Phase transitions entropy changes

The corrections are significant if the absolute value of reaction energy is very large thus, they mainly affect initiation reaction and radical recombinations. The first consideration regards initiation reactions. Unlike the case of gas phase, the entropy change is related to the fact that when the two radicals are formed, they remain caged and cannot fully develop their translational and external rotational degrees of freedom (internal rotations and vibrational frequencies remain more or less the same in the reactant and in the transition state). 

It should be noted that the methodology for a and b results in a ASf s associated with the phase change from a sohd at 0 K to the liquid at Tmit No entropy changes resulting from solid transitions are taken into account, and ASfus for a substance that undergoes such a transition will be overestimated by this technique. 

The entropy change AS/ - and the volume change AV/ - are the changes which occur when a unit amount of a pure chemical species is transferred from phase I to phase v at constant temperature and pressure. Integration of Eq. (4-18) for this change yields the latent heat of phase transition ... 

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. 

Observe how in each of these four events, H is zero until, at some critical Ac (which is different for different cases), H abruptly jumps to some higher value and thereafter proceeds relatively smoothly to its final maximum value i max = log2(8) = 3 at A = 7/8. In statistical physics, such abrupt, discontinuous changes in entropy are representative of first-order phase transitions. Interestingly, an examination of a large number of such transition events reveals that there is a small percentage of smooth transitions, which are associated with a second-order phase transition [li90a]. 

Experience indicates that the Third Law of Thermodynamics not only predicts that So — 0, but produces a potential to drive a substance to zero entropy at 0 Kelvin. Cooling a gas causes it to successively become more ordered. Phase changes to liquid and solid increase the order. Cooling through equilibrium solid phase transitions invariably results in evolution of heat and a decrease in entropy. A number of solids are disordered at higher temperatures, but the disorder decreases with cooling until perfect order is obtained. Exceptions are... 

To use Eq. 1 to calculate the entropy change for a substance undergoing a transition from one phase to another at its transition temperature, we need to note three facts ... 

Cp is the specific heat at constant pressure, k is the compressibility at constant temperature. The conversion process of a second-order phase transition can extend over a certain temperature range. If it is linked with a change of the structure (which usually is the case), this is a continuous structural change. There is no hysteresis and no metastable phases occur. A transformation that almost proceeds in a second-order manner (very small discontinuity of volume or entropy) is sometimes called weakly first order . 

From Eq. (6) it clearly can be seen that pressure and temperature are related by the changes in entropy and volume for the phase change. This equation also shows that once temperature is chosen, pressure must be fixed accordingly. It is easy to show that the change in entropy for the phase transition is simply the... 

As a result, there will be a continuous change in G as the transition of one phase into another takes place. However, for some phase transitions (known as first-order transitions), it is found that there is a discontinuity in the first derivative of G with respect to pressure or temperature. It can be shown that the partial derivative of G with pressure is the equal to volume, and the derivative with respect to temperature is equal to entropy. Therefore, we can express these relationships as follows ... 

Equation (1.53) applies to each substance in a reaction and a change in the standard entropy of a reaction (p is now p° = 1 bar) going from T to T2 is given by (neglecting for simplicity first-order phase transitions in reactants and products)... 

The variation of the phase transition temperature with pressure can be calculated from the knowledge of the volume and enthalpy change of the transition. Most often both the entropy and volume changes are positive and the transition temperature increases with pressure. In other cases, notably melting of ice, the density of the liquid phase is larger than of the solid, and the transition temperature decreases... 

Differences in the Debye temperature, or in other words the vibrational character of the two phases, will modify the transitional entropy to some extent. Still, this entropy change is normally not large for transitions where the coordination number is preserved. 

Since surface pressure is a free energy term, the energies and entropies of first-order phase transitions in the monolayer state may be calculated from the temperature dependence of the ir-A curve using the two-dimensional analog of the Clausius-Clapeyron equation (59), where AH is the molar enthalpy change at temperature T and AA is the net change in molar area ... 

---