1. Two reversible adiabatics cannot intersect each other
Entropy
Two reversible adiabatics cannot intersect each other
NOTE: Through one point there can pass only one reversible adiabatic

2. Clausius theorem NOTE:
Any reversible path may be substituted by a reversible zigzag path between the same end states, constituting of a reversible adiabatic followed by a reversible isotherm and then by a reversible adiabatic, such that the heat transferred during the isothermal process is the same as that transferred during the original process.

3. Clausius theorem
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4. Entropy – the property From the Clausius theorem, (Or)
Since R2 is reversible,

5. Entropy – the property
Therefore, is same for any reversible path between
same initial and final points
(Change in entropy)
where, S is called entropy of the system and hence is a property of the system.

6. Entropy – the property
NOTE: If a system is taken from an initial equilibrium state i to a final equilibrium state f by an irreversible path, since entropy is a point function and the change in entropy is independent of the path followed, the non-reversible path is to be replaced by a reversible path to integrate for the evaluation of the change in entropy in the irreversible process.