__Spontaneity, Entropy, and Free Energy.__

__Spontaneity, Entropy, and Free Energy.__

Spontaneity is a process which occurs by a natural tendency without any external cause.

Examples of spontaneous process: Water freezes spontaneously at temperature below 0 degree Celsius. Ball placed at the top of an incline spontaneously rolls down the incline. Heat flows spontaneously from a hot object to a cooler object. Scientists have found that all the spontaneous processes share a common property called entropy.

Entropy is related with the distribution of energy in the particles of a given system. A system that can be found in a large number of states are more disordered than a system that can found in a smaller number of states.

Therefore, entropy is associated with disorder, randomness, and positional probability of particles in a system.

Examples: Evaporation of water H20 (l) -----> H20 (g) In evaporation of water, entropy increases because positional probability, randomness, and disorder of water molecules increase since water molecules in gaseous phase have more space to move around. Similarly, in condensation of water, entropy decreases because of decreases in positional probability, randomness, and disorder. Entropy decreases in precipitation of solid from solution because of similar reason.

Examples of spontaneous process: Water freezes spontaneously at temperature below 0 degree Celsius. Ball placed at the top of an incline spontaneously rolls down the incline. Heat flows spontaneously from a hot object to a cooler object. Scientists have found that all the spontaneous processes share a common property called entropy.

Entropy is related with the distribution of energy in the particles of a given system. A system that can be found in a large number of states are more disordered than a system that can found in a smaller number of states.

Therefore, entropy is associated with disorder, randomness, and positional probability of particles in a system.

Examples: Evaporation of water H20 (l) -----> H20 (g) In evaporation of water, entropy increases because positional probability, randomness, and disorder of water molecules increase since water molecules in gaseous phase have more space to move around. Similarly, in condensation of water, entropy decreases because of decreases in positional probability, randomness, and disorder. Entropy decreases in precipitation of solid from solution because of similar reason.

__Relationship between entropy and probability.__

__Relationship between entropy and probability.__

Relationship between entropy and probability is given by

For example, in expansion of 1 molecule of gas from VA to 2VA, change in entropy is given by

If we have n moles of gas instead of 1 molecule, above equations can be written as

Therefore change in entropy (ΔS) for n moles of gas when volume increases from VA to VB given by