the listed entropies of disordering vary from 30 %, for polytetrafluoroethylene, to close to 100% for the polyphosphazenes. 

Real surfaces will generally also have defects analogous to those occurring in the bulk. As the temperature of an initially ideal surface is increased a certain amount of thermal disorder in the form of vacancies, interstitials and self adsorbed ions (and their complexes) will occur due to the balancing effect of the entropy contribution. The formation energies and entropies (vibrational) associated with such defects will be different from the corresponding bulk values and hence their densities will vary with depth into the crystal. Since ionic defects are of prime importance for conduction in many ionic crystals the properties of individual surface point defects are of fundamental interest in assessing surface conductance contributions. 

The first basic disorder type to be discussed is the Frenkel disorder. Here a few cations have left their regular positions, on accoimt of the favourable configurational entropy (thermal influence), thus leaving behind vacancies, and now occupy interstitial sites. Such defects typically occur in the cationic sublattice and preferentially in cases of high polarizabihty, such as in the Ag" " sublattices of the silver halides AgCl, AgBr and Agl (see Section 5.2). 

The pattern we have identified is one version of the second law of thermodynamics. The natural progression of a system and its surroundings (which together make up the universe") is from order to disorder, from lower to higher entropy. For practical measurements, a small isolated region, such as a thermally insulated, sealed flask or a calorimeter, is considered to represent the universe. 

The resulting equilibrium concentrations of these point defects (vacancies and interstitials) are the consequence of a compromise between the ordering interaction energy and the entropy contribution of disorder (point defects, in this case). To be sure, the importance of Frenkel s basic work for the further development of solid state kinetics can hardly be overstated. From here on one knew that, in a crystal, the concentration of irregular structure elements (in thermal equilibrium) is a function of state. Therefore the conductivity of an ionic crystal, for example, which is caused by mobile, point defects, is a well defined physical property. However, contributions to the conductivity due to dislocations, grain boundaries, and other non-equilibrium defects can sometimes be quite significant. 

We consider, first, the mutual solubility of two nonpolar liquids, whose molecules have practically equal sizes, and equal attractive and repulsive forces. When they are brought into contact, thermal agitation will cause m ntnal diffusion until the two species are uniformly distributed. The mixing process has produced maximum molecular disorder, and therefore entropy, which is given by the expression, for 1 mole of solution,... 

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