Energy can be transformed from one form to another in a closed system. But this type of process is irreversible. The direction of an irreversible process is determined by a change in a special property called the entropy of the system.
The analysis of a reversible process, using the second law of thermodynamics, leads to the concept of entropy. It is denoted by the letter S and is a property of all thermodynamic systems. It is defined by the relation.
dS = dQ/T
Where, dQ = heat exchange of a system in a reversible process at temperature T and dS = corresponding change in entropy of the system.
From dQ = TdS. Using this relation in the first law of thermodynamics, we get,
dQ = dU + dW
or, TdS = dU + pdV
Now, we note that dQ and dW are quantities exchanged between the system and the surroundings in a process. So, they depend on whether the process is reversible or irreversible.
Principle of Increase of Entropy:
Thermodynamic analysis shows that in every real process in nature, the sum of the entropies of a system and its surroundings always increases. The opposite process, in which the sum of the entropies decreases isn’t allowed in nature.
We may compare the situation with the law of conservation of energy (the first law of thermodynamics). This law states that the total energy of the universe is constant. It can never increase or decrease. In analogy, the second law of thermodynamics states that the total entropy of the universe increases in every process, it can never decrease. This is known as the principle of increase of entropy.
This principle states that every process in nature occurs in such a direction that the total entropy of the universe increases. Alternatively, no process, in which the total entropy of the universe decrease can occur in nature.