# Thermodynamics and spontaneity

The first law of thermodynamics is basically the law of conservation of energy as relevant to thermodynamic systems. The change in internal energy of a system, (ΔU) is equal to the sum of the heat and work (q + w) of the system.
The second law of thermodynamics describes whether or not a change is spontaneous, expressing it in terms of entropy.

Entropy (S), is the thermodynamic quantity that describes the disorder, (randomness) in a system. The entropy is related to the number of states a molecule has available to it. A molecule at high temperature has more vibrational states available than one at a lower temperature, and therefore has a higher entropy. A crystal locks molecules into a certain configuration, whereas molecules in a gas are free to move about and therefore have higher entropy.

The second law of thermodynamics states that the total entropy of a system and its surroundings always increases for a spontaneous process. Generally, we refer to this is the entropy of the universe, as the sum of the entropies of the system and surroundings must increase, however one may decrease and the process may still be spontaneous.

ΔSuniverse = ΔSsystem +ΔSsurroundings

We can restate this law so it refers only to the system, and as heat flows into or out of the system, the entropy goes with it. So, at a certain temperature, the entropy is associated with heat q;

ΔS > q/T for a spontaneous process

Therefore, for a spontaneous process at a certain temperature, the change in the entropy must be greater than the heat divided by the absolute temperature. For systems that are at equilibrium, the entropy is equal to the heat over temperature.

Phase changes:

The entropy of a phase change is derived from the equation above.

ΔS=ΔH/T

Where the ΔH is the heat of the phase change, and the temperature at which the phase change occurs.

Spontaneity:

Looking at entropy and enthalpy, we can determine whether or not a process is spontaneous, and we introduce the concept of free energy (sometimes called Gibbs’ free energy, ΔG), which is equal to:

ΔG = ΔH – TΔS

For a spontaneous process, ΔG ≤ ΔH – TΔS, (ie, negative). We want the TΔS term to be larger than the ΔH term, indicating that even if a reaction is endothermic, if ΔS is larger, the reaction will still proceed.