5. a) Explain the following:
i) Bose-Einstein condensation.
ii) Gibbs paradox.
A Bose-Einstein condensate is a phenomenon of excessive accumulation of bosons in a state of minimum energy for temperature very close to absolute zero. A large fraction of bosons occupy the lowest quantum state, at which point macroscopic quantum phenomena become apparent.
Gibbs paradox allows for the entropy of closed systems to decrease, violating the second law of thermodynamics.