Calculate entropy change in a process.
Entropy change has two distinct sources in most textbook problems. Heat flowing reversibly into a system at temperature T raises its entropy by q over T — the same heat matters more at low temperature, because it represents a larger relative disturbance. Separately, letting a gas expand into a greater volume increases the number of accessible microstates, contributing nR ln of the volume ratio regardless of any heat exchange.
Entropy from heat and expansion
delta S(heat) = q / T; delta S(expansion) = n R ln(V2 / V1); total = sum of both
Because entropy is a state function defined through the reversible path. For an irreversible process you calculate the entropy change along any reversible route between the same two states — the answer is the same even though the actual heat transferred is not.
Yes. The second law constrains the total entropy of system plus surroundings, not the system alone. Freezing water lowers the water's entropy while raising the surroundings' entropy by more.
Because entropy counts accessible microstates. Doubling the volume roughly doubles the positional options for each molecule, and Boltzmann's relation turns that multiplicity into nR ln 2 per mole.