What is Exergy,how it differs from Entropy,What is the clear boundary between them?

Energy is by definition the capability to do work or cause a change. A cascading waterfall can turn a mill and grind the meal...that's work. The waterfall has energy because it has the capability to do work.

Strictly speaking entropy has nothing specifically to do with energy. Entropy is just a measure of disorder, of chaos. The more disheveled something is the higher is its entropy.

Humpty Dumpty while sitting on the wall has low entropy; we know this because the slightest crack in his shell would be noticeable. But after the fall, with the Dump's shell and yolk splattered all over the King's land, the egg is in a high entropy state. Swish his innards all around and we couldn't tell, he'd still look like a smashed egg.

But we can also use the term entropy in the context of heat energy. Low entropy means the heat is organized and can be used to do work. But high entropy means the heat is chaotic and cannot be used to do work...its useless energy...like the energy derived from friction.

There is no "clear boundary" as they are not the same thing. One is a measure of order and the other is a capability to do work.

Exergy is the energy that is available to be used. After the system and surroundings reach equilibrium, the exergy is zero. Determining exergy was also the first goal of thermodynamics.

entropy is 1.

PHYSICS

a thermodynamic quantity representing the unavailability of a system's thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system.

2.

lack of order or predictability; gradual decline into disorder.

"a marketplace where entropy reigns supreme"