Q.What is the usual definition of entropy? What is the unit of entropy?

The first law only guarantees energy conservation -- it says nothing about DIRECTION, so it cannot explain why hot water cools spontaneously but cold water never spontaneously heats itself. The second law fills that gap by introducing entropy $S$, a state function measuring molecular disorder, defined via $dS=dq_{rev}/T$. Entropy statement: the entropy of an isolated system increases during a spontaneous process ($\Delta S_{total}>0$); for a reversible process, $\Delta S_{system}=-\Delta S_{surrounding}$ so $\Delta S_{total}=0$. Kelvin-Planck statement: no cyclic machine can convert heat COMPLETELY into work without dumping some to a cold sink -- explaining why even a frictionless engine can't be 100% efficient; Carnot sh …