Second Law of Thermodynamics

Look closely at two everyday spontaneous processes -- ice melting, and water evaporating -- and a common pattern emerges: in both, the RANDOMNESS or disorder of the system increases. In solid ice, the water molecules are locked into a highly organised crystal pattern, permitting almost no independent movement. As the ice melts, those molecules become disorganised and gain freedom to move; the freedom grows further still once the molecules escape into the vapour phase. Put another way: the randomness of the water molecules keeps increasing as ice melts into water, and again as water evaporates into vapour. Both of these are spontaneous processes, and both result in an INCREASE in randomness -- that is, in entropy. …

It is possible to calculate the actual, absolute entropy of a substance at any temperature above 0 K -- unlike internal energy or enthalpy, where only CHANGES are ever measurable, entropy has a genuine absolute zero point to measure from. The absolute entropy of a substance at 298 K and one bar pressure is called its standard entropy, $S^0$. The third law of thermodynamics (Section 7.12) states, following Nernst, that the absolute entropy of elements is exactly zero ONLY at 0 K in a perfect crystal, and that standard entropies of all substances at any temperature above 0 K always come out positive.

Once the entropies of the individual substances involved are known, the standard entropy change, $\Delta S_r^0$, for a chemical reaction can be calculated directly:

Standard entropy of formation, $\Delta S_f^0$, is defined as "the entropy of formation of 1 mole of a compound from the elements under standard conditions" -- calculable from the individual $S^0$ values of the elements involved, exactly the way $\Delta H_f^0$ is built from elemental enthalpies. …

When a substance changes state -- solid to liquid (melting), liquid to vapour (evaporation), or solid to vapour (sublimation) -- there is necessarily a change in entropy. Because the two phases are in equilibrium with each other during such a change, it can be treated as occurring reversibly at constant temperature, giving the general relation:

Entropy of fusion. The heat absorbed when one mole of a solid melts reversibly at its melting point is the molar heat of fusion, $\Delta H_{fusion}$. The associated entropy change is

where $T_f$ is the melting point.

Entropy of vapourisation. The heat absorbed when one mole of liquid boils reversibly at its boiling point is the molar heat of vapourisation, $\Delta H_v$. The entropy change is

where $T_b$ is the boiling point.

Entropy of transition. The heat change when one mole of a solid changes reversibly from one allotropic form to another, at its transition temperature, is the enthalpy of transition, $\Delta H_t$. The entropy change is

where $T_t$ is the transition temperature. …