Explain change in entropy of a system during a reversible process `Delta S = (q_(rev))/(T)`

Explanation

As entropy change is the difference in the entropies, when the system passes from initial state to the final state,
`Delta S = S_(F) - S_(1)`
where, `S_(F)` = entropy of the final state and `S_(1)` = entropy of the initial state.
The absolute value of entropy of a system cannot be measured, but the entropy change `(Delta S)` for a process can be calculated using thermodynamic data. Entropy change of a process is the ratio of quantity of heat absorbed to the absolute temperature when the process is carried out reversible and isothermally. If `q_("reversible")` is the heat absorbed at temperature T, then
`Delta S = (q_("reversible"))/(T) = (DeltaH)/(T)`
Eq. (1) is a mathematical form of stating the second law of thermodynamics.
Entropy change is used to predict the spontaneity of a process. It is found in an isolated system, a process proceeds spontaneously in the direction where entropy increases. In other words, a process is spontaneous when `Delta S` is positive. More positive the `Delta S`, higher will be the spontaneity.