Two Reversible Adiabatic Paths Cannot Intersect Each Other

# Let us consider two reversible adiabatic paths 1-3 and 2-3 intersect each other at point 3. 

# Also a reversible constant temperature processes 1-2 be drawn in such a way that it intersects the reversible adiabatic paths at 1 and 2.

# These three reversible processes 1-2, 2-3, 3-1 constitutes a reversible cycle.

# We know that the area under the p-v plot represents the net work output in a cycle. Therefore the area under the three reversible paths represents the net work output in a cycle.

# But such a cycle is not possible, since net work is being produced ia a cycle by a heat engine by exchanging heat with a single reservoir in the processes 1-2, violates the Law of Thermodynamics (Kelvin-Plank). Therefore the consideration of the intersection of the two reversible adiabatic process is wrong.

# Through one point, only one reversible adiabatic can pass.

# As two constant property lines can never intersect each other, it is observed that a reversible adiabatic path must denote some property, which is found later that it is entropy.