Let us consider entropy at the initial state 1 is S1 and entropy at the final state 2 is S2.
Hence, the change in entropy of a system, as it undergoes a change from state 1 to 2, becomes
S2 – S1 = 2∫1 (δQ / T) R …………….. (1)
If two states1 and 2 are infinitesimally near to each other, the we can omit the integration sign and hence, S2 – S1 becomes equal to dS
Therefore, the above equation can be written as:
dS = (δQ / T) R ………………… (2)
Where dS is an exact differential
Thus, from equation (2), we conclude that the change of entropy in a reversible process is equal to δQ/T which is the mathematical formulation of the second law of thermodynamics.
The third law of thermodynamics states” when a system is at zero absolute temperature, the entropy of the system is zero”.
It is clear from the above law that the absolute value of entropy corresponding to a given state of the system could not be determined by integrating (δQ / T) R between state at absolute zero and the given state. Zero entropy, however, means the absence of all molecular, atomic, electronic and nuclear disorders
Equation (2) indicates that when an exact differential δQ is divided by an integrating factor T during a reversible process, it becomes an exact differential.
Hence, practically we determine the change in entropy and not the absolute value of the entropy.
